ATOMIC ENERGY

FRONTIERS OF SCIENCE SERIES

General Editor

BERNARD LOVELL, O.B.E., Ph.D., F.Inst.P.

ATOMIC ENERGY

by

R. R. NIMMO

M.Sc. (N.Z.), Ph.D. (Cantab.)

SECOND IMPRESSION

CHAPMAN & HALL LTD
37 ESSEX STREET LONDON WC2
1949

IIA Lib.

First published ( Pilot Press Ltd.), 1947
Second impression , 1949

Catalogue No. 420/4

Printed in Great Britain by W. & J. Mackay & Co. Ltd., Chatham.

CONTENTS

PAGE

Preface 9

CHAPTER

I. Introduction II

II. Fundamental Ideas Concerning Electrons and Atomic

Structure 13

III. Radioactivity 20

IV. Mass and Energy 26

V. Observation of Individual Atoms 31

VI. Nuclear Physics : 1919-1930 42

VII. Nuclear Physics : 1932-1933 59

VIII. Neutrons 64

IX. Nuclear Fission 81

X. Release of Atomic Energy : Chain Reactions. . . 99

XI. The Realization of an Atomic Chain Reaction. . . 109

XII. The Production of Plutonium 125

XIII. The Atomic Bomb 138

XIV. The Separation of the Uranium Isotopes . .152

XV. Atomic Energy and the Future ..... 169

APPENDIX

I. Methods for Accelerating Charged Particles . . 180

II. Tracer Chemistry 186

III. Probability in Radioactivity 187

Energy Units 188

Table of Radioactive Transformations . . . 189

Table of Elements 191

The Periodic Table 193

Particles and Rays 194

Index 195

5

LIST OF ILLUSTRATIONS

PAGE

Fig. 1. Energy of electrons 15

Fig. 2. Diagram of atomic structure 17

Fig. 3. Variation of mass and speed of an electron with kinetic

energy 27

Fig. 4. Diagram of cloud chamber 33

Fig. 5. Cloud chamber tracks of a particles from ThC and ThC' . 34

Fig. 6. Cloud chamber tracks in hydrogen .... 35

Fig. 7. Cloud chamber tracks of a patricles from ThC' . . 35

Fig. 8. Cloud chamber photograph showing the result of a collision

between an oc particle and a helium atom ... 35

Fig. 9. Cloud chamber photograph of collision between a particle

and oxygen atom ....... 36

Fig. 10. Cloud chamber photograph of ionisation produced by

electrons 36

Fig. 11. Circuit used in a counter for recording the coincidences of

two Geiger-MQller tubes 40

Fig. 12. Rutherford’s apparatus foi observing protons arising from

a particle disintegration of nitrogen .... 43

Fig. 13. Cloud chamber photograph showing a particle disinte-
gration of nitrogen 47

Fig. 14. Packing fractions of stable elements .... 50

Fig. 15. Packing fractions of light elements .... 51

Fig. 16. The radioactive transformations of thorium C . . 55

Fig. 17. Potential energy of an <x particle in the neighbourhood of

the nucleus of an atom of atomic number 90 . . 56

Fig. 18. Head on collision between neutron and H l nucleus . 67

Fig. 19. Head on collision between neutron and He 4 nucleus . 68

Fig. 20. Collision between fast neutron and hydrogen nucleus . 71

Fig. 21. Cloud chamber photograph showing tracks of knock-on

protons 71

Fig. 22. Relation between capture cross section and neutron energy.

(No resonance levels) 74

7

75

Fig. 23. Relation between capture cross section and neutron energy.

(One resonance level)

Fig. 24. Oscillograph record of ionisation caused by fission frag-
ments from uranium 84

Fig. 25. Cloud chamber photograph of a single fission track in

hydrogen at reduced pressure 85

Fig. 26. Cloud chamber tracks in argon at reduced pressure of a pair

of fission fragments .85

Fig. 27. Distribution of kinetic energy of fission fragments . . 88

Fig. 28. Three stages in the nuclear fission process ... 94

Fig. 29. The behaviour of a nucleus possessing excitation energy

(Ef exceeds En) 96

Fig. 30. The behaviour of a nucleus possessing excitation energy

(En exceeds Ef) 96

Fig. 31. Some processes in a slow neutron chain reacting pile . 121

Fig. 32. The beginning of a fast-growing chain reaction . . 147

Fig. 33. The New Mexico atomic bomb explosion. 0.016 sec.

after detonation 148

Fig. 34. The New Mexico atomic bomb explosion. 0.053 sec.

after detonation 149

Fig. 35. Aerial photograph of the site of the New Mexico atomic

bomb explosion 28 hours after detonation . . .150

Fig. 36. The first stages of an ideal uranium diffusion plant . . 157

Fig. 37. Output stages of an ideal uranium diffusion plant . . 158

Fig. 38. Enrichment and stage size throughout uranium diffusion

plant 159

Fig. 39. The porous barrier diffusion plant at Oak Ridge, Tennessee 162

Fig. 40. Plan showing the arrangement for electromagnetic separ-
ation 164

Fig. 41. Focussing of ions in a magnetic field . . . .166

Fig. 42. A portion of the electromagnetic separation plant at Oak

Ridge, Tennessee 167

Fig. 43. The arrangement of the electrodes in a linear accelerator . 181

Fig. 44. A section showing the disposition of apparatus between the

poles of a cyclotron magnet 183

Fig. 45. A plan of cyclotron electrodes showing the ion paths . 183

8

PREFACE

In the pages that follow an attempt is made to describe the developments in
physics which first caused scientists to believe that a vast amount of energy is
locked up in atoms and which eventually led to its release. The story
has its beginning in the early years of the present century, and, as will be
seen, success in the release of atomic energy has been achieved because of the
efforts of many men, working at different times and in different places, each
making a contribution to atomic physics, or, not less important, to the
experimental methods of the subject. Knowledge of the atom has been
obtained gradually and as a result of painstaking investigations.

In order to obtain an understanding of modern views of atomic structure
and of the release of atomic energy, it is desirable to review the course of
scientific discovery in these fields. The story of atomic energy commences
with the discovery of radioactivity at the end of last century, when experiment
had just revealed the electrical nature of matter. This discovery that all
atoms contained electrons led to theories of atomic structure, but a consider-
able period elapsed before the picture of the atom contained sufficient detail
to explain the facts of radioactivity.

The account given in subsequent pages describes the growth of knowledge
of atomic structure and attempts to provide a background of knowledge to
enable the reader to obtain a clear picture of the circumstances in which
energy is obtained from atoms.

The amount of detailed explanation that a book can provide depends upon
the assumptions the author makes concerning the knowledge of the reader.
This book is intended primarily for those with some scientific knowledge ;
even if this knowledge is not extensive, or indeed very modern, it should
suffice to make the book comprehensible. No detailed knowledge of atomic
structure is assumed ; the necessary ideas are put forward in the first four
chapters. Chapters 5 to 8 give some account of modern experimental
techniques in atomic physics and of important discoveries to which they
have led. Subsequent chapters describe the details of processes which have
been found to yield atomic energy and the arrangements which are used to
release it on a considerable scale. The last chapter of the book is concerned
with the future of atomic energy and in it are considered some of the con-
sequences which may follow from the success already achieved.

9

ATOMIC ENERGY

The writing of a book on atomic energy is made difficult because some
information which is of interest and importance must be kept secret. In
consequence, there are certain matters on which I have knowledge that I am
not permitted to reveal, and there are many more on which I have no infor-
mation except that contained in Atomic Energy for Military Purposes
by H. D. Smyth.* In soiqe few places it is not possible to do more than
retell what Smyth has already told, but normally, with the help of his report
and the information published prior to the war, a reasonably detailed picture
of the means for releasing atomic energy can be presented.

I wish to place on record my gratitude for the help that has been given
me by two of my colleagues. Prof. P. B. Moon read my manuscript in its
early stages, and certain parts of the book have been influenced by my
discussions with him. Later on Mr. D. F. Bracher read the manuscript
with great care and has been instrumental in having removed numbers of
errors and obscurities. He has also taken much trouble and has rendered
most valued assistance in reading and correcting the proofs.

I also wish to express my thanks to Dr. A. C. B. Lovell, for the kind-
ness and helpfulness he has shown me during the preparation of this book.

Finally I am indebted to the Cambridge University Press for permission
to reproduce Figs. 5, 6, 7, 8, 9, 10, 13 and 21, to the American Institute of
Physics, Inc., for permission to reproduce Fig. 24, to Mr. Ejnar Munksgaard
of Copenhagen for permission to reproduce Figs. 25 and 26, to the Directorate
of Atomic Energy of the Ministry of Supply for the loan of photographs
from which Figs. 33, 34, and 35 are reproduced and to Major Robt. J.
Coakley of the War Department, Washington, D.C., for the supply of photo-
graphs which are reproduced as Figs. 39 and 42.

* Princeton University Press, Princeton, N.J., U.S.A. The text of this report is
published by H.M. Stationery Office: “Atomic Energy” (1945), S.O. Code No.
59-87.

10

CHAPTER I

INTRODUCTION

In the middle ages the transmutation of metals was widely accepted as a
possibility. Admittedly, the experimental support for this view was not
entirely satisfactory, and there were insuperable difficulties in achieving the
type of transmutation which was supremely desired, that of changing a base
metal into gold. But considerations of this sort were not sufficient to deter
many a philosopher from wasting years of his life in attempts to achieve
what we now know he had hopelessly insufficient means to effect. Belief in
the philosopher’s stone, though long-lived, could not be accepted in the face
of growing knowledge of chemistry.

As investigation proceeded, the laws of chemistry began to take shape. It
became clear that when a chemical reaction occurred the masses of the
reacting substances were just equal to the masses of all the products.
Furthermore, energy relations were discovered, and these showed that the
heat developed in a given chemical change was a constant, which did not
depend on the way in which the change was carried out. From experiments
investigating such matters arose two very important chemical laws, the law
of the conservation of mass and the law of the conservation of energy.

Further experiments served to verify that certain chemical substances could
neither be broken into simpler ones nor synthesized from others already
known. Eventually, between eighty and ninety of these substances were
recognized and were listed as the table of elements ; from consideration of
the properties and combining masses of these elements, the periodic atomic
table was drawn up. The atomic theory of matter was accepted, and formed
the basis of much of chemical theory. At that time there was no possibility
of detecting the presence of a single atom, and it was assumed, therefore, that
all atoms of a given element were identical. The evidence in support of this
view was overwhelming, for the only cases in which different samples of an
element were found to differ were just those in which an unsuspected impurity,
perhaps a new undiscovered clement, was present in one or other of the
samples.

It will be appreciated that the fundamental conception of an element
involved the assumption that one element could not be converted into
another. Not only had the quest for the philosopher’s stone been abandoned,
but the ideas commonly held towards the end of the nineteenth century were
based on the assumption that transmutation of any kind was impossible.

11

ATOMIC ENERGY

That was the period in which some physicists believed that physics as a science
was almost complete and that there were only one or two odd points to clear
up. There were of course many things to measure with greater and greater
accuracy, but to these people physics was about to become a dead science.
Not all the beliefs of those days were right ! By good fortune this was not
the direction in which physics developed.

In the last decade of the nineteenth century radioactivity was detected.
This discovery contributed to no small extent to the overthrow of the simple
ideas concerning atoms and the laws of conservation of mass and energy.
For much of chemistry these conceptions are as useful to-day as when they
were first proposed, but for physics, especially for atomic physics, great
advances have been made by refusing to accept the exact validity of these
ideas, despite their usefulness in the development of chemistry.

12

CHAPTER II

FUNDAMENTAL IDEAS

CONCERNING ELECTRONS AND ATOMIC STRUCTURE

(1) Electrons.

Before we discuss the discoveries that were made at the close of last century,
it is desirable to describe modem ideas of the structure of atoms and of the
arrangement of the elements in the atomic table.

Although knowledge of electrical theory was well advanced during the
course of the nineteenth century, the last decade was in its second half before
the existence of the negative electron was established. Not only did the
newly discovered electron provide an entity which was assumed to be a
constituent of all atoms, but it also provided a natural unit of electric charge ;
as was determined later this particle carries the very small charge of 1 .6 x 10 19
coulombs. Any charge, if negative, arises from the presence of so many
additional electrons, while a positive charge, which we find can be exactly
neutralized by a sufficient number of electrons, is also expressible in terms of
the same unit. This unit of charge is commonly used throughout this book.

The discovery of the electron was followed by investigations of its
properties, and once it was recognized as a charged body experiments were
made on electrons of given speed in order to determine their mass, their
charge and their velocity.

It was known that in a uniform magnetic field a charged particle travels in
a circle, the radius of which depends on the mass, the velocity and the magni-
tude of the charge carried by the particle, as well as on the strength of the
magnetic field in which it moves. Again, from their very nature, charged
particles are influenced by electric fields ; if then electrons move in the electric
field established between parallel conducting plates which are connected to
opposite terminals of a battery, the electrons will describe a parabola, the
dimensions of which depend upon the mass, the velocity and the charge of the
electron as well as on the strength of the electric field. Investigation of the
motion of charged particles in electric and magnetic fields, and in combinations
of these fields, has shown that it is possible to determine the velocity of the
particle and the ratio of its charge to its mass ; from such experiments it is
not possible to determine independently either the mass or the charge.

Although it was desirable to determine both the charge and mass of the
electron, it was realized that even the ratio of charge to mass was likely to
afford useful information concerning its nature. Faraday’s investigation of

13

ATOMIC ENERGY

Chap. II

the laws of electrolysis had shown that a certain electric charge, which we now
believe to be 9.65 x 10 4 coulombs, was necessary to liberate about 1.008 grams
of hydrogen or greater weights of other substances. On the views which had
long been accepted, electrolysis of water involves the motion of positively
charged hydrogen atoms within the liquid ; as we have just seen, these atoms
carry a charge of about 10 5 coulombs per gram. This figure has to be
compared with the results of measurements of the ratio of charge to mass of
the electron, measurements which showed that the electron was quite different
in nature from any known atom ; for an electron, the ratio of charge to mass
is 1.76 x10 s coulombs per gram. It was assumed that the positively
charged hydrogen atoms which took part in electrolysis were positively
charged because they lacked one electron ; in other words the positive charge
on the hydrogen atom was the same in magnitude as the negative electronic
charge. On this assumption, the mass of the electron was less than one
thousandth of that of the hydrogen atom.

(2) Energy of electrons : The electron volt .

One aspect of the motion of an electron in an electric field should be examined
before attention is directed to the theories of atomic structure which arose
from the discovery of the electron. When an electron moves from a point of
low potential to one of higher potential, it is assisted by the force imposed
by the electric field, and in consequence it gains kinetic energy ; the gain in
kinetic energy is proportional to the potential difference through which the
electron moves. It is useful to measure the kinetic energy of an electron in
terms of the potential difference through which it must fall from rest in order
to gain this energy. If e is the electronic charge, an electron starting from
rest at a point at zero potential will have kinetic energy Ve when it reaches,
by any path at all, a point at potential V. As the kinetic energy is Jmv 2 ,
where m is the mass of the electron, we have the equality

Ve = imv 2 ,

from which, if we wish, we may determine v, the velocity of the electron in
terms of V and e/m. This relation, however, is most useful as a definition of
a unit of energy. As the electron carries a charge of 1.6 x 10' 19 coulombs, it
possesses a kinetic energy of 1.6 x 10 19 joules after falling from rest through
a potential of 1 volt. We say that this electron has an energy of “ 1 electron
volt ” or 1 eV. Fig. 1 shows that the electron gains an energy eV in going from
potential zero to potential V ; the energy gained does not depend upon the
route between the starting point at zero potential and the finishing point at
potential V.

The use of the electron volt can readily be extended to measure the energy
of any particle, charged or uncharged. If we talk about a gas atom having

14

Chap. U

FUNDAMENTAL IDEAS

an energy of 10 eV, we mean that its energy is the same as that possessed by an
electron which has fallen from rest through a potential difference of 10 volts ;
as the unit is one of energy, it can be used in speaking of any kind of body,
although in practice it is useful to employ it only for measuring the energies
of atoms and molecules, sub-atomic particles and radiations.

A unit of energy of 1.6 xlO -10 joules appears to be an inconveniently
small one in which to measure energies, and for laboratory measurements
of heat energy, for example, where we are considering the total energy shared
among perhaps 10 ao atoms, this is indeed the case. On the other hand, the
unit is a convenient one in which to discuss the average energy possessed by
each of the atoms in the amount of matter being coasidered, for in atomic
processes, where we are concerned with the interaction between individual
atoms, it is essential to consider their energies. We illustrate the idea by
considering the kinetic energy of a single atom of a monatomic gas at a
temperature of 0°C. The average value of this energy is known to be 5.6 x 1 0 n
joules, or 0.035 eV, an energy which is very small compared with what is
readily communicated to electrons. A more striking example of the use of
the electron volt is obtained by using it to express the mean kinetic energy of
monatomic gas atoms at the very high temperature of 10* °C. At this
temperature, which is not normally attainable on the earth, the mean kinetic
energy of a gas atom is 2 x 10" 17 joules, or about 130 eV. Temperature is
a very powerful influence in breaking apart chemical compounds, but even
the very highest temperatures normally available to us cannot achieve results

15

ATOMIC ENERGY

Chap. II

which can readily be obtained by using electrons or other charged particles
which have been accelerated by falling through a few hundreds of volts.
There is no simpler way of emphasizing this than by expressing in electron
volts the mean kinetic energy of the atoms of a heated substance.

(3) Electrons and atomic structure .

Soon after the discovery of the electron, it was realized that this particle
was probably a constituent of all atoms, for electrons were found to be
present in any gas discharge tube through which an electric current was passed.
These electrons had evidently been detached from gas atoms within the tube,
for it was also possible to show the presence there of positively charged gas
atoms. This process by which gas atoms are divided into pairs of oppositely
charged particles is known as ionization ; some of the gas atoms are ionized
or transformed into ion pairs, each consisting, initially, of a positively
charged gas atom — a positive ion — and an electron. In some circumstances
the electron attaches itself to an electrically neutral gas atom or molecule to
form a negative ion. Ionization of gases occurs as a result of impacts
between gas atoms or gas molecules and electrons having energies of some
10 — 30 eV ; it can also be brought about by atoms of much higher energies
as well as by other processes.

■ It will be realized that as gas atoms are normally without electric charge,
they must contain a source of positive charge which is exactly neutralized by
the electrons within the atom. The early experiments did not afford any
experimental information concerning the nature of the portion of the atom
carrying this positive charge. For some time, therefore, it was assumed that
the positive charge consisted of a sphere of positive electricity within which
the electrons were embedded. It was also believed that different elements
differed chemically because of differences in the numbers of electrons within
their atoms, but at that time and for some considerable period afterwards
there was no accurate means of determining the number of electrons in an
atom of a given chemical element.

Theories of atomic structure were put on an experimental basis in 1911,
when Rutherford carried out investigations with the swift charged helium
atoms emitted by some radioactive substances. When these a particles, as
they are called, were allowed to fall on a thin sheet of gold, it was found that
a few of the particles were turned back on their paths. From this observa-
tion and further experiment it was concluded that atoms of gold contained
small and massive centres carrying very strong electric charges ; furthermore,
it was shown that the charged centre within the aluminium atom carried a
smaller charge than in the case of gold.

16

FUNDAMENTAL IDEAS

Chap. II

As a result of these experiments a new atomic theory — the nuclear theory
- — was proposed. It was believed that the atom consisted of a central core
or nucleus which contained almost the whole mass of the atom and carried a
positive charge equal in magnitude to that carried by the electrons which
completed its structure. These electrons were believed to rotate about the
nucleus in various orbits ; some orbits were close to the nucleus, others
were much further away. All these orbits, though small in themselves, were
enormous compared with the size of an electron or of a nucleus, so that the
region traversed by the electrons was very large compared with the size of
the particles of which the atom was composed. In many respects the atom
model was just a miniature solar system in which the forces were electrical
and not gravitational and in which the nucleus took the place of the sun and
the electrons that of the planets. Fig. 2 illustrates the structure at one time
assumed for an atom with three electrons rotating about a nucleus carrying
three positive charges.

This nuclear theory of the atom
was satisfactory as far as it went, but
there was one serious weakness in it,
for although it was realized that the
properties of an atom would be re-
lated to the number of electrons ro-
tating around its nucleus, this num-
ber was not known, and at that time
there was no accurate means of
measuring it, either directly or by
determining the value of the positive
nuclear charge.

(4) Atomic number .

As has been mentioned previously, the chemists had arranged the elements in
the order of their atomic weights and as a result of studies of the properties
of the known elements they had been led to the atomic table.* In this table
the elements were arranged primarily so as to exhibit their chemical properties,
but in all but one or two isolated cases the order of arrangement was also that
of their atomic weights. As the early theories of atomic structure were
developed, attempts were made to relate atomic properties to the magnitude
of the positive charge on the nucleus of the atom exhibiting the properties. In
this direction a great advance was made by H. G. J. Moseley, who, in 1914,
after making a study of X ray phenomena, proposed that the position of an

* On pages 191, 192 and 193 will be found a list of elements and the periodic table.

B 17

The nucleus is _

represented by the small
dot within the orbits. If the nucleus
were drawn to scale
it would be invisible. i i

I0“* cm.

Fig. 2

ATOMIC ENERGY

Chap. II

element in the periodic table was related to the number of positive charges on
its nucleus. In particular he believed that of two neighbouring elements in
the periodic table, the heavier one had one more charge on its nucleus than
had the lighter one. Moseley assumed that aluminium, the lightest element
he investigated, had thirteen positive charges on its nucleus, and from a
study of the atomic table he was able to determine the nuclear charges of all
the elements in the atomic table. The number of charges on a nucleus is now
known as the atomic number and is often represented by Z ; Moseley’s
work showed a way of determining the atomic number of every element.
But although Moseley determined correctly the charge on the nucleus and so
the atomic numbers of the elements, his approach was indirect, and it was not
until some years later that Chadwick verified that the nuclear charge was
indeed equal to the atomic number chosen by Moseley.

This idea of nuclear charge and atomic number is now realized to be most
important. The nuclear charge determines the number of electrons in an
atom and the number of electrons there determines the chemical nature of the
atom. For this reason the atomic number of a substance is just a numerical
name. If we give either the name of an element or its atomic number there
is equal certainty as to the chemical properties of the substance of which we
are talking. On turning to the table of elements, we see that the atomic
number of neon is 10. The neon atom has a nucleus with 10 positive charges
and around this rotate ten electrons. Now we shall see later that every neon
atom is not the same as every other neon atom, but every neon atom has ten
nuclear charges and every atom with an atomic number of 10 is a neon
atom. It is apparent from what has been said that the atomic number is not
directly related to the atomic weight of an element. In the periodic table the
elements are arranged in order of ascending atomic number ; in this order,
which is not always the order of ascending atomic weights,* the elements
show the repetition of chemical properties that we associate with that table.

(5) Atomic weight and mass number .

Some discussion must now be given of the atomic weights of the elements. ’ It
was proposed by Prout, in 1815, when the quantitative study of chemistry
was in its infancy, that all atoms were made from hydrogen atoms, and that
all atomic weights should therefore be multiples of that of hydrogen. Later
accurate measurements of atomic weights showed this view to be untenable ;
in many cases there was support for Prout’s hypothesis, but the instances in
which it did not apply were soon verified with sufficient accuracy to discredit
the hypothesis. Much more elaborate and difficult experiments were
needed before the essential truth of Prout’s hypothesis was patent. These

* Compare the pairs of elements Co and Ni, Te and I, and A and K.

18

FUNDAMENTAL IDEAS

Chap. II

experiments were commenced about 1913 when J. J. Thomson passed a beam
of fast positive ions of neon through electric and magnetic fields ; his obser-
vations could be explained only by assuming that the gas neon with an atomic
weight of 20.2 was not a single substance. It was apparent that it consisted
of one type of neon with an atomic mass of very nearly 20 and a small amount
of another type of neon with an atomic mass of very nearly 22. The atomic
masses of the two types of neon were measured indirectly, but the measure-
ments were sufficiently accurate to show that the experimental values were
very close to the integers 20 and 22. It was clear that there were two kinds
of neon, just as there were later found to be two kinds of chlorine. Of
course, both neons had the same atomic number of 10 just as both chlorines
had the same atomic number, in that case 17 ; furthermore, both neons had
the same chemical properties and so also with both chlorines. For this reason
the two neons were spoken of as the neon isotopes, and more generally when
we mention the isotopes of any element we mean all of the substances,
whatever their atomic masses, that have the atomic number and the place in
the periodic table appropriate to the element under discussion.* As a result
of the discovery of the existence of isotopes amongst light elements —
radioactive isotopes had been known for some time previously— and the
knowledge that the atomic masses of the individual isotopes were very
close to being integers, Prout’s hypothesis was revived and it was assumed
that the atomic mass of every isotope was an exact integer. Although this
is very nearly correct, it is only an approximation, as was found when more
accurate atomic mass measurements were made. Nevertheless this integer, to
which the atomic mass of any single isotope is found to approximate, is of
sufficient importance to be given a name and a symbol ; it is called the mass
number and is often represented by A. In these new terms we would say that
J. J. Thomson discovered that neon (Z = 10) consisted of two isotopes of
mass numbers 20 and 22. Similarly chlorine (Z = 17) consists of two isotopes
of mass numbers 35 and 37. We could go further and state the exact value
of the atomic mass of each of the isotopes specified above, but for the
present to do this would introduce unnecessary complications.

Further information concerning the subject matter of this chapter will be
found in the following : “ Ions, Electrons and Ionizing Radiations ”, J. A.
Crowthcr, (Arnold) ,* “ Electrons, Protons, Photons, Neutrons and Cosmic
Rays ”, Millikan, (Chicago).

* Isotope : literally “ the same place.”

19

CHAPTER III

RADIOACTIVITY

(1) Nature of radiations and resulting nuclear changes .

We now consider the discovery mentioned in the concluding paragraph of
Chapter 1. In February 1896, Henri Becquerel discovered radioactivity
when he performed an experiment similar to one which was carried out by
Rontgen a few months earlier and which resulted in the discovery of X rays.
Becquerel found that uranium salts gave out a radiation which was able to
pass through a thin silver sheet and fog a photographic plate. The details of
the phenomenon were not at that time understood, but BecquerePs discovery
was followed by great experimental activity in which Rutherford and the
Curies, amongst others, took a prominent part. As a result, by 1903, much was
known about the heavy elements which emitted radiations spontaneously ;
the novelty of these new phenomena, called radioactivity, was apparent.

It was soon realized that there were a large number of radioactive sub-
stances. Each of these was found to emit radiations spontaneously. Some
emitted radiations which Rutherford called a rays. These rays, now
usually called a particles, were found to be helium atoms carrying two
positive charges and moving at great speed ; they were able to produce
intense ionization along their paths, but as their penetrating power was small,
their effects in air at atmospheric pressure were confined to distances extending
only a few centimetres from their source. A radioactive element emitting a
particles was found to transform itself into a substance which was chemically
different from that from which the a particles came. The new substance had
an atomic weight smaller than the parent, and in terms of modern ideas its
mass number was 4 units less than that of the parent atom. If we take as an
example the substance radium, with a mass number of 226, we find that it
emits a particles, which are able to traverse 3.4 cm. of “ standard air,” i.e.,
air at 15°C. and 760 mm. pressure, and yields radon, a rare gas which is
itself radioactive and which has a mass number of 222. Now radium is
chemically similar to barium, and radon is similar to the rare gas xenon, and
in the atomic table radium is placed in the position corresponding to an
atomic number 88 while radon occupies the place of an element of atomic
number 86. This example — and many similar ones could be named — shows
that when an a particle is emitted, the new element has an atomic number two
less and a mass number four less than the substance from which it was formed.

20

RADIOACTIVITY

It is evident that the reductions of mass number and nuclear charge are a
direct consequence of the emission of the a particle, which carries off two of
the charges and four of the mass units originally part of the nucleus.

Not all radioactive substances emit a particles. Many emit p rays,
particles which have negative charges, high speeds of emission and very high
ratios of charge to mass. Careful measurements have shown that these
particles are simply high speed electrons. They, too, come from the nucleus
of the parent atom, but they carry so little mass that their departure involves
no change in mass number. On the other hand the removal of negative
charge involves an increase in the positive charge of the nucleus, and as the
electron takes off one negative charge the atomic number of the nucleus
increases by unity. As an example of this process we may take the radio-
active substance radium D. * Chemically this substance has all the properties
of lead, but it is distinguished from lead by its radioactive emission of p
particles. Now lead and radium D have atomic number 82, and radium D
has mass number 210 ; upon the emission of a p particle radium D is trans-
formed to radium E, still with mass number 210, and with atomic number 83.
Radium E, which is an isotope of bismuth, emits p particles and on doing so
becomes radium F or polonium, a substance with atomic number 84 and
mass number 210. Polonium emits a particles and gives rise to a substance
of atomic number 82 and of mass number 206. The atomic number of this
substance shows it to be lead, and in fact it is not radioactive and it is one of
the constituents of ordinary lead. From this example we see that when
there is successive emission of an a particle and two p particles, in any
order whatever, the initial substance is chemically identical with the final one,
but the two substances differ by four in mass number. These two kinds of
lead are of course isotopes ; the process has been discussed in detail in
order to show that normal radioactive transformations are likely to produce
numerous isotopes.

(2) Radioactive isotopes .

When one is told that the natural heavy radioactive substances comprise
nearly forty different kinds of atom, all of which have such atomic numbers
that they occupy ten places in the periodic tabic, t one can readily understand
why the existence of radioactive isotopes caused great confusion when early
attempts were made to explain radioactive processes and to make chemical
separations of the products of a substance such as radium. An understanding
of these radioactive transformation processes caused something of a shock to

* At the end of the book is a diagram showing the radioactive transformations
to which the heavy nuclei are subject.

t Compare the diagram of radioactive elements on page 193.

21

ATOMIC ENERGY

Chap . Ill

those who accepted the ideas usually held about chemical elements. Radio-
active processes were such that one element was being transformed steadily
into another ; the evidence was firmly established, and although radioactive
substances were regarded as exceptional, it was impossible to maintain any
longer that no element could be converted into another. Then, there was the
surprising existence of so many radioactive isotopes. Were the radioactive
elements again an exception or did other elements in the periodic table
possess isotopes on the scale exhibited by the heavy radioactive substances ?
This question was one to which an answer could not be provided in the early
years of the present century. Nevertheless, when later on it was shown
that many light elements possessed two or more isotopes, there were some who
were dubious about accepting the experimental evidence, even though this
evidence did no more than show that in this respect the radioactive substances
were not exceptional and occurred in a variety of isotopic forms just as did
non-radioactive substances.

It is probable that there was then little realization of the similarity between
radioactive and other elements. The existence of p radioactivity amongst
light elements, as was discovered thirty years later, was not predicted from
analogy with the heavy radioactive elements. In other words, radioactivity
continued to be regarded as an exceptional phenomenon, exhibited almost
exclusively by the very heavy atoms, and the properties of radioactive atoms
were not thought of as being those of atoms in general. There was one good
reason for this point of view and that was the spontaneity of the radioactive
processes. If we consider 1 gram of radium, we find that a constant number
of a particles is emitted every second, and a constant amount of radium is
transformed into radon. The rate of emission of a particles is unaltered by
any chemical or physical process to which the radium is subjected, and the
transformation of radium into radon is a process on which man’s experiments
have no perceptible effect. It was clear that the radioactive process involved
mechanisms which were of an entirely different nature from those experienced
in chemical reactions.

(3) Radioactive transformations .

It is not quite correct to say that the radium transforms itself at a constant
rate. In fact the number of atoms being transformed in one second is
proportional to the number N of radium atoms present, and is generally
written AN, where A is a constant called the transformation constant of
radium. It can be derived from this relation that the amount of radium
decreases exponentially with time, that is if there are N 0 radium atoms
present at time zero, the number N at any subsequent time t is given by
N = N 0 e“ xt . By making observations of the rate of emission of a particles

22

RADIOACTIVITY

Chap. Ill

from radium, we can determine the way in which it is reduced in amount with
time, and consequently we are able to determine A. Usually, we state the
disintegration rate of a radioactive substance in terms of its half life, that is
in terms of the time taken for a given sample of a substance to “ decay ”
to half its original strength. There is a characteristic half life for every
radioactive substance ; thorium has a half life of 1.65 xlO 10 years, radium
a half life of 1600 years and radon a half life of 3.825 days ; some substances
have half lives of a small fraction of a second. Although the half life of
radium is short compared with that of thorium or of uranium, it decays
sufficiently slowly to involve quite a small diminution in its activity during
the period of a man’s life.

(4) Energy liberated by radioactive substances .

Observations made as long ago as 1903 showed that radium maintained itself
at a perceptibly higher temperature than that of its surroundings. Measure-
ment showed that the rate of evolution of heat was such that 1 gram of
radium and its products evolve heat at the rate of more than 100 calories an
hour. Thisisa very small amount of heat energy and is to be compared with near-
ly 8000 calories produced when 1 gram of carbon is burned to carbon dioxide.
But in a year, in which the quantity of radium suffers a negligible diminution*
the total amount of heat evolved is more than 800 000 calories, a quantity
which is one hundred times that released when the same mass of carbon is
burned. By the time that the radium has all decayed, and it will be a long
time before this has occurred, the radium and its immediate products will
produce about 1.6x10° calories or 2x10° times as much energy as is
yielded by burning the same weight of carbon. Regarding the radium as a
source of heat, it has a calorific power of nearly one quarter of a million times
that of carbon. Here is a source of energy that far transcends any ordinary
fuel. Radium is not regarded as being suitable for use as a fuel ; it is most
expensive, it is available in very small quantities, it evolves its energy at a
very slow rate and in addition it produces y rays, radiations which though
useful in hospital treatment of cancer can have serious or even fatal con-
sequences to anyone who is exposed to considerable doses of them. * Despite
these disadvantages which are attached to the use of radium as a fuel, this
knowledge of the properties of radium made it clear that there were other
sources of energy besides the fuels with which we are so familiar ; the yield
of heat energy from a radioactive substance is of an entirely different order
of magnitude from the yield from any known fuel, or indeed from any
chemical process either known or imagined. The question that must occur to
anyone who considers the matter is that of determining the origin of the
* Compare Chapter 12, p. 130

23

ATOMIC ENERGY

Chap . Ill

energy liberated by radioactive substances. Little more was clear than that
the process was not an ordinary chemical one, and almost the only possible
, answer was that the energy came from the radioactivity of the substances
producing it ; and this was no answer at all.

(5) Emission of y rays from radioactive substances.

As was stated above, radium emits y rays. These radiations are electro-
magnetic in nature, and are similar to X radiation ; indeed, means are now
available by which very high voltage X ray tubes can be made to generate
radiations which are identical with the y rays emitted by the nuclei of
radioactive atoms, y rays were not discussed in connection with radio-
active transformations because the emission of y rays is a secondary phenome-
non. The emission of a y ray causes no change in atomic number or in
mass number, and so causes no atomic transformation ; it simply serves to
remove energy from an atomic nucleus which for one reason or another has
more than its normal amount. The emission of y rays is important in
relation to theories of nuclear structure, just as the emission of visible spectral
radiations is important to the theories of the structure of the extra-nuclear
portions of the atom.

y rays have many of the properties of other electromagnetic radiations
such as light or wireless waves ; their frequency may be determined from
measurement of their wavelength, although in practice this experiment is
feasible only for rather low frequency y rays. From the point of view of
nuclear physics, it is found to be most useful to imagine that y rays are
particles carrying energy. A y ray makes itself apparent only when it
interacts with matter, in which circumstances all or part of its energy is
transferred to atoms or more usually to electrons. When a y ray gives all
its energy to an electron, a determination of the energy of the y ray may be
made from a measurement of the speed or energy of the electron.

For completeness it should be mentioned that the frequency of a y ray is
proportional to its energy E, that is to the maximum energy the y ray can
transfer to a single atom or electron. If v is the frequency of the y ray we
have the relation

E = hv ;

here h is a constant called Planck’s constant ; its magnitude is 6.55 x 10“ 34
joule-sec. When a nucleus emits a y ray of a given frequency, the energy
withdrawn from it is given by the equation above ; occasions will occur on
which this same energy is transferred by the y ray to an electron. In dis-
cussion of phenomena involving y rays, it is unusual to mention their

24

RADIOACTIVITY

Chap. Ill

frequency ; in general we talk of their energy which we usually express in
electron volts.

Further information concerning the subject matter of this chapter will be
found in the following books : “ Radioactivity and Radioactive Substances ”,
Chadwick, (Pitman) ; “ Radiations from Radioactive Substances ”, Ruther-
ford, Chadwick and Ellis, (Cambridge University Press) ; “ Radioactivity ”,
Hevesy and Paneth, (Oxford University Press).

25

CHAPTER IV

MASS AND ENERGY

(1) Increase of mass with energy .

The early days of the present century were remarkable in that accepted
beliefs were being questioned and new and unlikely sounding alternatives
were being proposed. In the period under review there appeared the Quantum
Theory of Planck and the Theory of Relativity of Einstein. It is with one
aspect of the latter that we are concerned, and by good fortune our discussion
of it is in no way difficult.

The special theory of relativity is based on two postulates. These are
that there is no way of determining whether one is or is not at absolute rest
and that the velocity of light is the same to all observers, even in the case in
which two observers are moving relative to one another. Of course this
second postulate is not what is expected by people who compare the measure-
ment of the velocity of light with the results to be obtained from measuring the
velocity of slowly moving terrestrial bodies ; it is not therefore surprising
that the theory of relativity makes deductions which are as unexpected as
the postulates.

The particular relation in which we are interested is one which shows that
there is an increase in the mass of any body when there is an increase in its
kinetic energy. If we increase the kinetic energy of a slow electron, we first
cause a large increase in its speed and a small increase in its mass ; a stage
can be reached when the speed of the electron is close to that of light, and
then a further increase of kinetic energy results in a very small increase of
speed and in a further increase of mass. Such changes of mass and speed
with kinetic energy are illustrated for the case of an electron in Fig. 3. In
this case, and indeed in all cases, the increase in kinetic energy can be shown
to be equal to the increase of mass multiplied by the square of the velocity of
light, or writing it algebraically

€ = juc a ;

here e is the increase in kinetic energy, /x is the increase in mass and c is the
velocity of light in vacuum. More generally the total energy of the electron,
E, is written as me 2 , where m is the mass of the electron at the speed being
considered. The relation is assumed to be correct at zero speed when the
electronic mass is m 0 ; the electron must then possess energy m 0 c a , called its
rest energy. When the electron moves, its energy is greater than its rest

26

MASS AND ENERGY

Chap- IV

0 0 1 0-2 0 3 0-4’ 0-5 0*6 0*7 0*8 0-9 10 M 1*2 1-3 1*4

Kinetic Energy of Electron in millions of eV.

Flg.3. Variation of mass and speed of an electron with kinetic energy.

energy by the amount of its kinetic energy, (m — m 0 )c a . Einstein’s theory
shows that a particle of rest mass m 0 has, at a velocity v, the mass

m 0

V 1 - v a /c a 9

thus the kinetic energy of an electron moving with a velocity v is

m 0 c 2 1')

W 1 — v a /c 3 /

At low velocities this expression is almost exactly equal to lm 0 v a and so is in
accord with the Newtonian laws of dynamics which apply to slowly moving
bodies. The points to be stressed are that an increase of kinetic energy of
an electron, or in fact of any other particle or material body, involves an
increase of mass and that the increase in energy is just equal to the increase
of mass multiplied by the square of the velocity of light.

Now c, the velocity of light in vacuum, is 3 x 10 8 metres per sec., and so an
increase of mass of 1 gram corresponds to an energy of 9 x 10 13 joules.* If

* If mass is measured in kg. and velocity in metres per sec., the energy is measured
in joules.

27

ATOMIC ENERGY

Chap. IV

we consider the kinetic energy of a mass of 1000 kg. moving at the speed of a
jet plane, or say 250 metres per sec., we find that it amounts to about 3 x 10 7
joules. At this speed, masses increase by about one part in three million
million, and our mass of 1 metric ton is increased by only i microgram.

While this is an interesting consequence of the theory of relativity, it is not
very easy to verify experimentally if ordinary particles are used. On the
other hand electrons can be made to travel at very high speeds and it is found
that their mass does indeed increase in just the fashion that the theory of
relativity predicts. There is however, another aspect of the matter to which
attention should be directed. The discussion above maintains that energy
given to a moving body appears as an increase of mass ; nevertheless, when
the body ceases to move it gives up its energy and the additional mass
disappears. The whole process seems to be a very temporary one. Not
every case is as temporary as the one we have been discussing, for if we give
heat energy to a body, we increase the velocity of motion or vibration of the
atoms of the body, and to this increase in velocity there must correspond an
increase in mass. But the change is very small. If we heat 1 gram of
copper by 100°C. we need about 9 calories of heat energy, or expressed in
mechanical units we need nearly 40 joules ; this amount of heat energy will
increase the mass of the copper by a little more than one part in three million
million.

(2) Conversion of mass into energy .

These increases in mass are so small that the whole phenomenon might be
regarded as trivial were it not for the attention that has been directed to the
very large amounts of energy that could be made available if mass were
converted into energy on any appreciable scale. If a mass as small as 1 mg.
is changed into energy the amount released is no less than 9 x 10 10 joules or
25,000 kWh. Discussions along such lines lead to the conclusion that if we
wish to obtain large amounts of energy we have only to arrange to convert
mass into energy.

There is nothing false in this point of view, but it seems better to regard the
mass energy relation in a rather different way. It should be realized that in
any process at all in which energy is released, there is a corresponding
decrease in mask. If we bum a quantity of carbon, the original mass of the
carbon and the oxygen required to bum it is greater than that of the products
of combustion, the difference being equal to the mass of the energy released
in the reaction. Hence, in a closed system from which neither the products of
combustion nor heat energy can escape, there is no change of mass arising

28

mass and energy

Chap, iv

from chemical change. Further consideration of the matter shows that the
mass energy relation no more tells us how to obtain energy from matter
than does the first law of thermodynamics tell us how to turn heat into mecha-
nical energy. Nevertheless, if heat is turned into work, the first law of
thermodynamics tells us that for every calorie so converted 4.2 joules of
energy are produced ; it tells us nothing that helps us to decide upon a
suitable method for such a production of mechanical energy from heat
energy. The analogy with the mass energy equation is complete. If there
is any kind of reaction which yields energy, and if eventually the energy is
Withdrawn from the products of the reaction, the products must then have
less mass than did the materials from which they were formed. But the mass
energy relation gives no indication as to which processes will yield large
amounts of energy ; to determine this other principles of physics must be
applied. We should then say that because a certain reaction yields a large
amount of energy there must be a considerable diminution of mass rather
than say that there is a large yield of energy because of a considerable
diminution of mass ; it is true that one cannot occur without the other, but
visually our ideas of physical processes are adequate to explain in terms of
forces the reason for the release of energy.

As an example of the release of energy and the consequent diminution of
mass, we may consider what happens when an a particle is emitted by a
radioactive atom. For simplicity we suppose that the nucleus is so heavy
that only the a particle has appreciable energy. At the moment of emission
the a particle has a considerable amount of kinetic energy and in consequence
its mass is greater than its rest mass ; this state of affairs is not altered until
the a particle loses some energy, for it is only then that it parts with some of
its excess mass. This excess mass does not of course disappear ; it is simply
shared amongst a large number of atoms or molecules to which the a particle
imparts its energy. Thus, some of the energy of the radioactive nucleus is
converted into heat energy of molecules ; that amount of energy caused the
original nucleus to have more mass than the rest masses of the two particles
into which it was transformed.

Viewed in this way, the mass energy relationship is important because it is
one of the fundamental relations of physics. Its form was so long hidden
only because it is difficult to communicate to a piece of matter, even to a very
small piece, enough energy to make a measurable change in its mass. Never-
theless, a simple argument can be given to show that the absorption of light
energy gives an increase of mass of the absorber.* This argument depends

* Compare “ Atomic Physics ”, M.Bom, (Blackie and Sons Ltd.), 1935, Chap.
Ill, p. 46.

29

ATOMIC ENERGY

Chap. IV

on a knowledge of the pressure of light and on the assumption that the
emission of light within a closed system cannot give rise to a force on the
system ; it leads to the conclusion that on the absorption of energy E there
is an increase in mass of E/c 2 , i.e., to the mass energy relation. These
considerations, and others like them, show us that energy has mass ; this
can also be shown by experiments on electrons or on very fast atomic
particles.

30

CHAPTER V

OBSERVATION OF INDIVIDUAL ATOMS

(1) Measurements of the properties of ionizing particles .

Earlier chapters have described some of the basic information which became
available within a period of about ten years after the discovery of radio-
activity. At a very early stage radioactive phenomena were recognized as
being atomic, and it was from this point of view that they were discussed by
those working on them. Unfortunately atoms are very small and impossible
to observe, and the progress in atomic physics depended vitally on the pro-
vision of methods which were capable of revealing the presence of an indivi-
dual atom, or rather of the radiation emitted by it.

To measure the properties of radiations in quantity is fairly simple, even
when the amount of radiation is small. Information was most readily
obtained concerning the properties of a particles, largely because they
ionized intensely, they travelled in straight lines and all the a particles
emitted from a pure radioactive substance had almost the same range.*
Information was first obtained by measuring directly, perhaps with a relatively
simple gold leaf electroscope, the ionization produced by these particles. It
should be realized that even this electrical method is comparatively sensitive,
and is readily capable of detecting ionization currents of the order of 10" ia
amp., i.e., about 6 million ions per second. Now as a single a particle will
produce about 10* ion pairs in its path in air, a matter of 1000 a particles per
second gives rise to an ionization current that can be detected with an
electroscope and is capable of reasonably accurate measurement with
electrometers of the type that have long been available. Not only can we
arrange to detect the arrival of a few a particles ; it is not difficult to measure
the relative ionization produced at different points along the range of a beam
of a particles and to obtain information concerning the average number of
ions produced by an a particle of given velocity of emission and the distri-
bution of ionization along the path of this particle.

The p particles were less easily investigated because of their variable range
and their practice of travelling in tortuous paths. There was also a compli-
cation arising from y rays, which arc emitted after the disintegration of some
P rayt emitting substances. These y rays are sometimes absorbed in the

* Compare Figs. 5 and 7 on pp. 34 and 35.

t The radiations from radioactive substances were once known as a, (3 and y rays.
We now know that a and p rays are particles, but the term “ ray ” is still used
when it is unnecessary to emphasize the corpuscular nature of the radiation.

31

ATOMIC ENERGY

Chap . V

material of the p ray source, perhaps even by the electrons surrounding the
nucleus from which they come, and as a result the source emits high energy
electrons which are often difficult to distinguish from p particles arising
directly from nuclear transformations. Nevertheless, by patient work much
information was obtained about radioactive disintegration processes, and
gradually a good deal of data became available concerning the emission
energies of a particles, p particles and y rays.

(2) Scintillation method for detecting individual a particles .

Many methods were developed for observing single fast particles, especially
a particles. The first of these, which was extensively used by Rutherford in
much of his work, was the scintillation method. When an a particle falls on
a piece of zinc sulphide, it gives rise to a faint green flash. From multitudes
of such flashes arises the green glow given by some luminous watches and
clocks ; in suitable circumstances a separate flash can be made visible for
each a particle falling on a zinc sulphide screen. Experiments involving the
use of zinc sulphide were carried out in some such way as this : — The screen
was prepared by covering a piece of glass with a thin layer of small crystals
of zinc sulphide, and this screen was viewed through a microscope of great
light-gathering power. The observations were made in a darkened room ;
for the best results it was necessary that the observer should not begin his
observations before his eyes were dark-adapted, the particles had to be
arriving at a suitable rate which was about twenty per minute, and the
observer required frequent rests to avoid making errors owing to visual
fatigue. This arrangement made it possible to count the number of a particles
hitting the zinc sulphide screen, and with it most important results were
obtained. It is sufficient to mention that the investigations of the scattering
of a particles by thin metal foils* depended wholly on this method of
counting them. Fortunately physicists do not now have to carry out such
painful experiments in order to obtain data concerning the emission of
a particles. The scintillation method was of no use for counting p particles.

(3) Expansion or Cloud Chamber.

Most methods of detecting single particles from radioactive substances
depend upon making use of the ionization that these particles produce.
The available methods take a number of forms, not all of which are worth
discussing fully here. The most beautiful of these methods, and in some ways
the most powerful, is the cloud chamber or expansion chamber devised by

* These investigations were mentioned in Chap. 2, p. 16.

32

Chap. V

OBSERVATION OF INDIVIDUAL ATOMS

C. T. R. Wilson. This cloud chamber is a simple device which makes visible
the paths of ionizing particles that pass through the chamber.

The construction of a simple form of cloud chamber is shown diagram-
matically in Fig. 4. The chamber consists of a short glass cylinder with a
sheet of plate glass sealed to its end ; the movable floor of the cylinder con-

Fig. 4. Diagram of a simple type of Cloud Chamber. Expansion occurs when the
rubber bung is drawn to the right so as to allow the air under the piston to flow Into
the evacuated flask. After the expansion, the bung Is replaced, the tap is opened
and, as air enters the space below the piston, this rises eventually to its inltila

position.

sists of a blackened plate which is part of a piston which makes the cylinder
air tight and also enables the volume of the cylinder to be changed at will.
For proper operation, arrangements must be made so that the piston can.be
rapidly moved downwards. Very often the gas in the cylinder is air, satu-
rated with water vapour ; initially the air may be at or near atmospheric
pressure, and when the expansion occurs the movement of the piston is such
that the height of the chamber is increased by about 30 to 33% of the initial
height. The expansion of the air is rapid enough to be adiabatic so that the
air in the chamber is suddenly cooled, and the water vapour in the air is
greater in amount than the saturation value at the lowered temperature. As
a result of the supersaturation of the air, water vapour condenses on anything
that is available, and if any ions are present in the chamber water drops are

c 33

ATOMIC ENERGY

Chap . V

formed upon them. The water drops formed are not usually very large, but
if they are suitably illuminated they can readily be seen and photographed.
Unfortunately they do not long remain in the places in which they were first
formed because the air in the chamber soon commences to warm up, and
when this happens air currents destroy the cloud tracks.

In practical arrangements certain precautions are needed. In the first
place the air in the chamber must be clean and free from traces of certain
organic vapours. Furthermore, means must be adopted for dealing with
any ions formed in the chamber before the expansion takes place ; these
may arise from radioactive sources which are being used near the chamber,
from X rays or other penetrating electromagnetic radiation, or from cosmic
rays. To remove these ions an electric field is maintained between the floor
of the chamber and a metal ring on the plate glass cover, and this electric
field sweeps away most of the unwanted ions formed before the expansion ;
naturally precautions are taken to minimize the ionization in the chamber
during the period before the expansion, but it is not usually practicable to
reduce this ionization to zero. The expansion should be made quickly,
preferably in less than 0.1 sec.; immediately the piston has gone down, the
ionizing particles are momentarily allowed to enter the chamber. There is

a short period after the

expansion when water
drops will condense on any
ions in the chamber, and
this condensation process
is so rapid that any ions
then formed are fixed in
their positions of origin by
the growth of water drops
around them. ' Ideally,
then, the radiations to be
studied should be allowed
to enter the chamber only
during this period. If the
ion pattern is to be recorded
by photography, a short
flash of intense illumina-
tion is arranged to occur
just after the radiation has

Fig. 5 Cloud chamber tracks of oc particles from
ThC and ThC 7 .

(From The Newer Alchemy, Rutherford, Cambridge Univer-
sity Press.)

entered the chamber and
the water drops have con-
densed on the resulting

34

Chap. V OBSERVATION OF INDIVIDUAL ATOMS

«=i«- «• Cloud chamber tracks in
hydrogen. The two dense tracks
are caused by a particles, the
other tracks by £ particles.

(From Radiations from Radioactive Substan-
ces, by Rutherford, Chadwick and Ellis
Cambridge University Press.)

Fig-7- Cloud chamber tracks. I he
last 3 cm. of the tracks of 8.6 cm. a part-
icles from ThC'. This picture shows
small variations in a particle ranges.
The particle making the third track on
the right collided with a heavy atom,
probably a nitrogen atom.

(From Radiations from Radioactive Substances,
by Rutherford, Chadwick and Ellis, Cambridge
University Press.)

Fig. 8. Cloud chamber
photograph showing the
result of a collision be-
tween an a particle and
a helium atom.

(From Radiations from Radio-
active Substances, by Ruther-
ford, Chadwick and Ellis,
Cambridge University Press.)

35

ATOMIC ENERGY

Chap. V

/'

Fig. 10. Cloud chamber photograph
showing the feeble ionization produced
by a high speed electron with a straight
path, and the curved paths and denser
ionization arising from slower electrons.
(From The Newer Alchemy , Rutherford, Cam-
bridge University Press.)

Fig. 9. Cloud chamber photograph.

The fork arises from a collision between
ana particle and an oxygen atom.

(From The Newer Alchemy, Rutherford, Cam-
bridge University Press.)

ions. Shortly afterwards the piston is raised and preparations are made
for the next expansion.

It is difficult to give an adequate description of what is seen in an expansion
chamber ; even Figs. 5 to 10 give an impression rather different from the one
obtained by observing a chamber in operation. The actual tracks are

Chap. V OBSERVATION OF INDIVIDUAL ATOMS

hardly as white as they appear in a photograph, but their existence in three
dimensions gives information which is not recorded in a single picture. These
photographs bear out our description of a and p particles. After seeing
such photographs as are given here one believes that a particles produce
intense ionization along paths which are approximately straight and of
uniform length ; one also appreciates what happens when an a particle is
deflected by making a close collision with a heavier atom. It is clear, too,
that when a p particle* moves in a straight path it produces few ions per cm.
of path ; near the end of the track of a p particle more ions arc produced and
the path is tortuous. In order to obtain a general picture of ionization
processes, nothing is more instructive than to make observations with a
Wilson cloud chamber.

Although the whole affair sounds simple and is capable of giving most
valuable insight into phenomena connected with the passage of fast particles
through gases, and at the same time most beautiful pictures of these pheno-
mena, it is not easy to operate an expansion chamber so as to obtain records
of the highest quality. The great wonder is that C. T. R. Wilson was
successful in showing that the arrangement would work and in obtaining
with this apparatus records of such quality as have rarely been equalled since.

Although, as we have seen, the apparatus is capable of showing in detail
the whole course and intense ionization of an a particle, it has unfortunately
two serious disadvantages. The shallowness of the chamber and the neces-
sity for confining the observations to the relatively small region near the
object plane of the camera are sometimes serious limitations. Far more
serious is the slowness with which observations are made. Although auto-
matic arrangements have been made for photographing what occurs in an
expansion chamber, these do not take more than a few photographs a minute.
Any increase in the rate of operation of the cloud chamber is accompanied
by a marked deterioration in the quality of the tracks. When one remembers
that an expansion chamber will make visible the radiations entering the
chamber during a period of about 0.1 second at the time of expansion, one
can appreciate that many thousands of photographs must be taken, and much
time must elapse, before a few records are obtained of some rarely occurring
event. Nevertheless, the expansion chamber continues to be used because of
its ability to record the whole track of an ionizing particle, and in this respect
it is paramount amongst the devices which can detect single "particles. It has
proved itself time and again by its usefulness in providing unassailable
evidence for the existence of a new particle or of a now atomic reaction.

* The tracks of Fig. 10 are similar to what might be produced by ft particles
although the electrons causing these tracks were not emitted as ft particles from a
radioactive body.

37

ATOMIC ENERGY

Chap. V

(4) The use of the photographic plate for recording heavy ionizing particles

Another device of much power is the photographic plate used as an indicator
of the passage of heavy particles. A swift heavy particle has only a sm all
range in a photographic emulsion, but after its passage and the subsequent
development of the plate, a microscope will show where the particle has gone.
The photographic plate is a kind of expansion chamber on a microscopic
scale. The short ranges of the recorded particles are disadvantageous, but
against that can be set the advantage that the photographic plate is sensitive
to radiation for periods of the order of years, and with its help some rare
processes may be simply studied. Furthermore, the examination of a single
phonographic plate may be incomparably more attractive than the necessary
examination of thousands of expansion chamber photographs, when very few
indeed show the particular type of phenomenon which is sought.

(5) Counters : Linear amplifier and Geiger Counter .

Despite the power of the methods just described, much modem work is
carried out with various types of “ counters ”, instruments which can record
on a dial the arrival of a particle to which the active part of the counter is
sensitive. Two types of counter are in common use, the linear amplifier type
and that using a Geiger-MMer tube.

The linear amplifier counter is very simple in principle and is appropriate
to the observation of a particles, protons* or swift particles of higher masses.
All of these ionize intensely as they pass through air at ordinary pressures,
and even in a path of a few millimetres length an appreciable number of ions
is formed ; if the negative ions are collected on an electrode connected to the
input of a high gain valve amplifier, it is possible to arrange that the passage
of a heavy ionizing particle in the neighbourhood of the collecting electrode
gives rise to a momentary pulse of current in the output circuit of the amplifier.
This pulse, the height of which is proportional to the number of ions
reaching the collecting electrode — hence the term “ linear ” amplifier —
can be passed to a galvanometer, the response of which can be recorded on
sensitive paper ; or it may be used to give a visible displacement of the spot
of a cathode ray tube ; alternatively the pulse may be used to actuate a
mechanical register by which the Dumber of pulses is recorded. When
suitable precautions are taken these counters can easily be arranged to record
particles arriving at average rates of 100 per second or more. The informa-
tion which was acquired in a few days as a result of scintillation counting can
be obtained by modem valve amplifiers and mechanical registers in the

* A proton is a swift hydrogen nucleus. See Table of Particles and Radiations
at the end of the book.

38

Chap . V OBSERVATION OF INDIVIDUAL ATOMS

course of a few minutes. It is not necessary to dwell on the consequences of
the development of such devices as these, for it is obvious that they have
contributed in no small measure to the recent increased rate of progress in
atomic research. Although it is not appropriate to give here any extensive
details of the amplifiers used in these counters, it may be of interest to mention
that they usually incorporate negative feed-back and have sufficient gain to
show on a cathode ray tube the “ electrical noise ” in the grid and anode
circuits of the first valve of the amplifier. The choice of this first valve is
important, as its noise level determines the smallest amount of ionization that
can be detected in the output of the amplifier ; the valve chosen as the first
one is operated in such a fashion as to give maximum signal to noise ratio
in the output of the amplifier.

We now consider the Geiger-Miiller tube, * an instrument which responds
to fast electrons such as (3 particles, the electrons resulting from the inter-
action of radiation with matter or those from a suitable discharge tube or
electron accelerator. These particles produce too few ion pairs to give
adequate response from a linear amplifier, and recourse is had to a process
which even to-day is not completely understood, that of ionization by collision.
A typical Geiger-Miiller tube consists of a glass envelope within which is a
thin wire surrounded by a cylindrical metal electrode ; in the space between
these two electrodes is a gas at low pressure. When a sufficiently high
electric field is established between these electrodes, a very sensitive condition
can be attained in which apparently a single ionizing electron within the tube
is able to produce a small but appreciable discharge between the electrodes.
The initial ionization of the particle is multiplied by collision, a discharge
starts and after a small quantity of electricity has been transferred from one
electrode to the other the discharge ceases. After a short time— between
perhaps 10 and 100 microseconds — the tube has recovered its sensitive
condition and is ready to respond to another particle. The amount of
electricity transferred by the discharge is not great enough to actuate a
recording meter, but this can readily be achieved after a small amount of
amplification. The Geiger-Miiller tube is thus capable of high operating
speeds ; it is very much used when making measurements on properties of
P particles or of other high speed electrons, even though the tube may not
record every particle which passes through it. The type of Geiger-Mttller
tube described above is one of the simplest ; the actual form chosen in any
given case will depend very much on the particular circumstances of the
experiment being performed and on the properties and energies of the particles
about which information is required. In any case the tube must be arranged
so that the electrons being investigated traverse the space between its electrodes.

* This tube is often called a Geiger counter or a G-M counter.

39

ATOMIC ENERGY

Chap . V

The amplifier used with a Geiger-Miiller tube is much simpler than a linear
amplifier. The voltage pulse from the tube is relatively large and bears
no proportionality to the ionization which gives rise to it ; consequently, the
amplifier need not be linear nor need it give large gain. In many cases,
however, it is advantageous to use amplifying circuit constants so chosen that
the amplifier yields a steep-fronted narrow pulse on every occasion on which
the Geiger-Miiller tube operates.

Fig. II. Circuit used in a counter for recording the coincidences of two Geiger-

M tiller tubes.

In concluding this chapter, it is appropriate to mention a technique which
can be used to determine whether two events happen simultaneously or
consecutively. Fortunately the valve circuits used with counters are very
easily adapted to giving this information ; used in this way they are known
as coincidence counters. Those who are familiar with wireless technique
may be interested to see the details of the very simple arrangement used to
indicate coincidences between pulses coming from two or more Geiger-Miiller
tubes. In Fig. 1 1 is a circuit diagram of the simplest type of arrangement in
which a valve circuit responds only when there is a coincidence between the
pulses arising in two different circuits. These pulses must both be negative
pulses of the same shape ; each circuit supplying them is connected to the
control grid of a pentode valve. These pentodes have very little bias on
their grids, but the total anode current is limited because the anodes are
connected in parallel and are fed from the high tension supply through a
resistance which drops the anode potentials to within a few volts of the
cathodes. This resistance must be of sufficient magnitude to ensure that, as

40

Chap . V OBSERVATION OF INDIVIDUAL ATOMS

long as the grid potential of one valve retains its normal value, the anode
potential does not rise by more than a negligible amount ; thus not until
negative pulses arrive at both grids simultaneously, or within a time interval
less than the resolving time of the coincidence counter, will the anode poten-
tials rise by a sufficient amount to record a coincidence. This resolving
time, which depends on the values of the components used in the circuits,
can be made as short as 1 microsecond or even less. Coincidence counters
of short resolving times have proved invaluable in the investigation of
phenomena in which two or more atomic processes occur within a very short
interval of time.

Further information concerning the subject matter of this chapter will be
found in the books on radioactivity listed at the end of Chapter 3 and in
“ Electrical Counting ”, W. B. Lewis, (Cambridge University Press).

41

CHAPTER VI

NUCLEAR PHYSICS : 1919—1930

(1) Early attempts to cause nuclear transformations using a particles .

The a particles from radioactive substances are emitted with very large
initial energies. The most energetic a particles arise from ThC', a radio-
active substance of very short half life which is always present in preparations
of thorium C ; these a particles have an energy of 8.76 MeV.* Even the
shorter range a particles from radon and radium A have energies in excess of
5 MeV and the energy of the a particles from radium C' exceeds 7.5 MeV.
That these energies are large may be realized by noting that the average
energy of an atom in a mass of helium gas at a temperature of 5 x 10 10 °C. is
only of the order of 5 MeV.

It was early suggested that the large energy content of a particles was
possibly sufficient to bring about atomic transformations, or disintegrations
as they are often called, and a number of experiments were made to test
this possibility. In typical experiments various substances were mixed with
radon so that they were subjected to a particle bombardment by the a parti-
cles from radon, radium A and radium C'. After the radon and its immediate
short lived products had disappeared, the substances under investigation
were carefully examined for the presence of the products of disintegration ;
none was definitely found. Cameron and Ramsay, who performed such
experiments in 1907, first announced positive results, for it was believed
that under a particle bombardment water was transformed into neon and
argon ; later on, however, it was established that the a particle bombardment
simply liberated chemical elements which were initially present in the sub-
stances being bombarded. As subsequent events have shown, the idea
underlying these experiments was right, but the methods of detection were
insufficiently sensitive to show whether or not atomic disintegration was
achieved.

(2) Rutherford's disintegration of nitrogen .

Atomic disintegration by a particles was first detected in 1919 by Ruther-
ford in the following circumstances. He had made some experiments on the
effects of collisions between a particles and other atoms, especially hydrogen
atoms. He had shown that what occurred experimentally was in accord
with theoretical predictions, and that when a hydrogen atom was struck by
* For millions of electron volts we write MeV.

42

Chap, VI

NUCLEAR PHYSICS, I919-I93O

an a particle it was possible for the struck particle to have a velocity and
range greater than that of the striking oc particle. This observation was of
vital importance because most radioactive sources of a particles contain
traces of grease or other hydrocarbons, and from these protons are ejected.
Whenever long range particles are found to arise from a source of a particles,
it must first be assumed that these are protons which have suffered nearly
head-on impacts with the a particles produced by the source. Now Ruther-
ford had found, as had been predicted from theoretical considerations, that
these “ knock-on ” protons had a range of about four times that of the
a particles giving rise to them. This means that a source of radium C',
which gives a particles of 7 cm. range in standard air, will not give any long
range protons which exceed 30 cm. in range, and if suitable precautions are
taken the source can be prepared so as to give only a very few protons of
shorter ranges.

Rutherford had been examining the long range particles from a radium C'
source. This a particle source was mounted within a box which could be
exhausted or alternatively filled with any desired gas. A diagram of the
apparatus is shown in Fig. 12. Opposite the source D was a thin silver foil

Fig. 12. Rutherford’s apparatus for observing protons arising from a particle dis-
integration of nitrogen.

S, which served to close the box and also to allow the passage of any
a particle which had a range in air in excess of 6 cm. Outside the box was a
zinc sulphide screen Z, on which could be observed the impact of any particle

43

ATOMIC ENERGY

Chap. VI

which was energetic enough to pass through the silver screen and any other
absorbing material which was placed between the silver foil and the scintil-
lation screen. When the box was filled with nitrogen, scintillations were
observed on the screen even when the absorbing material between the source
and the screen was much in excess of that necessary to prevent the a particles
from reaching the screen. These scintillations might have arisen from
hydrogenous material in the source— and, indeed, the particles causing the
scintillations had about the same ranges as would be expected of par ticles of
this origin — but this was not the correct explanation, for the scintillations
disappeared when the gas in the box was replaced by oxygen or carbon
dioxide. Measurements of the effect produced when these particles were
deflected by a magnetic field indicated that they were protons. And yet
they were produced when a particles bombarded nitrogen atoms. The
method was both simple and sensitive, for calculation and the observed
scintillations showed that only about one a particle in one million gave rise
to a proton. Not only, then, did the experiment prove that an atomic
transformation was occurring, but it showed why Ramsay’s experiments gave
negative results ; the disintegration process occurred so rarely that with the
a particle sources available there was no reasonable hope of collecting
sufficient of the products of the disintegration to make possible a chemical
determination of their nature or even to allow their presence to be detected.

Further careful experiments showed that the disintegration protons
produced by a particle bombardment of nitrogen had appreciably longer
ranges than protons arising from collisions between a particles and hydrogen
atoms. The sensitivity of this method of detecting disintegrations arises
almost entirely because of the very long range of the ejected protons. Many
elements were examined with the use of similar experimental methods, and it
was found that boron, nitrogen, fluorine, sodium, aluminium and phosphorus
were disintegrated on a particle bombardment and gave rise to very long
range protons. Little could be said with certainty about other elements
except that if they were disintegrated the protons produced were not suffi-
ciently many or of sufficiently long range to be distinguished from those
arising from impacts between a particles and hydrogen atoms.

As the following considerations show, it was useful, when using materials
that did not give long range disintegration protons, to look for short range
protons in a direction at right angles to the incident bombarding a particles.
As theoretical considerations showed that no proton arising from the a par-
ticle source could be deflected through 90°, it was clear that any protons
observed would establish the occurrence of a disintegration process. Further-
more, as observation had shown that disintegration protons from aluminium,

44

Chap . VI NUCLEAR PHYSICS, I919-I930

and from other elements as well, were emitted in all directions relative to the
bombarding « particles, there was some assurance that, if disintegrations
occurred upon a particle bombardment, an appreciable number of protons
would be observed in the experimental arrangement proposed. Consideration
of the possible origins of particles ejected at right angles to the direction of
the incident a particles made it apparent that any particle which exceeded
the range of the a particle and which was observed could only arise from a
disintegration process. A slight complication, which is easily seen to be
unimportant, arose from the fact that the source of a par ticles, RaC', al-
though ejecting most of them with a velocity which gives them a r ang e of 7 cm
in air, ejects a few long range particles with ranges up to 11 cm.; but in the
experiments being discussed, there was a negligible chance of such par ticles
being scattered in such a direction as to make them apparent on the observing
screen. Such experiments, as well as those described earlier, showed that
with the exception of carbon and oxygen all the elements in the atomic
table from boron to potassium were disintegrated on a particle bombard-
ment. The experiments also showed that fast a particles were more effective
in causing disintegrations than were slower ones. In particular, for a par ticles
having a range of 7 cm. in air, it was estimated that every million particles
produced about 20 disintegrations on being absorbed in nitrogen, about
half that number when aluminium replaced nitrogen, and only about one
disintegration in heavier elements such as chlorine, argon and po tassium.

The disintegration process is popularly known as “atom splitting”
because of the appearance of the fast proton which is ejected as a result of
a particle bombardment, but despite this description it has been established
that when nitrogen is disintegrated a proton is ejected and the a particle and
what remains of the nitrogen nucleus form a single entity which is more
massive than the nitrogen nucleus. This may be shown by the following
equation :

He* +N7= HJ +0"

On the left side of this equation we have symbols for the bombarding
« particle, a helium nucleus of mass number 4 and atomic number 2, and for
the struck atom, here a nitrogen atom of mass number 14 and atomic number
7. After the reaction we have, as is stated by the symbols on the right side
of the equation, a fast proton of mass number 1 and atomic number 1 together
with an oxygen atom which has atomic number 8, as indeed all oxygen
atoms do, and the rather unusual mass number of 17.* It will be noted

* There is no direct evidence to show that O 17 results from o particle disintegration
of nitrogen, but in addition to the evidence discussed below there is indirect evidence
that leaves no room for doubt.

45

ATOMIC ENERGY

Chap. VI

that the subscript numbers are the nuclear charges and add up to 9 on each
side of the equation, and that the upper numbers are the mass units and add
up to 18 on each side of the equation. Equations like these are frequently
used in the discussion of nuclear reactions, and although they are sometimes
written a little differently from the equation above, they must always satisfy
the condition that the total mass number and the total atomic number are
the same on each side of the equation.

Let us discuss the experimental evidence which shows that the equation
above is the correct one. That protons are ejected was established by
Rutherford’s disintegration experiments ; the formation of O 17 was more
difficult to prove. The necessary evidence was provided in 1925 by Blackett,
who carried out experiments with an automatic Wilson cloud chamber.
He arranged to “ fire ” into the chamber the a particles from thorium C ,*
in the chamber was a gas consisting of 90% nitrogen and 10% oxygen
together with sufficient water vapour to saturate it. About 23 000 photo-
graphs were taken, and on an average there were 18 a particle tracks per
photograph ; two thirds of the tracks were made by 8.6 cm. a particles from
ThC' and the remainder were made by the 4.8 cm. particles from ThC. The
work of taking these photographs, and the careful examination of them,
was a task of considerable magnitude, but very interesting results were
obtained. Besides a large number of forked tracks arising, from close
collisions between a particles and the heavier gas atoms in the expansion
chamber, there were eight examples of a different type of process. In each
case there was seen what was undoubtedly a proton originating from a
point on the track of an a particle. Seven of these protons were ejected in
the same general direction as that of the bombarding a particle, but in one
case the proton was ejected in the backwards direction. Now beyond the
point of origin of the proton there was only one other track ; apparently
the bombarding a particle entered the nitrogen nucleus and the resulting
atom, which had mass number 18 and atomic number 9— it was fluorine of
mass number 1 8— immediately disintegrated to give the proton and O 1 7 . The
disintegration process is then one of exchange in which a heavy projectile
enters a nitrogen nucleus where it remains ; a lighter particle is ejected. All
the data which could be obtained fromBlackett’s photographs were consistent
with this hypothesis, and the process just described is regarded as typical of
disintegrations which are caused by a particles and result in the emission of
fast protons. In Fig. 13 is a reproduction of one of Blackett’s nitrogen
disintegration photographs.

Blackett’s photographs made possible a determination of the energy

46

NUCLEAR PHYSICS, I919-I93O

b alance occurring in the disintegration process.

Chap . VI

The results were not very
consistent, but they showed
that the energy of the
proton and the O 17 nucleus
was some 20% less than
that of the incident a part-
icle. In the case of the
disintegration of alumin-
ium, however, the energy
resulting from the disin-
tegration process was found
to be greater than that of
the incident a particle so
that the experiments with
aluminium represent the
first case in which man was
able to arrange an experi-
ment giving a few instances
of a process in which
atomic energy was released.
Admittedly only a neglig-
ible fraction of the a
particles used were prod-
uctive in this way; most
of them simply failed to hit
the very small target repre-
sented by the aluminium
nucleus and wasted their
kinetic energy in collisions
with the outer electronic
structure of the atoms
amongst which they moved.

One cannot consider these
experiments without being
struck by the simplicity
and sensitiveness of Ruth-
erford’s experimental tech-
nique. It is amazing that
progress in the development of nuclear physics should be made by carrying
out experiments which succeed on only one occasion “ 1

thousand.

Fig. 13 . Cloud chamber photograph showing a
particle disintegration of nitrogen. The key dia-
gram assists In an interpretation of this photograph.
(From The Newer Alchemy, Rutherford, Cambridge University
Press.)

in one hundred

47

ATOMIC ENERGY

Chap . VI

(3) Accurate measurements of atomic masses .

During the period when artificial atomic disintegrations were being investi-
gated, Aston was making accurate measurements of the relative masses of the
atoms of most of the elements. His line of investigation arose from the
earlier work of J. J. Thomson which resulted, as already described, in the
discovery that neon consisted of two isotopes of masses 20 and 22 ; it was
clearly desirable to see whether all elements consisted of isotopes having
masses which were apparently integers. Aston devised new apparatus,
capable of comparing atomic masses with an accuracy of about 1 part in
1000. This apparatus made use of means for producing high speed positive
ions of the element under investigation ; these ions were passed through
electric and magnetic fields so disposed as to bring to one point on a photo-
graphic plate all ions with the same ratio of charge to mass. As every ion
carries one or at most a very few electronic charges, it is possible to use the
apparatus for the comparison of masses. For this reason Aston called this
device a mass spectrograph. With it he reached the conclusion that if the
oxygen atom was given the mass of 16 all atoms but those of hydrogen had
masses which were whole numbers. By assuming this whole number rule,
which in fact his apparatus was incapable of verifying exactly, and by
making additional use of his mass spectrograph measurements to determine
the relative abundance of isotopes of an element, Aston was able to deduce the
chemical atomic weights. Such atomic weights, which involve the properties
of materials in bulk, had been determined with great accuracy from experi-
ments made with the naturally occurring mixtures of isotopes. In some
cases Aston’s measurements gave atomic weights which were close to the
chemical ones, but as this did not occur in every case it became apparent that
the hypothesis underlying his determination of chemical atomic weights
was unjustified. It is now certain that atomic masses are not identical with
mass numbers, but it was not only for this reason that Aston’s measurements
did not give the atomic weights that had been determined by the chemists.

As is well known the chemical atomic weights are relative numbers only and
take their accepted values when the weight chosen for natural oxygen is exactly
16. Aston also chose 16 as the atomic mass of the oxygen atom, for when he
took this step he did not realize that his oxygen was not the same as the
chemist’s oxygen. Natural oxygen is mostly O xe but there are isotopes O 17
and O 18 which are present in small amounts. When, for example, the mass
spectrograph is used for a determination of the atomic mass of fluorine, an
element which has only one naturally occurring isotope, the mass of a fluorine
atom is compared with that of an atom of O 18 ; but the chemist has compared
the mass of millions of fluorine atoms with that of the same number of

48

Chap . VI NUCLEAR PHYSIC S, 1919-1930

natural oxygen atoms, some few of which are O 17 and O 18 atoms. Thus the
chemical atomic weight of fluorine is lower than the atomic mass of the fluorine
atom. To state the difficulty in another way, we can say that on the basis of
chemical atomic weights pure O 18 would have an atomic weight just less than
16 ; in fact its value would be 15.9963.

The discovery of the existence of O 18 , which is the more plentiful of thetwo
rare isotopes of oxygen, had an important consequence. When oxygen was
believed to be a single isotope, the mass of O 18 was compared by the mass
spectrograph with the mass of H l . The result obtained gave the mass of
hydrogen as 1.00778, agreeing closely with the accepted value of the chemical
atomic weight of hydrogen, viz., 1.00777. When oxygen was known to
contain appreciable amounts of O 18 , it was apparent that natural oxygen was
heavier than pure O 1 ® ; if the ratio natural oxygen : natural hydrogen was in
fact the same as O 16 : H 1 as determined by the mass spectrograph, natural
hydrogen was heavier than H 1 and hydrogen must contain a heavy isotope or
isotopes. As appeared later, Aston’s mass of H l and the chemical atomic
weight were both in error, and although hydrogen did contain a heavy
isotope, it was present in smaller amount than was at one time anticipated ;
nevertheless, direct evidence for the existence of H a was sought and found,
and eventually methods were devised for separating this hydrogen isotope
from water. As water made from this hydrogen isotope is more dense than
ordinary water, it is known as heavy water ; the H a isotope of hydrogen is
called heavy hydrogen or deuterium and is represented either by H“ or D“.
The early methods of preparing heavy water were troublesome, but they
nevertheless made it possible to obtain commercially, though at great cost,
small quantities of this material. Deuterium is of great importance in nuclear
physics and as we shall see later in the production of atomic power. The
war-time interest of the Royal Air Force in the Norwegian heavy water plant
must be attributed to the belief that the deuterium being separated there was
destined for use in Germany in the preparation of material for atomic bombs.

(4) Atomic masses and stability of nuclei .

Further experiments with improved apparatus were needed to provide more
accurate values of atomic masses and to-day the modern mass spectrograph,
which continues to compare atomic masses by passing positive ions through
electric and magnetic fields, is capable of giving values in close agreement with
those obtainable by other methods. These precise atomic masses are of
value in a discussion of the stability of atoms. As the actual values of the
atomic masses are very close to the atomic mass numbers, it is useful to
consider a quantity which may be called the mass defect, that is the mass by

D 49

ATOMIC ENERGY

Chap . VI

which the atomic mass of an element exceeds* its mass number. Alternatively,
we may usefully talk about the packing fraction of an atom, this quantity
being defined as the mass defect divided by the atomic mass number. We
can give a physical significance to these terms : the mass defect of an element
is the amount of mass which would disappear if the element was broken up ^
into particles, each with one unit of mass, that is with a mass of ^ of the O 18
atom. Where the packing fraction is negative it is the average amount of
mass lost for each particle of mass unity required to form the element in
question. As is seen from Figs. 14 and 15, packing fractions are large and
positive for the light elements, are negative and between 0 and 7.5 x 10~ 4 for
elements with mass numbers between 16 and 166 and thereafter are positive
and quite small until the heavy radioactive elements are reached. By using
the mass energy relation, we find that a packing fraction of 10 -3 corresponds
to an energy per particle of about 0.9 MeV. If then an atom of mass number
60 with a packing fraction of —7 x 10 -4 could be made from particles with
mass unity, there would be liberated for each particle used an energy of
about 0.63 MeV. On the other hand, if we assume that the same atom is
built up from particles having the mass of the hydrogen atom, the energy
liberated will be very much more and will in this case amount to nearly 8 MeV
per particle. In fact we don’t make atoms up in this way, but the supposition
is of some significance for the energy liberated in the assumed synthesis may
give us some idea of the amount of energy needed to split up the atoms that
axe at our disposal. When account is taken of the fact that the radioactive

* Although it is illogical, an atom like hydrogen with a mass greater than its mass
number is usually regarded as having a positive mass defect.

50

Chap. VI

NUCLEAR PHYSICS* I919-I930

atoms not only split up naturally but liberate considerable amounts of
energy in doing so, it is apparent that the forces that hold atoms together
are not so strong as would be anticipated if atoms were constructed from
particles having the mass of hydrogen atoms. That oc particles, rather than
protons, are emitted from some radioactive elements is in accord with this
conclusion.

However this may be, the relative stability of atoms is likely to be indicated
by the value of the packing fraction, and on this basis both the light elements
and the very heavy elements might be expected to be the least stable. It is
not supposed that there is any precise connection between packing fraction
and stability, although it is indeed the case that the heavy elements disintegrate
spontaneously, and that many of the light elements are those most easily
disintegrated by a particle bombardment. Nevertheless, as we shall see

51

ATOMIC ENERGY

Chap . VI

later, accurate determinations of atomic masses were of much more value
than in their application to this rather hypothetical consideration of the
structure and stability of the atom.

(5) Evidence in favour of the identity of all atoms of given atomic number
and mass number.

From the time of the discovery of the neon isotopes, it was assumed that
neon was made up of two classes of atom, and that every atom of one class
was identical with every other atom of that class. As it turned out, the
development of the technique of measuring the masses of atoms served to
confirm this early belief. As far as could be determined, every atom with
given atomic number and mass number had the same mass as every other
atom. There was no evidence of a range of masses amongst the atoms of
one isotope of a given element.

This piece of information was in accord with what was to be expected from
a study of a particle emission from radioactive elements. For here every
a particle was emitted with the same energy, and as every a particle appeared
to have the same mass the emission of an fc particle from any atom of a given
radioactive substance resulted in a constant reduction of mass of the parent.
The obvious assumption, indeed the only satisfactory one, was that all atoms
of both parent and product were identical. Information concerning P ray
emission did not confirm this view, for not all p particles are emitted with
the same energy, and from the point of view of the mass energy relation this
might mean that not all atoms lose the same mass in a p ray disintegration.
Some of the missing energy is associated with the y rays that are frequently
emitted after the emission of a p particle, but even so it is clear from experi-
ment that the mean energy emitted as p and y radiation upon a given P ray
disintegration is not as great as the maximum energy with which a few p parti-
cles are found to be emitted. It is felt that this is only an apparent difficulty
which arises because of our inability to detect some of the energy which is
released at the time of a p ray disintegration, for it is believed that the atomic
mass of a given p ray emitting atom is decreased by a constant amount as a
result of the emission of the p particle. Because of the evidence from
a particle emission measurements, and the confirming evidence from mass
spectrograph experiments, it became accepted that all atoms of a given
isotope were identical in mass and as far as was known in all other respects.

(6) Nature of the Particles within the Nucleus .

Nevertheless very serious difficulties were appearing in the light of growing
knowledge of the nucleus. For many years it had been assumed that the
nucleus was built up from protons and electrons. Neon with its atomic

52

Chap . VI NUCLEAR PHYSICS, I919-I93O

number of 10 and mass number 20 was supposed to have a nucleus composed
of 20 protons and 10 electrons. Ne aa had two more protons and two more
electrons. This assumption was made for two reasons. The only two
fundamental particles then known were the proton and the electron. Further-
more, in the case of radioactive bodies the nucleus actually emitted electrons.

Now it was possible to make some estimate of the size of a given nucleus.
This was determined fiom calculations based on the results of experiments
in which some element, for example aluminium, was bombarded with
a particles. These bombarding particles are sometimes deflected or scat-
tered by the intense opposing field existing near the nucleus of aluminium.
Experiments have shown that two point electric charges exert mechanical
forces which are inversely proportional to the square of the distance between
them ; it was reasonable to calculate the distribution of scattered a particles
on the assumption that their paths passed through an inverse square law
electric field arising from the positively charged aluminium nucleus, and to
compare the calculated and observed scattering patterns. As soon as the
a particles approach sufficiently close to the nucleus they may be expected to
experience different forces which will alter the pattern in which they are
scattered. Experiments on these lines show that there is a breakdown of
the inverse square law when an a particle makes a close approach to a
nucleus ; we regard the region of validity of the inverse square law as being
outside the nucleus and the point at which the law just fails as representing
the boundary of the nucleus. This interpretation is to be regarded as
useful rather than precise, especially as head-on collisions with low speed
a particles indicate a different nuclear size from that indicated by collisions
with a particles of higher speed. Nevertheless it is found that for light
elements the nucleus lies within a sphere of radius less than 10 -12 cm. and
even for heavy elements it is expected that the radius of the nucleus will not
greatly exceed this quantity, although on this matter no experimental data
are available, for a particles are not sufficiently energetic to penetrate so far
into the nuclear field of an atom as heavy, for instance, as mercury.

The size of an electron is even more indefinite than that of a nucleus, but
it possibly has a radius in excess of 10- 13 cm. Although this is considerably
smaller than the radius of a nucleus, it is not sufficiently small to make us
happy with the idea of a nucleus of uranium, supposed to contain 238 protons
and 146 electrons, all in the space of a sphere of radius about lO -12 cm. This
is a difficulty, but in view of our lack of experience of particles as small as
this when packed into small spaces, too much should not be made of it. The
other difficulty is more troublesome to understand, but it was much more
serious. The y rays are believed to arise in the nucleus; calculations

53

ATOMIC ENERGY

Chap. VI

showed that if these radiations arose because of motions of electrons in the
nucleus, they could not consist of radiations having discrete frequencies;
on the contrary the motion of electrons would give rise to y ray energies and
frequencies* which were distributed over some appreciable range. But
experiment showed, with all the appearance of conclusiveness, that the y rays
were very much “ sharper ” than if they were produced by the motion of
electrons. Either there must be no electrons in the nucleus or they must
behave abnormally in order to produce sharp y rays.

(7) Theories of a particle emission .

Finally there were serious difficulties about the emission of a particles from
radioactive substances. The general position is quite easily understood by
reference to the case of uranium I, which emits an a particle with the rather
low energy of about 4 MeV. This energy is obviously obtained from the
repulsion of the a particle by the electric field in the neighbourhood of the
nucleus of the atom formed from the a decay of uranium I, and as the
a partide carries two charges it must arise in a region where the electric
potential is about 2 x 10® volts ; since a small fraction of the initial potential
energy of the electric charges is given to the recoiling nucleus, the a particle
from a uranium I nucleus must arise at a point where the potential is slightly
higher than this. In itself, this requirement can be accepted without much
difficulty, although it involves the supposition that the a particles originate at
a point about 6 x 10- la cm. from the centre of the nucleus, a state of affairs
which seems to contradict the estimate of size given in the paragraph above.
But despite the reasonableness of believing that a particles originate so far
from the centre of the nucleus, there were even stronger reasons for the
belief that they did not originate there. For when uranium is bombarded by
7.5 MeV a particles, which must be capable of probing the space from which
the uranium I a partide would be supposed to originate, there is not the
slightest evidence of the existence of any charged particle within this space.
Indeed, the use of even the swiftest a partides available has given no evidence
of anything but emptiness in the immediate vicinity of the uranium I
nucleus.

Another difficulty was brought to light by the so-called long range a particles
emitted by ThC. The radioactive transformations of this substance and of its
immediate products are shown in Fig. 16. A source of ThC, which always
contains ThC', emits a particles which are mainly of ranges 4.8 and 8.6 cm.,
but in addition there are a few particles of range up to 11 cm. or more. As
there are only about 250 long range particles for every million particles of
range 8.6 cm. the long range particles were difficult to investigate. It was

* The relation between y ray energies and frequencies was given in Chap. 3, p. 24.

54

Chap . VI

NUCLEAR PHYSICS, I919-1930

ThC (60.5 min)

ThD (Stable)
Lead

Fig. 16. The radioactive transformations of thorium C.

believed that they came, not from ThC itself, but from ThC', a very short
lived product formed after p decay of ThC and the source of the 8.6 cm.
particles. Here then was a very unfortunate state of affairs in which it was
apparently only an approximation to suppose that all a particles emitted
by ThC' had the same energy of emission. The position was not apparently
improved by the discovery that the 4.8 cm. a particles emitted by ThC itself
had not all the same velocity of emission. In this case, however, the range
of velocity was quite small, and again only a few particles were in any but
the most plentiful velocity group. The existence of these long range a par-
ticles and the discovery of the variety of ranges associated with the particles
from ThC were profoundly disturbing, and doubt arose as to whether the
accepted picture of radioactive phenomena was not falsely simple. Perhaps
our ideas would have to be changed entirely before we were able to fit these new
discoveries into the scheme of things. But, in fact, these small variations in
a particle ranges were details that in the end gave reality to the existing
views of the nucleus ; in connection with them there was no revolution of
thought.

55

ATOMIC ENERGY

Chap . VI

These difficulties with a particle emission were the first to be explained.
The explanation must be examined in some detail because of the light it
throws on the structure of the nucleus of the atom. The position is best
considered with the help of Fig. 17, which shows the potential energy of an
a particle in the vicinity of a nucleus of atomic number 90, i.e., with a nuclear
charge of 90 electronic units. As we approach the nucleus we find that the
potential energy is inversely proportional to the distance from the centre of
the nucleus*; experimentally this law of force is found to hold at all approach-
able distances in the vicinity of a heavy nucleus. In 1928 Gamow, and at
the same time and independently Gurney and Condon, assumed that this law
did not hold in the region of the nucleus to which the swiftest a particle
cannot approach ; they believed that at places nearer to the centre of the
nucleus there were strongly attractive forces of very great power but of short

Distance from Centre of Nucleus

Fig. 17. Potential energy of an a particle in the neighbourhood of the nucleus of
an atom of atomic number 90.

range. There was assumed to be a region where these short range attractive
forces completely overcame any electrostatic repulsions, and where the poten-
tial energy of the a particle was small or even negative. This picture gives,
in the neighbourhood of the centre of the nucleus, a potential barrier ; the
bamer is so high that no natural a particle is able to reach its top. Now
the a particles of a radioactive substance are initially on the inside of the
potential barrier ; on the simplest view this barrier must be ass ume d to
enclose the nucleus completely, and in consequence no a particle will be able
to escape unless it either is able to pass over or through the barrier. As
the a particles are emitted with energies smaller than 10 MeV they have

* The potential energy vanes in this manner in a region in which electric charges
experience an inverse square law of force.

56

Chap. VI NUCLEAR PHYSICS, I9I9-I930

insuffic ient energy to enable them to surmount the barrier; apparently
escape is impossible even though it would be accompanied by release of
energy. Consideration of the properties of the large material particles with
which we make contact during our lives goes to confirm this view. But
then modem physics has progressed because it has been realized that atoms
and electrons do not behave as do ordinary material particles. The branch
of mathematical physics which deals with die behaviour of an « particle in a
nucleus is a complicated one which cannot profitably be discussed here. It
must suffice to say that on the theory of Gamow the a particles are sometimes
able to escape, even though they have not enough energy to go over the top
of the barrier.

We may suppose the a particle within the nucleus to be in motion ; it
will then possess kinetic energy as well as the potential energy appropriate
to its position. When the a particle is emitted, it will leave the nucleus with
almost the same energy as that which it possessed when in the nucleus, and
for this reason the speed of emission of an a particle, and its range in standard
air, are related to its energy in the nucleus. On Gamow’s theory, high
energy a particles escape from a nucleus more readily than do a particles of
smaller energy; consequently those substances which emit a particles of short
ranges may be expected to have longer half lives than substances which emit
a particles of longer ranges. The detailed theory gives a numerical relation
between the half life of a radioactive substance and the energy of the a par-
ticles emitted by it ; this theoretical relation is in close accord with experi-
mental data. Although the theory gives no picture of the way the a particle
passes through the potential barrier, it explains so much that its correctness
can hardly be doubted ; if improvements are needed they must be in matters of
detail.

The theory explains the problem of the origin of the low energy « particles
from uranium I.* These particles are within the potential barrier where of
course they have no influence on the scattering of any a particles with which
uranium is bombarded. Furthermore, this theory led to further experiments
which served to explain the origin of the long range a particles. Careful
measurements of the energies of these long range particles gave a value for the
energy difference between such a particle and a normal 8.6 cm. a particle
from ThC'. As this energy difference corresponded closely with the energy
of a y ray, emitted by ThC' just after its formation from its parent ThC,
it became clear that the long range « particle must be regarded as an alter-
native to the emission of a y ray and then an a particle of normal range.
Apparently, after ThC had emitted a p particle, the resulting ThC' nucleus

* See above, p. 54.

57

ATOMIC ENERGY

Chap. VI

was sometimes left with excess energy which was either emitted as a y ray
or was carried off as the additional energy of a long range a particle. This
simple picture accorded closely with theory and with all the known facts,
and it co nfir med the growing belief that there was a constant amount of
energy liberated when one radioactive nucleus transformed itself into another
nucleus lower down in the radioactive series. This energy might appear
in alternative forms, but if the various alternatives were compared, it would
be found that in each the same amount of energy was liberated. A further
simple example was provided by the « particles from ThC, where, as men*
tinner! above, there are some few os particles which have ranges slightly
different from the most usual range. It was found that these range differences
arose because the a particle did not carry off with it all the available energy;
some of this was left behind with the nucleus, and was subsequently emitted
as a y ray- Such a theory must be tested against measurements of the
energy emitted in the alternative processes ; when this test was made there
was found to be no room for doubt as to the correctness of the theory, for
each of the possible processes liberated the same amount of energy.

For further information see the books on radioactivity listed at the end
of Chapter 3 and “The Newer Alchemy”, Rutherford, (Cambridge
University Press) ; “ Mass Spectra and Isotopes”, F. W. Aston, (Arnold).

REFERENCES

1 Dempster, A. J., Phys. Rev., 5a, 869, 1938.

58

CHAPTER VII

NUCLEAR PHYSICS 1932—1933

(1) Review of outstanding discoveries .

The period 1932-3 was remarkable for the discoveries then made in atomic
physics. There were many reasons for the advances of these years and of
them two are particularly important. The new quantum theory had been
formulated and had become established, and in some cases its predictions
suggested new experiments. Of greater importance, however, was the
development in the experimental techniques of atomic physics, particularly
in the direction of counting single ionizing particles by electrical means.
Although these devices were discussed in Chapter 5 they had not reached a
useful stage of development until about 1930, when they began to be used to
an increasing extent and to assist greatly in the acquisition of knowledge of
nuclear processes.

It is useful first to review the discoveries of the years 1932-3 and then to
discuss their significance in some detail. In 1932 Cockcroft and Walton 1 des-
cribed how lithium atoms were disintegrated when bombarded by high speed
protons which had been accelerated after their formation in a discharge
tube. Here was the first nuclear transformation process in which the fast
particles as well as the disintegration process had been arranged by human
agency.* In the same year Chadwick 2 announced the discovery of the
neutron, a particle having a mass nearly the same as that of a proton but
carrying no charge. The possibility of the existence of such a particle had
been discussed much earlier by Rutherford 3 , and its existence was known
for some short time before its nature was appreciated. Also during 1932
Anderson 4 in U.S.A. discovered the positive electron, or positron as it is
now usually called. The existence of this particle had been predicted as a
result of theoretical studies, but although positrons are produced when
penetrating y rays pass through heavy elements such as lead, they were
first detected in expansion chamber photographs of cosmic rays. And
finally during the year 1933 F. Joliot,and his wife Irene Curie, demonstrated
artificial radioactivity 6 . They showed that it was possible to bring about
atomic transformations which yielded radioactive forms of some of the
common elements.

* Cockcroft and Walton’s disintegration process had not occurred previously
upon the earth. Many of Rutherford’s disintegrations had been carried out in
nature for millions of years.

59

ATOMIC ENERGY

Chap . VII

All these discoveries have played an important part in the development of
nuclear physics and indirectly in the discoveries which have led to the large
scale release of atomic energy. Of the four discoveries, the most important
was that of the neutron. The properties and behaviour of this particle are so
vital to us that the next chapters must be devoted to their consideration ; it
is appropriate to mention here, however, that the discovery of the neutron
made it unnecessary to believe that the atomic nucleus contained electrons.
It was accepted immediately that the nucleus contained only neutrons and
protons and that isotopes had the same numbers of protons but differed in
mass because their nuclei contained different numbers of neutrons. We
consider here the consequences of the other discoveries ; we commence
by describing the properties of the positron.

(2) Positrons .

This particle has a unit positive charge and the mass of an electron. It is
formed when y rays traverse the intense electric fields which exist near the
nucleus of a heavy element with a high atomic number. The energy of the
y ray is used to create an electron pair — a positive and a negative electron —
and to give these two components kinetic energy; the original energy of
the y ray is greater than the kinetic energy of the electron pair by the amount
of energy equivalent to the mass of two electrons. The positron has not a
very long independent life ; quite soon it combines with an electron and the
kinetic energy of the positron and the mass of two electrons are converted
into y rays. The process is interesting from many points of view, but
particularly so to us because it provides a very good example of a way in
which energy can be converted into mass and mass into energy. This
process has an air of mystery about it, and it may suggest that it is possible to
find means by which matter of every kind is converted into energy, with
the result, as has already been pointed out, that there is a yield of large
amounts of energy for the consumption of quite small amo unt s of mass.
This, however, is never likely to be possible. As has already been explained,
if the laws of physics show that a process will yield a certain amount of
energy, we may use Einstein’s relation to determine the resulting diminution
in mass. The numerical relationrhips connecting mass and energy should
not prompt us to believe that mass can be converted into energy whenever
we wish.

(3) Artificial disintegration of lithium .

Cockcroft and Walton’s experiment was in some respects a very simple one,
but at the time at which it was performed the results were very surprising. It
had been realized for some considerable time that fast protons might be

60

Chap. VII NUCLEAR PHYSICS, 1932-1933

able to carry out atomic transformations, but most people assumed that
energies of many MeV would be needed before such transformations could
be effected. This belief was substantially correct, but there are cases in which
much less energetic particles are able to bring about nuclear reactions, and
Cockcroft and Walton investigated one of these. Some of the details of
their experiment are of interest and importance to us. They arranged to
have a high voltage supply by which they could accelerate hydrogen ions
drawn from a low pressure electric discharge in hydrogen ; these ions were
speeded up by a potential of about three quarters of a million volts, and they
then fell on to a target of lithium. The resulting reaction, in which the more
plentiful of the two lithium isotopes is involved, is described by the following
equation :

u; + h; = He; + He;

From this one sees that the reaction yields two helium atoms, which, on
account of the large amount of energy liberated in the reaction, have high
velocities and so are simply artificial a particles. Each of the two helium atoms
has a range in standard air of somewhat more than 8 cm., corresponding to
a total energy liberation of about 17 MeV. Here is a reaction which yields
much more energy than that supplied by the bombarding particle. Cockcroft
and Walton had available protons with energies up to about 0.75 MeV but
such energies are not essential to carry out this atomic transformation ; it
will work with protons with energies as low as 0.1 MeV, although it them
occurs rather less frequently than when faster protons are employed. Un-
fortunately, in any case, it occurs far too rarely to be of practical use in the
production of energy. When 0.2 MeV protons are used to bombard atoms
of Li 7 , only one disintegration occurs for every hundred million bombarding
particles.

Let us return to the equation above and see how we can use it to determine
the true mass of the lithium atom. We know from recent mass spectrograph
measurements that the mass of the helium atom at rest is 4.0039 mass units
and from the mass energy equation that 1 MeV is equivalent to 1.073 xl0“ 3
mass units. Thus the mass equivalent of two helium atoms and an energy
of 17 MeV is 8.0260 mass units, and this must be the mass equivalent of the
bodies which, on interaction, give the two swift helium atoms. The mass of
the hydrogen atom is 1.0081 and if we neglect the energy of the incident
proton we conclude that the lithium atom* must have a mass of 7.0179. We
have obtained this figure by taking mass spectrograph figures for the atomic
masses of hydrogen and helium, and by assuming that all Li 7 atoms have

* Although the reactions are between nuclei, atomic and not nuclear masses are
inserted in the equations.

61

ATOMIC ENERGY Chap. VII

the mass and that in all transformations by protons of Li 7 to helium
atoms an energy of 17 MeV is released. The mass obtained for the lithium
atom— 7.0179— can be compared with a mass spectrograph determination,
qr>H in this way a check can be made on the mass values given by the mass
spectrograph and on the validity of our us© of the mass energy equation. It
is clear, however, that if mass energy equations are used to determine masses,
it is possible to build up a table of atomic masses which depends on a few
mass spectrograph determinations and on the study of many nuclear reactions.
Proceeding in this way, it will often be possible to obtain several values for
the precise mass of an atom of atomic number Z and mass number A;
these values will be consistent only if the initial mass spectrograph values
are correctly related to one another and if it is valid to use the mass energy
equation as we did to determine the mass of Li 7 . In fact this has been done ;
initial discrepancies were removed by a redetermination of the mass spectro-
graph value of the ratio He 4 : O 1 ® and to-day there is a reliable table of
atomic masses, some of which are most accurately known from measurements
of the energy balance in nuclear transformations, and many of which have
been determined only in this way. Thus the study of nuclear transformations
has shown that the fullest information is to be obtained from nuclear reaction
equations when the energy balance of the reaction as well as the reacting
particles are shown in the equation. When this is done the nuclear reaction
equation has on each side of it the same total nuclear charge or atomic
number, the same total mass number, and the same total of mass and energy
taken together.

These conclusions did not arise immediately from the work of Cockcroft
and Walton ; they initiated a line of investigation which was extended by
them and by other experimenters who later possessed more powerful means of
accelerating particles* than were available to Cockcroft and Walton in 1932,
and it was from all these investigations that the validity of this use of the mass
energy equation was verified.

(4) Artificial radioactivity .

It had long been appreciated that the radioactive elements were still found
on earth because of the very long lives of the parent elements, thorium and
uranium. It is quite possible that other radioactive elements were once
present upon this planet, but they have disappeared because they had lives
which were short compared with the period which has elapsed since their

* These include the cyclotron which was developed during the period under
discussion and to which modem nuclear physics owes so much. Appendix I gives
bnef details of some methods of accelerating charged particles.

62

Chap . VII NUCLEAR PHYSICS, 1932-1933

formation. Nevertheless, the possibility of producing artificial radioactive*
elements, that is radioactive forms of common elements, was not regarded
seriously until the Joliots showed in 1933 that after the bombardment of
aluminium by a particles there was present a short lived radioactivity with
a half period of about 3 minutes. 5 It was possible to perform chemical
tests to determine whether aluminium or some other element was responsible
for this radioactivity ; it was found to arise from phosphorus, a discovery
which was in accord with the information available concerning its formation*,
information which suggested that the material was P™. Now this radio-
phosphorus, as it was called, possessed the remarkable property of emitting
positively charged particles which were identified as positrons. Its radio-
activity caused it to be converted into Si™, a stable isotope of silicon which
is present to the extent of a few percent, in naturally occurring silicon ;
this is the isotope of silicon which results, on the instantaneous emission of
a proton, when aluminium is bombarded by a particles, the reaction which
was discovered and investigated in Rutherford’s early disintegration experi-
ments. Further investigation showed that a particle bombardment of other
light elements gave rise to further artificial radioactive substances, many of
them, like phosphorus, emitting positrons, and all of them having half lives
which are reckoned in minutes. We shall discuss later the importance of
these and other artificial radioactive elements but as they are not usually
prepared by a particle bombardment, it seems appropriate to defer considera-
tion of this matter.

* The reaction is AlX+HeJ =*P™+nJ ; n\ represents a neutron.

REFERENCES

1 Cockcroft and Walton, Proc. Roy. Soc., A136, 619 1932.
Cockcroft and Walton, Proc. Roy. Soc., A137, 229, 1932.

2 Chadwick, Proc. Roy. Soc., A137, 692, 1932.

3 Rutherford, Proc. Roy. Soc., A97, 374, 1920.

4 Anderson, Phys. Rev., 43, 491, 1933. .

5 Curie and Joliot, C.R., Acad. Sci., Pans, 198 254, 1934.
Curie and Joliot, C.R., Acad. Sd., Paris, 198, 559, 1934.

63

CHAPTER VIII

NEUTRONS

(1) Production of neutrons .

The story of the discovery of the neutron is an interesting one, but in the
present context it must be omitted in order to give space for consideration
of the properties of neutrons. It must suffice to mention here that neutrons
are produced when beryllium is bombarded by a particles of sufficient
energy. Neutron sources are often provided by mixing beryllium powder
with radium, in which circumstances the neutrons arise in the main from
bombardment of the beryllium by the a particles emitted by the short lived
products of radium. Neutrons may be produced in other ways, one of
which is so impoitant that it is mentioned here. If heavy hydrogen nuclei—
deuterons— are given an energy of the order of 2 x 10 5 eV, as may be done by
using relatively simple accelerating tubes, and if these deuterons are allowed
to bombard stationary heavy hydrogen atoms in the form, for example, of
heavy ice, a reaction takes place between pairs of deuterium nuclei. It
appears that some collisions result in the release of neutrons, while others
give two hydrogen atoms, one a radioactive substance with mass 3 and
the other the common hydrogen isotope of mass 1. The neutron-yielding
reaction is described by the following equation:

H 2 +H:= He* + ni + 3.2 MeV.

This reaction, which is often referred to as the D on D reaction, is of interest
because it results in the production of He 8 ; its main importance, however,
lies in the fact that it produces neutrons which carry a considerable fraction
of the energy balance of the reaction. By using high energy deuterons,
which may be obtained from a cyclotron, neutrons of high energy may be
produced.

As has already been mentioned, the neutron is a particle of mass number
unity, and without charge. Apart from its lack of nuclear charge, it is very
similar to a proton, and yet it is this lack of charge which makes it so diffe-
rent from any other particle.

(2) Passage of neutrons through matter.

The most remarkable property of a neutron is its ability to pass freely through
matter which is impervious to any kind of atom. We can give a picture of
the manner in which a neutron passes through matter by considering a

64

NEUTRONS

Chap. VIII

greatly magnified model of a piece of graphite sheet. Suppose that the
sheet is 1 cm. thick and that it is magnified 10 10 times. If we take our
earlier estimates of nuclear dimensions, we see that a nucleus of 10“ la cm.
diameter is magnified to be 0. 1 mm. across ; the electrons will be rather
smaller than this. But what is more surprising is the very great distance
between neighbouring nuclei. These were actually separated by about 2.3 x
10“ 8 cm. and in our magnified model they will be 2.3 metres apart. Now a
cube of graphite of 1 cm. side contains about 1.2xl0 aa atoms. In the
expanded model one face of this cube has an area of 10 20 cm. 2 so that each
cm. 2 of the model has behind it, in a depth of 10 l ° cm., 1200 atoms, each of
which has a nuclear area of about 10* 4 cm. 2 As the total area of the 1200
atoms is only 0.12 cm. 2 the area of the nuclei is about 12% of the area of
the sheet containing them. Perhaps the electrons should also be included,
for, although they are smaller than the nuclei, they are more numerous ; but
even if they are considered we find that the total area of all nuclei and electrons
in this centimetre thick graphite sheet is probably less than half the area of the
sheet. A sufficiently small particle will find many routes by which it can
pass directly through such a piece of material ; and the neutron is such a
particle. Not all neutrons will avoid collisions as they attempt to pass right
through a thin sheet of graphite or other material ; but in many cases the
collisions which occur are elastic collisions which result in little more than a
change in the direction of motion of the neutron. Some of the neutrons
which make such collisions will pass quickly through the material ; others
may have their directions reversed and some of these leave the material on
the side on which they entered it. The result is that neutrons can escape
fairly easily from a container made from a material which is experimentally
found to be quite impervious to all gases. The rate of escape of neutrons
will depend on a number of factors, one of which is the velocity of the neutrons.
But if the nuclei have the sizes we have assumed, there is no way in which
we can confine neutrons, for there is no material into which they cannot
pass.

This discussion of the very tenuous nature of matter in bulk naturally
raises a question. Why cannot protons or even hydrogen atoms move
through matter just as easily as does a neutron ? The case of the hydrogen
atom is easily seen to be quite different from that of the neutron, for the
hydrogen atom is a proton with an electron attached to it, and the diameter
of the electron orbit is of similar dimensions to the distance between atoms in
a solid. The hydrogen atom cannot move very far through a homogeneous
material unless it leaves its electron behind it and then it is not a hydrogen
atom.

Experimentally, even a proton does not go very far through solid matter,

E 65

ATOMIC ENERGY

Chap. VU1

and this for a very good reason. The neutron may find our estimates of
atomic sizes fairly accurate, but the proton experiences nuclear fields at
distances much in excess of 10 -12 cm. from the centre of the nucleus. Thus
to a proton the nuclei are much bigger than they appear to a neutron, and a
“ hole ” through which a neutron can readily pass may not even exist for a
proton. Not only is the transparency of a material different for a neutron
and a proton ; it differs enormously for protons of different speeds. The
slower the proton goes, the fewer the places in which it can move, and the
greater the chance that it will experience a change of direction, and a loss of
energy, in its passage through the electric field of a nucleus.

Although the picture, just given does not describe all the features of the
motion of neutrons through matter, it does serve to show why materials
which are impervious to hydrogen atoms or fast ions can be readily traversed
by neutrons. The crucial difference is the absence of charge on the neutron,
and for this reason the neutron has many fewer interactions with matter
than a proton for example. It is partly for this reason also that radioactivity
was studied for over thirty years before the neutron was discovered.

Let us consider in more detail what happens to a neutron which moves into
a thin sheet of material. There are several possibilities, one of them being
that the neutron takes a path that allows it to pass straight through. But
not all possible paths will avoid the nuclei of the atoms in the sheet, and some
neutrons will make collisions ; whenever there is a collision there are two
consequences : the neutron loses some of its energy and also changes the
direction of its path.

(3) Energy lost by a neutron in an elastic collision.

Let us first examine the circumstances which determine the amount of energy
transferred by a neutron to a struck nucleus as a result of a collision. The
energy transferred will depend on the path and energy of the neutron and on
the mass of the struck nucleus. The collision, if it is elastic, as we shall
suppose, will be such that the energy and momentum of the neutron before
the collision will equal the total energy and momentum, respectively, of the
neutron and the nucleus after the collision. These requirements enable us
to determine the nature of the collision between a neutron and a nucleus of
given mass in which there is the maximum transfer of energy from the
neutron to the struck nucleus ; we find, as we might expect, that this occurs
with a head-on collision. For this simple type of collision we can readily
determine what happens and easily calculate the energy transferred. For if
m is the mass of the neutron, u its initial velocity, and v its final velocity, we
have from the conservation of energy the following relation :

Jmu a = Jmv 2 + iMV 2 .

66

NEUTRONS

Chap . VIII

Here M is the mass of the struck nucleus and V its final velocity. Again,
from the condition that momentum is conserved we also have :

mu = mv + MV.

If we eliminate v from these equations and calculate the kinetic energy of
the struck nucleus, i.e., iMV 2 , we find that it is equal to

4Mm
(M + m) a

This is the energy transferred by the neutron to the struck nucleus. Now if

M is equal to m, as would be the case if the collision was between a neutron
and a hydrogen nucleus, the energy transfer amounts to imu®, i.e., the neutron
gives up all its energy to the hydrogen nucleus ; this type of collision is
illustrated in Fig. 18. Of course not all collisions between a neutron and a

hydrogen nucleus are head-on collis-
ions, but some few are, and in these
the neutron gives all its energy to
the struck nucleus ; in other close
collisions between a neutron and a
hydrogen nucleus, the neutron trans-
fers appreciable amounts of its
energy to the nucleus, but not the
whole of it. Thus when a neutron
moves through material containing

Before Collision
** O- .

Neutron f

Hydrogen Nucleus

After Collision

Fig. 18. Head-on collision between
neutron and H 1 nucleus. The lengths
of the arrows represent the speeds of the
particles.

hydrogen it occasionally makes collis-
ions with hydrogen nuclei and as a result it loses energy, the amount
of energy lost depending upon the nature of the collision. If the neutron is
a fast one, it is sufficiently accurate to imagine that the hydrogen nucleus is
at rest, and in this case the colliding neutron loses a fraction of its energy
which can be quite simply stated in terms of the angle through which the
collision deflects it. In the case of slower neutrons it may be necessary to
consider the finite velocity of motion of the hydrogen atom ; this is certainly
the case with neutrons having energies close to the mean kinetic energy of
thermal agitation of a gas molecule at the temperature of the matter through
which the neutron moves. Such neutrons are known as thermal neutrons.
At any given collision between a thermal neutron and a hydrogen nucleus
there may be either gain or loss of energy, for when the neutrons have the
same average kinetic energy as is possessed by the molecules amongst which-
they move, on balance they neither gain nor lose energy. Individually,
however, neutrons regularly gain and lose energy as a result of collisions,
and consequently, amongst thermal neutrons, there will be a considerable

67

ATOMIC ENERGY

Chap. VU1

range of neutron energies, just as there is a range of energies of the molecules
of a gas. Thus the neutrons which pass through hydrogenous material
suffer a loss of energy consequent upon collisions with hydrogen nuclei ; this
loss of energy continues until the neutrons are reduced to thermal energies
in which circumstances they remain in temperature equilibrium with the
matter within which they move.

Contrast what happens when a neutron makes a collision with a nucleus
of a heavy atom, and let us consider as the simplest case a head-on collision;
in this case, as our formula shows, the struck nucleus has transferred to it
only a small fraction of the initial energy of the neutron. The directions of
motion before and after the collision are the same as those in Fig. 19. A

neutron passing through a lead
plate may make collisions with lead
nuclei with consequent changes in the
direction of motion, but as it transfers
only 2% of its kinetic energy on a
head-on collision with a lead
nucleus, it will not lose its energy
by elastic collisions at a rate which
is in any way comparable with that
achieved when it passes through a
, . , , , . material, such as water or paraffin

wax, m which hydrogen is one of the main constituents.

We shall see shortly that means for slowing down neutrons are of impor-
tance m some methods for releasing atomic power. In view of the needs of
su sequent chapters, it is appropriate to determine here the energy transfer
^ n Q a n f utron a head-on collision with a deuterium nucleus or

1x1 1116 first case 8 / 9 of the neutron energy is trans-
terred to the deuterium atom, but in the second case only about 2/7 of the

t0 th ! carbon atom - 11 spears, then, from these
* 1 h i!f y hydrogen — deuterium— is almost as effective as hydrogen
in slowing down neutrons, but that carbon, and of

WvaiLTf" ^ markedly less efficient; the really

heavy atoms are relatively useless for this purpose.

(4) Neutron scattering.

SStowSmJS °^ Utr0n scattering on a quantitative basis, we
passing through * eutron makes an elastic collision when

a narrow paraHel Lam < ^. mat ® nal of . kn own composition. Let us imagine
narrow parallel beam of neutrons, in the path of which is placed a thin

68

Before Collision

Neutron Helium Nucleus

-A <£.

After Collision

Fig* 19. Head-on collision between a
neutron and a He 4 nucleus. The lengths
of the arrows represent the speeds of the
particles.

NEUTRONS

Chap. VIII

sheet of scattering material. If this sheet is thin enough, only a few neutrons
will make nuclear collisions which are close enough to deflect them appreciably
and of these few neutrons an entirely negligible number will make two
nuclear collisions. In these circumstances a measurement is made of the
number of neutrons scattered out of the beam. By using different thicknesses
of the scattering material it may be shown that the number of neutrons
scattered is proportional to the thickness of the scatterer, as long as this
thickness is not too great ; or in other words that the number of neutrons
scattered is proportional to the number of atoms per cm. 2 of the scattering
material. As we know the absolute masses of atoms we can readily calculate
the number of atoms in a cm. 3 of material and then the number of atoms
per cm. 2 in a sheet of the material of thickness t, and finally the scattering
effect per atom. If, for example, we consider a piece of paraffin wax of
density 0.9 g. per cm. 3 and suppose that it contains two hydrogen atoms for
every carbon atom, we see that 14 g. of wax will contain 1 g. atom of carbon
and 2 g. atoms of hydrogen. Now in 1 g. atom there are about 6 x 10 33
atoms, so that in 7 g. of paraffin wax there are 6 x 10 23 hydrogen atoms and
in 1 cm. 3 about 8 x 10 22 hydrogen atoms. If we find that the hydrogens in a
piece of wax 1 mm. thick scatter 9% of the neutrons in the beam, we can say
that all the hydrogen atoms in the piece of wax produce a target for neutrons
which has an area of 9% of that of the piece of wax ; the hydrogen atoms
in each cm. 3 of wax thus present an area of 0.09 cm. 2 , and each atom provides
a target of 12 x 10 -24 cm. 2 This area is called the scattering cross section of
the hydrogen atom for the neutrons in the beam. The use of the idea of
scattering cross section is universal in the discussion of the behaviour of
neutrons passing through matter, and it is for this reason that it has been
discussed in some detail. It will be noticed that the figure given above,
which is derived from experiments on the passage of neutrons through
paraffin wax, is appreciably larger than might have been anticipated from
our earlier estimates of nuclear sizes. If we looked at the matter from the
point of view of the collision of two elastic spheres, we would assume that
these scattering experiments gave cross sections which depended on the
size of the neutron as well as on the size of the hydrogen nucleus, and in part,
perhaps, this contributes to the high value obtained. But when experiments
are made in different circumstances, it becomes clear that no precise figure
can be given for the size of the hydrogen nucleus. It is sufficiently encourag-
ing to find that estimates of nuclear size derived from a particle and neutrons
scattering experiments arc sometimes of the same order of magnitude.

The figure given for the neutron scattering cross section of hydrogen, viz.
12 x 10" 24 cm. 3 , has not much significance for anyone who does not deal fre-
quently with the processes of neutron interaction with matter, and for this reason

69

ATOMIC ENERGY

Chap. VIII

it is desirable to give the relationship between this cross section and the average
distance the neutron will move between collisions with hydrogen atoms. It
is easily shown that this distance, which we will call the mean free path for
neutron collision, is inversely proportional to the collision cross section
and to the number of nuclei available for collision in 1 cm. 3 of material.
The exact relationship is given by the equation:

Collision cross section x number of nuclei per cm. 8

1

mean free path.

For the case of a paraffin wax in which there are 8 x 10 22 hydrogen atoms
per cm. 8 , each with a collision cross section of 12 x 1(H 4 cm. 2 , the mean free
path will be nearly 1 cm. This may suggest that neutrons do not pass
very readily through paraffin wax, but it will be realized that even a mean
free path of 1 cm. is very large compared with the range of an a particle or
of a proton in solid matter.

(5) Detection of neutrons .

We have discussed for some time the passage of neutrons through matter,
but nothing has been said concerning the way in which neutrons are detected!
It will be realized that neutrons pass easily through matter because of their
infrequent interactions with atoms ; for this reason they are difficult to
detect. The simplest way of showing the presence of fast neutrons is to pass
them into an expansion chamber which is filled with hydrogen. Some
neutrons will make close collisions with hydrogen nuclei and as a consequence
considerable amounts of energy will be transferred to the struck nuclei,
which will then be able to form tracks in the chamber ; these energetic
hydrogen nuclei are conveniently called “ knock-on hydrogens ” or “ knock-
on protons. Occasionally, when there is a head-on collision, the neutron
will transfer all its energy to the hydrogen nucleus, and in such cases the
direction of the track of the knock-on proton will be the initial direction of
the neutron, and from the length of the track the energy transferred to the
hydrogen nucleus may be estimated ; this energy is the initial energy of the
neutron. If die neutrons come from a source of small dimensions, their
directions in the cloud chamber are determined, and neutron energies can be
estimated in the case of collisions in which only a portion of the energy of
the neutron is transferred to the struck hydrogen nucleus. In such collisions,
one of which is illustrated in Fig. 20, the direction of the proton track does
not correspond with that, of the motion of the neutron either before or after
the collision, but the energy transferred to the knock-on hydrogen depends on

f f + ^ e ^ ut ^ on on to® an Sl e between the initial neutron
pati and that of the knock-on hydrogen. Fig. 21 shows an expansion

70

Chap. VIII

NEUTRONS

Neutron

^ 7

Point of Impact

Knock-on proton

F 5' 20 C . Coll,s,on between a fast neutron
and a hydrogen nucleus. The lengths of
the arrows represent the speeds of the
particles.

Fig. 21. Wilson Cloud Chamber photograph showing tracks
of knock-on protons. The source of neutrons was at S and gave
2.4 MeV neutrons from the D on D reaction.

(From The Newer Alchemy , Rutherford, Cambridge University Press.)

71

ATOMIC ENERGY

Chap. VIII

chamber photograph of the tracks of hydrogens knocked-on by neutrons.
Although this method of observation is in some ways satisfactory, it is far
from sensitive. As we saw above, some neutrons have a mean free path in
paraffin wax, where there are 8 x 10 2S atoms per cm. 3 , of about 1 cm.; these
neutrons will have, in hydrogen at atmospheric pressure, where there are only
5xl0 19 hydrogen nuclei per cm. 8 , a mean free path of about 16 metres.
This arithmetic shows that only a few of the neutrons passing through an
expansion chamber of moderate size will yield the knock-on proton tracks
which alone reveal their presence. It is to be remembered, also, that although
the method gives information about neutron energies, it is only suitable for
neutrons with energies in excess of a few tens of thousands of electron volts,
for which neutrons the collision cross section is even smaller than the value
assumed in the calculation above.

(6) Neutron capture processes .

There are other ways of detecting the presence of neutrons, some of them
much more sensitive than the expansion chamber method already discussed,
but before these are described, it is desirable to make some further examina-
tion of the phenomena occurring when neutrons pass through matter. For
clarity of discussion we will assume that means are available to enable us
to measure the energy of neutrons. For neutrons with energies of the order
of 1 MeV, paraffin wax is more transparent than for the slower neutrons we
have been discussing in our example above ; at this high energy the scattering
cross section of a hydrogen atom is little more than 10" 24 cm. a , giving a mean
free path in paraffin wax of about 10 cm. For neutrons with less energy, the
mean free path in paraffin wax is shorter than 10 cm.; neutrons with an
energy of 1 eV have a mean free path of approximately 1 cm., and neutrons
with an energy of about 1/30 eV — the same energy as the kinetic energy of
an atom in a gas at room temperature — travel about 0.3 cm. between collisions.
For still slower neutrons, the mean free path will be even smaller than this.
It appears then that the mean free path of neutrons in paraffin wax is a
quantity which depends on the velocity of the neutrons, and that for neutrons
with low energies it is about 1/30 of its value for high energy neutrons.
Now for neutrons with energies of about 1 /30 eV — these are called thermal
neutrons because, as has just been mentioned, they have the same energy as
the thermal energies of gas molecules at room temperature — not only does
elastic scattering occur between neutrons and hydrogen nuclei ; some of
the neutrons are actually captured by the hydrogen nuclei. We again intro-
duce the idea of the cross section of the nucleus, but this time we call it the
capture cross section. For thermal neutrons the capture cross section of the
hydrogen nucleus is very small, and amounts to about 0.4 x 10- 84 cm.*, a

72

NEUTRONS

Chap . VIII

cross section which would give a neutron a mean total path of about 30 cm.
in paraffin wax. This figure refers to thermal neutrons which have a mean
free path of about 3 mm. in paraffin ; on the average, then, these thermal
neutrons make about one hundred collisions with hydrogen nuclei before
capture takes place. For faster neutrons hydrogen has a still smaller capture
cross section, and in fact any neutron entering a hydrogenous material such
as paraffin wax will almost certainly be slowed down to thermal energies
before it is captured by a hydrogen nucleus ; but eventual capture is certain
unless of course the neutron leaves the hydrogenous material. Even after
the neutron has been reduced to thermal energies, it has the prospect of a
path of 30 cm. in paraffin wax ; but as its velocity is then about 2 x 10 s
metres a sec. its life time in paraffin wax is only of the order of 10‘ 4 sec. What
if it does escape ? It may make a close collision with some nucleus by which
it is captured, or alternatively, it is believed, it may convert itself into a
proton and an electron. In view of the difficulty of confining neutrons this
possibility is an awkward one to verify ; but the neutron has s uffi cient mass
to make this process possible from the point of view of the mass energy
equation, and there are good reasons for believing that this transition may
actually occur. It can only be important, however, when alternative pos-
sibilities of capture are exceedingly small, and in most cases it need not be
considered.

The passage of a neutron through matter involves a number of processes
which may be summarized as follows. In the first place the nuclei are
spaced at great distances compared with their own dimensions, and through
the holes between them the neutrons are able to pass freely because they are
unaffected by the strong electric fields existing between the nuclei. Never-
theless, occasionally the neutrons make collisions with nuclei and either the
neutron is captured by the nucleus or else it rebounds after an elastic collision
in which some of the energy of the neutron is transferred to the nucleus and
the direction of motion of the neutron is altered. The relative importance of
the two processes, and indeed the probability of hitting or missing a given
nucleus, depends on the velocity or kinetic energy of the neutron. Numeric-
ally the various possibilities are expressed by stating the elastic collision and
capture cross sections of a given nucleus for neutrons of a given energy.

It is a matter of interest and importance to consider how the capture cross
section of a nucleus may be expected to vary with neutron velocity. The
simplest case, of which the capture of slow neutrons by hydrogen is an example,
involves a capture cross section which is large only at low neutron velocities.
The cross section is inversely proportional to the neutron velocity, or put in
other words it is proportional to the length of time for which the neutron

73

ATOMIC ENERGY Chap . VUI

remains in the immediate vicinity of
the capturing nucleus. Fig. 22 shows
the variation of capture cross section
^ to be expected in such a case.

\ Usually, however, neutron capture

\ cross sections show a much more

complicated variation with neutron
velocity, and in particular there are

o ooi "o-o t "?TTo frequently certain neutron velocities

Neutron Energy (*v) for which the neutron capture cross

Fig. 22. Relation between capture cross section is very high. The capture
section and neutron energy. (No reson- process then occurring has some sum-
ance levels.) larity to resonance phenomena which

are found in physics in connection
with electrical and mechanical oscillations, and for this reason it is known as
resonance capture. In electrical resonance, for instance, a circuit gives large
oscillations for an applied voltage of one particular frequency. In the case
of resonance neutron capture, the neutron is readily captured because it has
the correct energy. Upon neutron capture the nucleus generally has more
energy than it can retain for any appreciable length of time ; in terms of
the description usually given the nucleus is “excited,” and it proceeds
immediately to dispose of the “ excitation energy ” so as to reach an equili-
brium state in which it can remain. When resonance capture takes place,
the energy transferred to the nucleus by the captured neutron is such as to
make it fit readily into the structure of the new nucleus arising from its
absorption, a state of affairs which is usually described by saying that the
energy of the neutron corresponds to that of a particular resonance capture
level. For a given nucleus there may be many of these resonance neutron
capture levels, but they give rise to large neutron capture cross sections only
where they occur at neutron energies close to the thermal region, for it is
only then that the neutron passes a nucleus sufficiently slowly to give rise to
a high chance of capture.

In some cases resonance capture cross sections are large and in others
they are small ; some levels are broad and others narrow. In the region of
low neutron energies, heavy elements have neutron capture resonance levels
which are irregularly spaced at distances of about 10 eV. For light elements
the resonances are much broader and although they are more widely spaced
than for heavy elements they sometimes overlap. This overlapping also
occurs in the general case of the capture of neutrons of higher energy ; here
no discrete resonances are found and the capture cross section falls with
increasing velocity, at first inversely as the velocity, but at energies of the

74

cm* 4 j
Capture Cross y
Section x I0* 4

2

I

NEUTRONS

Chap. VIII

order of 1 MeV the capture cross section decreases inversely as the energy.

A representative neutron capture cross section curve for slow neutrons is
shown in Fig. 23, where it is supposed that only one resonance level exists.
’The position of the resonance level is taken as the neutron energy at which
the capture cross section is maximum ; the width of the level is the range of
neutron energy for which the capture cross section is greater than half the
resonance value. In the diagram of Fig. 23 the resonance level is at 2 eV and

cm. 2 10

o

Capture Cross
Section x I0 22 ^
4
2

12 3 4

Neutron Energy (eV)

23. Relation between capture cross section and neutron energy. (One reson-
ance level.)

it has a width of 0.5 eV. This value is a reasonable one for a heavy capturing
nucleus.

It should be realized that the overall shape of a neutron capture cross
section curve is determined by two factors, one of which is the situation and
nature of the resonance capture levels. It is sometimes useful to think of
this as the only factor involved and then, to obtain a true picture of the
variation of capture cross section with neutron velocity, to take account of the
fact that the capture cross section is also inversely proportional to the neutron
velocity. In this way we obtain a clear picture of the reasons for observed
variations of capture cross section. In the neighbourhood of a sharp reson-
ance capture level, the shape of the curve depends almost entirely on the
nature of the resonance level ; at considerable distances from resonance
capture levels the effect of the time spent by the neutron in the vicinity of a
capturing nucleus is of much greater importance, and the curve shows that the
cross section is inversely proportional to the neutron velocity.

75

ATOMIC ENERGY

Chap, nil

There are two cases in which the capture cross section of a material
is inversely proportional to the velocity of the neutrons. The first is
that just discussed ; it arises when the resonance energy of the lowest
level is some considerable distance above thermal energies, and when the
resonance level is sharp. Then, for neutron energies up to about one tenth
of the resonance value, the capture cross section is inversely proportional to
the neutron velocity. The other case is that in which the width of the
resonance level is great. If, for example, a resonance level situated at 10 eV
has a width of 100 eV, the resonance capture curve itself* will give rise to
very small changes of cross section in the region from 0 to perhaps 25 eV;
when account is taken of the effects of increasing neutron velocity, it is seen
that for neutron energies up to 25 eV the capture cross section varies inversely
as the velocity. Boron and lithium both have very wide resonance capture
levels, and for slow neutrons both show a capture cross section that is inversely
proportional to the velocity of the neutron.

(7) Neutron reactions.

Let us now discuss the consequences of neutron capture. As should be
quite clear, the capture of a neutron does not alter the chemical nature of the
atom by which it is captured. To take the simplest example, consider the
capture of a thermal neutron by a hydrogen atom. The result is the for-
mation of a heavy hydrogen atom. As the sum of the masses of the hydrogen
atom and the neutron is somewhat in excess of that of a heavy hydrogen
atom, the nucleus resulting from neutron capture has excess energy which it
liberates by emitting radiation in the form of y rays. This reaction is
written

H; + n l 0 = H= + 2.17 MeV.

In view of the fact that radiation is emitted after the capture of the neutron,
this process is commonly referred to as radiative capture.

Now this is a particularly simple case of neutron capture, but because of
its simplicity it is worthy of further consideration. As might be suspected
the reaction is reversible ; if high energy y rays are sent through heavy
hydrogen, some of the y rays are absorbed ; their energy is given to a
deuterium nucleus which may then split into a proton and a neutron, of
which the kinetic energy will depend upon the amount by which the energy of
the y ray used exceeded 2.17 MeV, the energy of the y ray emitted on the
capture of a neutron by a hydrogen atom. The process by which heavy
hydrogen is disintegrated by y rays is known as photo-disintegration.

* Momentarily we are overlooking the effects arising from the time spent by the
neutron in the neighbourhood of the nucleus by which it may be captured.

76

NEUTRONS

Chap. VIII

In general, however, we do not find that a stable nucleus is formed as a
result of neutron capture. The new nucleus may immediately split up, or
alternatively it may be a radioactive atom which disintegrates within a short
or longer time after its formation ; it is found, too, that neutron capture is
not invariably followed by the same reaction. We have already met alter-
native reactions in the case of heavy hydrogen bombardment of heavy hydro-
gen — D onD— and in connection with a particle bombardment of aluminium,
where there are sometimes protons emitted and on other occasions the for-
mation of radio-phosphorus. In a similar way, on neutron capture, a
nitrogen nucleus may give a carbon nucleus and a proton or alternatively
a beryllium nucleus and an a particle. Consequently there is a very large
number of reactions resulting from neutron capture, and there is no advantage
in mentioning many of these. It seems desirable, however, to discuss some
typical cases and to mention some reactions which are of use in the detection
of neutrons. This chapter will give no discussion of nuclear fission, for
although this is one of the consequences of neutron capture it is a process of
such importance and interest to us that a separate chapter is devoted to it.

The simplest neutron reaction, radiative capture, is represented by the
capture of neutrons by hydrogen. The neutron capture gives an isotope of
the capturing nucleus ; this isotope has a mass number one greater than the
nucleus from which it was derived. In general this isotope is formed in a
condition in which it possesses more than its normal energy ; the surplus
energy is radiated as a y ray.

There are a great number of reactions of this type, and of these the cases
of cadmium, silver, indium and rhodium are worthy of mention. Cadmium
is of interest because it has a very large capture cross section for thermal
neutrons ; the resulting cadmium isotope appears to be stable. Silver,
indium and rhodium, which exhibit resonance capture of the type discussed
above, all show considerable capture cross sections for neutrons which have
slightly greater energies than those possessed by thermal neutrons, and all
give rise to short-lived artificial radioactive elements which emit p particles.*
Since a Geiger-Miiller tube responds to single p particles, these radioactive
substances form convenient indirect detectors of neutrons of the appropriate
energy.

As has already been mentioned, neutron capture by a nitrogen nucleus is
sometimes followed by the immediate emission of a proton. A similar
reaction occuis with a number of other elements, especially light ones. The

♦The eventual radioactive transformation of these nuclei occurs long after the
neutron capture process ; it is not believed that radiative capture in the case of
cadmium is essentially different from that occurring when, for example, silver
captures neutrons.

77

ATOMIC ENERGY

Chap. VIII

new element resulting from this reaction has the same mass number as the
element which captured the neutron, but there is a decrease of unity in
atomic number. In some cases the product nucleus is radioactive. The
reaction for nitrogen may be taken as typical. For it we have

K + = c 1 ; + h;

From the point of view of this book a reaction of this type is not important.

The last type of reaction to be considered is a rather rare one. It is the
case of neutron capture resulting in the immediate emission of an a particle,
a type of reaction which sometimes occurs as an alternative to that described
above when a nitrogen nucleus captures a neutron. Two important reactions
of this type are those occurring on neutron capture by lithium or by boron.
The reactions are

Li: + n ; - H< + H-;

B l ; + n; = He: + LiJ

In both cases the capture cross section for slow neutrons is reasonably large,
especially in the case of boron, and in both cases appreciable energy is libera-
ted as a result of the reaction, so that the particles released are capable of
forming a considerable number of ions.

Both these reactions are of importance because they provide satisfactory
means for detecting neutrons. The methods previously mentioned— the
examination of knock-on protons arising from neutron impacts, and the use
of artificial radioactive substances formed on neutron bombardment — are
subject to serious limitations. The use of knock-on protons is of great
historical importance, and it is still of use for the detection of high energy
neutrons, especially as the method can be used to measure the energy of the
neutrons. Again, silver is a satisfactory detector for neutrons just above the
thermal range of energy, but it is unsuitable for thermal neutrons and in any
11 “ *°t. ver y sensitive. On the other hand thermal neutrons are captured
byboffihthmm and boron, and on capture they give rise to the emission of
raft njuum atoms which give sufficient ionization to make them easily
detected. In a slow neutron detector use is made of an ionization chamber
dScV 1^®" ^Plifier and counter. The inside of the ionization
boro “ or llthium compound or alternatively the
b0r0n tr '? uoride : when a thermal neutron passes into
w i? I reas °nable probability of capture by the boron or the
nartM^^ni rfth ? hap . pe] ? s there ls high probability that the resulting fast
Sut of^SlT 10 ™? n “ ^ chamber and a large pulse at the

S b^n^nn^S' 2 ^ W ^ y satisfac t°ry neutron-sensitive chambers
have been constructed, and these have been invaluable in making measure-

78

Chap. VIII NEUTRONS

ments of neutron intensities and in measuring scattering and capture cross
sections of different elements.

A few remarks should be made concerning the methods used for measuring
the energy of neutrons, particulaily of the slower neutrons. At first sight
this looks a difficult problem and so it has proved to be. In the case of fast
neutrons we have already seen that their energies may be determined from the
ranges of knock-on hydrogens with which they have made head-on collisions.
In some cases the energy of slow neutrons can be deter mine d directly. Where
neutrons are emitted from a source as a result of bombardment by particles
accelerated by a high voltage, it is often possible to arrange that the high
voltage is applied periodically for short intervals of time. By this means the
neutron source is made to yield a series of short bursts of neutrons, and by
measuring the time taken for these neutrons to travel from the source to a
distant detector, the velocity of the neutrons may be determined. Alter-
natively, bursts of neutrons may be obtained by mechanical means ; when
thermal neutrons are being investigated, cadmium shutters, built into a
rotating disk, are used to cause a periodic interruption of the neutrons so as
to make possible a direct measurement of their velocity.

Many of the determinations of neutron energies, however, make use of the
known variation of boron or lithium neutron capture cross sections with
neutron velocity. If a beam of neutrons is passed through an absorbing
screen containing boron, neutron capture will occur, but as this occurs more
frequently for slow neutrons than for fast ones, the beam is made relatively
poorer in slow neutrons. The extent to which boron absorbs the neutrons
responsible for some particular resonance capture process is then an indication
of the velocity of these neutrons. If for example the capture cross section of
boron for thermal neutrons is ten times as large as that for the neutrons that
are captured by silver to form radioactive silver, we deduce that the latter
neutrons have ten times the speed and one hundred times the energy of
thermal neutrons or in other words an energy of about 3 eV.

By the use of such principles, determinations have been made of the
neutron energies at which various resonance capture processes occur, and
consequently at the present time there is not a great deal of difficulty in
determining the energy range of the neutrons in a neutron beam. It should
be borne in mind that a beam of neutrons is not like a beam of charged
particles ; it is difficult to arrange that it is well defined in width and to ensure
that all the neutrons in the beam have the same energy ; in many ways a
beam of neutrons more closely resembles a beam of neutral molecules than
it does a beam of protons or electrons. Fortunately, however, we now know
enough about neutrons to make it easy to detect them, and in fact the methods

79

ATOMIC ENERGY Chap. VIII

of detection of neutrons compare favourably in sensitivity with those used
for detecting charged particles.

In 1932, when the neutron was discovered, the task of finding out much
about it must have appeared very difficult or hopeless ; as things have
turned out, some properties of neutrons are very favourable for the investi-
gation of the neutron and of the reactions in which it takes part, and to-day
there is an immense amount of detailed information concerning it. This
information, and the experimental methods used to obtain it, were of the
utmost assistance in the nuclear studies that led to the realization of atomic
energy and the atomic bomb.

In the following there is some information concerning the properties of
neutrons: “ Why Smash Atoms ? ”, A. K. Solomon, (Pelican Books, A 141) ;
“ The Newer Alchemy ”, Rutherford, (Cambridge University Press) ; “ Ele-
ments of Nuclear Physics ”, F. Rasetti, (Blackie and Son, Ltd.)

80

CHAPTER IX

NUCLEAR FISSION

(1) The bombardment of uranium by neutrons .

Amongst the substances which were early subjected to bombardment by
neutrons were the heavy radioactive elements, uranium, protoactinium and
thorium. These are a particle emitting elements of rather long life, and they
occupy, in the order given, the three highest places in the periodic table.
Particular interest was attached to the case of uranium, for if this behaved as
did so many other elements it would capture neutrons and from U a38 would
be obtained U 239 , a substance of higher atomic weight than any other known
to occur naturally upon the earth. There was no reason to assume that U 230
would emit a particles as do uranium I and II and actino-uranium (U 238 ,
U 234 and U 23fi ) ; U 23B might behave as do so many other nuclei after neutron
capture, and emit p particles, giving rise in this case to a new element of mass
number 239 and atomic number 93.

Investigation showed that bombardment of uranium by neutrons did
indeed produce radioactivity in which p particles were emitted ; presumably
new elements were being formed — elements with higher atomic numbers
than 92. After chemical treatment of uranium which had been subjected to
bombardment by neutrons, it was found possible to isolate substances which
showed p radioactivity and which were chemically different from uranium ;
in addition it appeared that there was some p ray activity from an element
which was chemically identical with uranium. To clarify the position it was
desirable to establish the identity of these new radioactive elements. If they
were elements of atomic number higher than that of uranium, their precise
chemical properties would be unknown, in which case these properties could
be predicted only by making use of the periodic table after first assuming a
value for the atomic number of the unknown clement being investigated.
Reference to the periodic table shows that a substance of atomic number 93
may have properties similar to those of manganese, masurium or rhenium ;
it probably would precipitate with one or other of these elements. If we mix
our unknown substance with manganese, and we find on precipitating the
manganese that the unknown is not brought down with the precipitate we will
be suspicious of our assumption that it is of atomic number 93 ; but as it hap-
pens that many different elements precipitate with certain manganese com-
pounds, a positive result is encouraging but it is not in the least conclusive.
Further tests are needed.

F

81

ATOMIC ENERGY

Chap. IX

If the new elements were not of atomic number 93 or higher, they might
be of atomic number 90 or 91 ; it was hardly likely that they would be still
lower than this. And experiment soon showed that they were not identical
with any element between uranium and mercury. There appeared to be no
doubt ; the elements in question must have atomic numbers greater than 92.
These elements were called the trans-uranic elements, and they were the
subject of extended researches.

Information soon obtained showed that there appeared to be a large
number of trans-uranic elements formed by the successive emission of
P particles. The problem was to ascertain the nature of these elements and
to determine the transformation constants of the radioactive decay ex-
hibited by them. Although this problem appeared straightforward, it proved
to be unexpectedly difficult of solution ; there were so many of these short-
lived radioactive substances. Not only were there a great many trans-uranic
elements ; many of these, though chemically identical, appeared in a number
of alternative nuclear forms, each of which had its own period of radioactive
decay. These alternative forms were of course isotopes, but they were more
than this, for on any reasonable view of their mode of formation they had
identical mass numbers as well. The existence of radioactive isotopes with
identical mass numbers and different radioactive transformation constants is so
rare that the discovery of examples of this type of isomerism amongst the
trans-uranic elements made it appear that their radioactivity was different
from anything previously known.

In endeavours to ascertain the atomic numbers of these trans-uranic
elements, many chemical experiments were made, and of these two are of
particular interest to us. The Curie- Joliots found that if a compound of the
rare earth lanthanum was added to uranium which had been subjected to
neutron bombardment, one of the resulting radioactive substances could be
precipitated with the lanthanum. They were struck with the great similarity
between the chemical properties of this radioactive substance and those of
lanthanum, but as they believed that the two substances were not identical,
they assumed, for reasons which are apparent on examining the atomic
table, that they were dealing with an isotope of actinium. In a similar way,
they discovered that if barium replaced lanthanum some of the trans-uranic
radioactive substances could be precipitated with barium. As is well known
from the work of Madame Curie, barium and radium are chemically similar,
so much so, indeed, that they are quite difficult to separate. It was natural
then, to suppose that the radioactive substance which precipitated with barium
was a new form of radium. But this conclusion, and similarly the belief that
at least one of the radioactive substances was actinium, involved serious

82

NUCLEAR FISSION

Chap. IX

difficulties. It was not very satisfactory to be faced, a short time later, with
the necessity of recognizing the existence of four new short-lived types of
radium. But even more difficult was the problem of explaining how radium of
atomic number 88 was formed from uranium of atomic number 92 ; this
would require the immediate emission of two a particles, an unlikely con-
sequence of the capture of a neutron by a heavy atom. And there was no
evidence at all that neutron bombardment of uranium led to the emission of
any oc particles.

This difficulty was finally overcome when Hahn and Strassmann 1 investi-
gated the properties of the new short-lived radium that was precipitated with
barium. For they found, to their astonishment, that the so-called radium
did not behave as expected, for even when Madame Curie’s methods were
used, the new radioactive substances could not be separated from barium.
Only one conclusion was possible ; the short-lived radium was not radium
at all ; it was barium ! And just as certainly, the actinium which the Joliots
precipitated with lanthanum was not actinium but was lanthanum itself.

Immediately upon the publication of Hahn and Strassmann’s paper,
Frisch 1 suggested that neutron bombardment of uranium caused it to split into
two massive fragments, one of which was a radioactive barium. He called
the process uranium fission, and he estimated that the fission fragments should
possess a total kinetic energy of the order of 200 MeV. Particles emitted with
an energy of 100 MeV must give rise to very large amounts of ionization, of
the order of ten times that produced by the fast a particles from ThC'. An
ionization chamber and linear amplifier should easily provide conclusive
evidence of intense bursts of ionization of this type. And so it proved.
Frisch, at that time in Denmark, physicists in many parts of the U.S.A., the
Joliots in Paris and workers in England quickly carried out experiments
which showed without doubt that neutron bombardment of uranium did give
rise to bursts of ionization which were about twenty times as large as those
produced by the normal uranium a particles. Fig. 24 gives an example of
the records obtained in an experiment of the type described. Later on, as a
result of more precise electrical measurements of the ionization produced by
the products of fission, it was found that each fission fragment had a kinetic
energy of about 100 MeV, just as was expected. But even the earliest tests
confirmed the views that Frisch first put forward to explain the presence of
barium in a sample of uranium that had been bombarded by neutrons.

The fission process gives fragments which are capable of forming easily
visible tracks in the expansion chamber, and not long after the discovery of
fission, photographs were published in which the tracks of the fission frag-
ments could be seen. These tracks are rather short — about 3 cm. in standard

83

ATOMIC ENERGY

Chap. IX

air — and in one respect
they are different in
appearance from an a
particle track. The heavy
fission fragments make
frequent close encounters
with the nuclei of lighter
atoms to which they com-
municate appreciable
amounts of energy. In
consequence, the tracks
themselves show occasion-
al spurs, which arise from
those encounters resulting
in a sufficient transfer of
energy to enable the struck
atom to ionize. On ac-
count of the high mass of
the colliding fission frag-
ment, its direction of
motion is relatively little
affected by such
encounters. Figs. 25 and 26 illustrate the appearance of fission fragment
tracks in the expansion chamber.

This process of nuclear fission is quite different from any other nuclear or
atomic process previously known. In other nuclear reactions, protons,
neutrons, and even a particles are ejected from atoms when they are subjected
to suitable bombardment, but no heavier particle than the helium nucleus had
ever been found to be emitted in a nuclear disintegration. In the case of
uranium fission, bombardment of uranium by neutrons sometimes brings
about such instability that the uranium nucleus splits into two nearly equal
portions. As these fragments of the uranium nucleus both carry many posi-
tive charges, they repel strongly as soon as they have become separated from
one another. Even when the centres of the fragment nuclei are within 10 11
cm., and this represents a separation of the order of ten nuclear diameters,
the repulsive force between the fission fragments is about the same as the
force of the earth’s attraction on a mass of 4 lbs. These forces fall off
rapidly as the fragments separate, but they are maintained for sufficient
distances to impart tremendous energies to the two particles into which the
uranium atom divides. The total energy acquired by these two particles as
a result of their mutual repulsion is readily estimated in terms of their charges,

84

Fig. 24. Oscillograph record of ionization caused
by fission fragments from uranium. The length
of each long black line is proportional to the ioni-
zation from a single fission fragment. The a
particles from uranium I do not give sufficient
ionization to show on this record.

(From the Journal of Applied Physics , Vol. II, p. 5 (19-40),

ATOMIC ENERGY

Chap. IX

if some reasonable assumption has been made as to their distance apart at
the time of their separation ; the result obtained from such a calculation
shows that the total energy involved is of the order of 200 MeV. This new
process of fission releases much more energy than is set free in any other
single atomic process known.

In view of this large energy release, it is rather remarkable that nuclear
fission was not discovered earlier. In fact, fission was so different from all
previously known nuclear processes that nobody was on the look out for it.
There were, indeed, a few occasions on which it was nearly discovered, but
by some mischance of experimental arrangement, evidence of its occurrence
was obscured.

(2) The nature of the fission fragments .

What is the nature of the fission fragments? The mass number of uranium I is
238, so that prior to fission the uranium nucleus has a mass number of 239 ;
its atomic number is 92. We have already mentioned that barium is one of
the products of uranium fission and that lanthanum is another ; if we assume
that the fission fragments sometimes consist of these nuclei and that the
atomic numbers of the fission fragments add up to 92, barium must be
accompanied by krypton and lanthanum by bromine. But if we determine
the total mass of the heaviest known stable isotopes of these pairs of elements,
we find that it is 224 in the case of Ba and Kr and 220 in the other case. This
leaves, respectively, 15 or 19 mass units for which we have yet to account.
An earlier chapter of this book may prompt the supposition that some of the
mass has been converted into energy ; this is quite true, but as the amount
so converted is considerably less than one mass unit, this process has little
bearing on the question of the disposal of the total mass of the uranium
atom.

It must be remembered, however, that the fission fragments are radio-
active to such an extent that they suffer several successive p ray transforma-
tions before they become stable atoms ; this p radioactivity is only possible
because the primary fission nuclei are much heavier than stable atoms of the
same element. Considered in numerical detail, we may have overestimated
somewhat the mass number by which the masses of the primary fission nuclei
exceed those of stable nuclei, for it is known that one to three neutrons are
released, in the process of fission, and it is also known that in many cases the
original unstable uranium nucleus is formed from U a3S and so is lighter than
we have assumed by three mass units. But even when allowance is made for
these possibilities, we find that some of the fission fragments have abnormally

86

NUCLEAR FISSION

Chap . VC

high masses, much higher than those of the artificial radioactive substances
which have been produced by means other than nuclear fission.

It is desirable to determine the atomic numbers and mass numbers of the
primary fission fragments, and although this problem presents some diffi-
culties because of the short lives of some of the radioactive substances invol-
ved, it can certainly be solved. For, if a chain of (3 ray transformations is
followed through, the original fission fragment will eventually become an
artificial radioactive nucleus the mass and properties of which are known
from other experiments ; in such a case the two substances will be chemically
identical and will also have the same radioactive transformation constants.
From the mass number of this substance and the details of the chain of (3
ray transformations, the mass number and atomic number of the primary
fission fragment can be determined. For example it is known that one form
of the substance which was once thought to be radium and was later found to
be barium has a half life which is the same as that of radioactive barium,
Ba 139 , prepared by neutron bombardment of the natural barium isotope
Ba 138 ! This particular example serves to show that eventually the identity
of the fission products will be established. Nevertheless, if Ba 189 is a primary
fission nucleus, it is much lighter than would be anticipated in view of the
facts stated above.

Little general information is available concerning the identity of the fission
products and the proportions in which they are produced. Experiment-
have shown that bromine, krypton, rubidium, strontium, yttrium, molyb,
denum, antimony, tellurium, iodine, xenon, caesium, barium and lanthanums
as well as other elements,* are produced after uranium has been subjected to
neutron bombardment. These substances have been detected because they
are formed with radioactive properties ; in addition there must be non-
radioactive elements formed, but these are much more likely to arise from the
radioactive decay of other fission products than as primary fission nuclei.

It is of interest to consider briefly the results of experiments in which
measurements have been made of the ionization produced by the fission
fragments, and from which the energies of these fragments have been deter-
mined. Fig. 27 shows some of the results. It will be seen that the most
frequent energies of emission are 40 MeV and 85 MeV and that energies
differing from these occur frequently. After examining such data it seems
reasonable to suppose that fissions result in the production, on one occasion
or another, of pairs of most of the elements mentioned above. The process
of fission appears to take place in a great variety of ways, and on any one

* The Smyth report states (7.35) that the fission products of uranium include
thirty elements.

87

ATOMIC ENERGY

Chap. IX

3

Z Kinetic Energy of Fragment’

Fig. 27. Distribution of kinetic energy of
fission fragments.

occasion the identity of the two immediate fission products seems to be
determined by chance.

The nature of the fission products is, however, closely related to the energy
balance in the fission process. If we consider the phenomenon as a process
which transforms the original unstable uranium atom into a number of
lighter stable atoms, we see that the energy released in the fission process is
to be calculated from the difference between the mass of the uranium atom
plus a neutron, and that of the ultimate fission products, i.e., the sum of the
masses of the stable atoms which are finally formed from the fission products
by radioactive decay. If we assume that a uranium atom of mass 238
absorbs a neutron and then splits into two masses of 140 and 99, we find that
the heavier mass is stable when its atomic number is raised by (3 emission to
the value of 58 ; the lighter mass becomes stable when its atomic number is 44.
If this happens, the ultimate fission products are then cerium and ruthenium
nuclei which have atomic masses of 139.958 and 98.942. If we take the mass
ofU m as 239.134 we see that there is a disappearance of a total mass of 0.234
mass unit, to which corresponds an energy of 21 8 MeV. The greater part

88

NUCLEAR FISSION

Chap, IX

of this energy appears as the kinetic energy of the fission fragments ; the
rest of it is released in the ten (J ray transformations which convert the imme-
diate fission fragments into stable cerium and ruthenium nuclei. We could
calculate the kinetic energy of the fission fragments directly, if we knew their
precise masses. But as the isotopes involved are unusual, and as their lives
are so short, it has not yet been possible to obtain this information experi-
mentally, and the best that can be done is to employ masses which are derived
by using theories of nuclear structure and the most accurate information
available concerning the masses of stable elements.

From such calculations we can obtain an estimate of the energy emitted
in the p ray disintegrations which convert the primary fission fragments into
stable end-products. The magnitude of this energy depends on the nature of
the primary fission fragments, and in a number of cases it will amount to
about 40 MeV; in others it departs somewhat from this value. If this figure
is appropriate to the case of the fission fragments discussed above — and it
should be remembered that the fragments chosen do not necessarily represent
a possible fission process— their total kinetic energy will be close to 180 MeV .

We might prefer to calculate the kinetic energy of the fission fragments in
terms of the electrical forces of repulsion during their release ; this approach
to the problem has great advantages over the use of the mass energy equation,
but it does not yield a reliable result. For to use it, we require to know the
nuclear charges of the fission fragments, and their distance apart and kinetic
energy at the moment when they are sufficiently separated to make negligible
the attractive forces that earlier held the nucleus together. This is not yet
possible, and despite the attractions of calculating the kinetic energy in terms
of the forces which give rise to it, the results of such a calculation are too
approximate to be of significance.

It is established that the two fission fragments are unequal in mass ; one
fragment lies usually in a mass range near 140 while the other fragment lies
in a mass range in the neighbourhood of 100. It is believed that momentum
is conserved in the process of fission ; in consequence the lighter fragment
carries the larger portion of the energy. For fragments of masses 99 and 140,
and a total kinetic energy release of 180 MeV, the lighter particle has an
energy of about 105 MeV and the heavier one carries the balance of 75 MeV .
These figures are given by way of example only ; they depend on so many
assumptions and approximations that they can only serve as a rough guide.
Nevertheless, the information afforded by Fig. 27 is in general accord with
the statements just made. In that figure we see that there is a low energy
group of particles with a maximum energy of about 70 MeV and a high

89

ATOMIC ENERGY

Chap, IX

energy group with energies up to 100 MeV*; the sum- of these two maxima
is reasonably close to our estimate of 180 MeV. The figure shows, however,
that not every pair of fission fragments carries this maximum amount of
energy ; nor is this surprising. For we know that a few neutrons are pro-
duced when a fission takes place ; furthermore, the primary fission fragments
may be formed in an excited state, in which case they carry energy which
might have appeared as kinetic energy of the fission fragments, but which
in fact is emitted as y rays immediately following fission and before the first
p transformation. When proper account is taken of these possibilities, we
will obtain for the mean kinetic energy of the fission fragments a value
considerably less than that derived from calculations such as have been
described above. Nevertheless, experiment, in confirmation of approximate
calculations, shows without doubt that the fission fragments are emitted with
far more kinetic energy than is carried by the particles released in any other
known nuclear reaction.

(3) The theory of the fission process .

Before we discuss further the available experimental data concerning fission,
it is desirable to consider some theoretical aspects of the problem. Our
theories of nuclear reactions are very much influenced by the work of the
Danish physicist Niels Bohr, and in the particular case of fission itself by the
work of Bohr and Wheeler, 2 published in 1939. In the course of what
follows, an outline will be given of Bohr’s theories, and of their application to
nuclear fission as explained in the papers by Bohr and Wheeler.

Let us turn for a few moments to a discussion of present-day views of
nuclear structure. It is believed that an atomic nucleus is composed of
neutrons and protons. If we consider, for example, U 8 ™, we see that this
nucleus must consist of 92 protons and 147 neutrons. The protons are of
course positively charged and the consequent electrostatic forces must bring
about intense mutual repulsion between the protons in such a nucleus. Since
many nuclei are found to be stable, we must postulate other forces which
hold the nucleus together, forces which arise from attractions between neutrons
and from attractions between neutrons and protons. It is difficult to ap-
preciate the nature of these forces, but as the protons themselves repel one
another powerfully, it is clear that the neutron-neutron and neutron-proton
forces must also be intense when the interacting particles are as close as they
are in a nucleus ; furthermore, the range of these forces must be short, for
otherwise an a particle would not be able to escape from a radioactive

♦ Fig. 27 is derived from data given by Booth, Dunning and Slack 3 . It is
probable that the energy scale attached to Fig. 27 underestimates the energy of the
tission fragments.

90

NUCLEAR FISSION

Chap. IX

nucleus. It is thought that there are also short range proton-proton attrac-
tive forces, but although these may help to hold the nucleus together, they
must be smaller than the electrostatic repulsive forces between protons. It
should be mentioned here that p particle emission is to be regarded as
involving the conversion of a neutron into a proton and an electron ; the
electron is ejected from the nucleus and the proton remains within, where it
contributes an additional unit to the atomic number of the nucleus.

Although we occasionally talk about individual particles in a nucleus, it is
sometimes better to think of the nucleus as a single entity and to consider the
energy of the nucleus as a whole rather than the energy of the individual
particles of which it is composed.

The view which is at present held — a view that has led to fruitful predictions
concerning the behaviour of the nucleus — is that the nucleus may be likened to
an electrically charged drop of liquid. Here there is a force of surface tension
which holds the drop together ; the molecules of the liquid have a perfectly
definite mean energy, but individually they move about in a random fashion
with velocities which differ widely. The mean energy of motion of the
molecules depends on the temperature of the drop, and fcr those molecules
with energies near this mean value, escape is effectively prevented by the
surface tension forces. On the other hand, a particularly fast molecule may
have sufficient speed to pass through the force system that gives rise to the
effects of surface tension, and if its motion is suitably directed it will escape.
In any drop of liquid there will always be a few of these fast molecules —
they gain their high energy quite by accident as a result of favourable collisions
with other molecules — and in consequence, in the case of a volatile liquid,
there will always be molecules escaping through the surface of the drop.

It must not be imagined that the nucleus is to be regarded as behaving in
exactly the same way as does a drop of liquid— there are too few particles in
a nucleus to make it possible to carry the analogy very far — but there is
sufficient similarity to enable us to use the analogy to obtain an understanding
of the process of heavy particle emission by a nucleus. As we shall see, the
analogy also gives a useful picture of the mechanism of fission.

Let us consider the process of neutron emission. First of all we require to
know the binding energy of the neutron. This is the amount of excess energy
possessed by a nucleus which has just captured a very slow neutron, or,
looking at it from the viewpoint of the mass energy equation, the energy
equivalent of : mass of neutron -f mass of original nucleus — mass of nucleus
formed by neutron capture. If this amount of energy is supplied to a
nucleus, the emission of a neutron is energetically possible but it does not
follow that a neutron will escape, for the energy tends to be shared out amongst

91

ATOMIC ENERGY Chap. IX

all the particles in the nucleus ; neutron emission will occur only if one
neutron obtains sufficient of the total energy of the nucleus to enable it to
overcome the attractive forces of the rest of the nucleus and escape from the
region in which they act. The analogy between this process and the escape
of a molecule from a liquid drop is close indeed, for just as with the neutron,
scape of a molecule can occur only if a sufficient amount of kinetic energy
is commmucated to one individual molecule. When we give a little extra
o a drop,we increase the total energy of the molecules of which one or
wo may thereby be enabled to escape. But if the molecules do not carry off
the extra energy by escaping from the drop, this energy will be lost, perhaps
y radiation. Somewhat similar alternatives are available in the case of a
nucleus to which has been communicated an energy in excess of the neutron
. I*™? » ^ a neutron does not obtain sufficient of the nuclear energy

ena e it to escape, the excess energy of the nucleus will be emitted as y
ys. the case of the nucleus the excess energy is quickly disposed of, for
tbe y ray emission occurs within about lfru sec. of the moment at which the
excess energy is supplied, unless of course the neutron is emitted previously.

. , n we colder the liquid drop analogy of the fission process, we need to
r . electrical charge which the drop must be supposed to

carry. is well known that an electrically charged soap bubble tends to
mutual e ^ ectr ical repulsions, and in the case of a charged
. . P , ® glVes a *" orce ™ opposition to the surface tension forces

^°P together. It we gradually increase the amount of the
rT’ 'T smularI y increase the disruptive forces, and a time will

dr , op 1S ^stable and flies apart of its own accord. Even with
Hrnn^t tlus ~ a char ge that is not large enough to make the

aay “ certail circumstances be able to break up.
attain^n^ u S?* 0 ?** 1 , smtabl y and sufficiently, a configuration may be
ttceleancal disruptive forces are more than sufficient to

tn«««>u>r Th °J CCS °u su !i face tensicm , which are now unable to hold the drop
dr °F brealc . s “ t0 two Portions with, in addition, a few small
£ie P rf f T° m , L portions of liquid at one time near the

stable anrl that — e < * ro **' ^ *>e noted that the drop was initially

occurred 88 a resu lt of a finite amount of distortion.
ene^^ 7 „fS ® nerg ^ must be communicated to the drop, the amount of
sS^Snn HT** 0n rclative uuagnitudes of the electrical and
SSfflSSft “ u *** of ® ven si2e and surface tension, the
5L charge, the smaUer will be the energy needed to produce

the distortion that results in the break up of the drop.

Bohr views nuclear fission as being similar to the process just described.

92

NUCLEAR FISSION

Chap . IX

The equivalent of the surface tension force is the neutron-proton and neutron-
neutron attractive forces ; the charge of the protons in the nucleus is respon-
sible for the disruptive electrical force. According to the theories of Bohr and
Wheeler, nuclei with charges much greater than 92 are likely to be unstable
and so incapable of existence. If Z denotes the nuclear charge and A the
mass number of a nucleus, it has been estimated that this nucleus cannot be

Z a

stable if— is more than some 30% greater than the value appropriate to U 238 ,

A

(92) 3

that is, . From this calculation, it appears that the heavier elements

23o

are near the condition of instability, and it is to be anticipated that relatively
small distortions may be sufficient to cause them to disrupt. The argument
suggesting that fission occurs as a result of a sufficient distortion is similar
to that given for the case of the liquid drop. Here the distortion causes a
considerable decrease in the neutron-neutron and neutron-proton binding
forces and a much smaller one in the electrical forces of repulsion. From a
small distortion the nucleus may recover ; from a larger one it may recover
or it may split in two ; from a still larger distortion of a suitable kind the
nucleus will in no case maintain its existence. It is to be noticed that fission
will not occur unless the nucleus is first supplied with sufficient excess energy
to bring about the necessary distortion, and even if this amount of energy is
provided the distortion occurring may not be such as to give fission, and the
excess energy of the nucleus may be radiated. If we again describe a nucleus
with excess energy as an excited nucleus, we may say that fission can occur
only if the nucleus possesses sufficient energy of excitation ; as, however, the
nucleus is in any case liable to lose its excess energy by radiation or neutron
emission within 10“ ia sec. of acquiring it, if fission does not occur within a
very short time after the excitation of the nucleus, it will not occur at all-
in Fig. 28 is given a sketch of the stages which are believed to occur in the
process of nuclear fission.

Which nuclei are likely to undergo fission upon neutron bombardment ?
We will suppose that the element being bombarded captures a neutron;
as a result it will have an amount of excess energy equal to the neutron binding
energy plus the kinetic energy of the neutron, for, as explained above, the
neutron binding energy is the energy of excitation of the nucleus when a
slow neutron is captured by it. Now there will be negligible probability of
fission unless the excitation energy of the nucleus is as great as that required
to distort the nucleus to the extent necessary to permit fission. This latter

Z 3

energy, which is denoted by E f , is found to depend on — ; in Bohr and

93

Atomic energy

Chap. IX

CO

(a) A neutron about
to enter U 835 nucleus.

o—

\

(b) Uranium nuc-
leus after neutron
capture. The excess
energy (excitation
energy) of the nuc-
leus causes distor-
tion which leads to
fission.

(c) After fission : Two fission
fragments move in opposite direc-
tions. In this case there are
three fission neutrons.

Fig. 28. Three stages in the nuclear fission process.

Wheeler’s paper are given values of E, and of neutron binding energies for
a number of heavy nuclei. If the neutron binding energy exceeds E f , any
captured neutron at all will be able to cause fission, and on occasion it will
do so. But if E f exceeds the neutron binding energy, fission can be brought
about only by neutrons having a kinetic energy greater than the amount by
which the neutron binding energy falls short of E f . In Table 1 are given
Bohr and Wheeler’s values of Ef and of neutron binding energies for nuclei
formed from various heavy elements by neutron capture. The table also

Z a

lists values of — - for the five nuclei listed in the second column.

Table 1.

Original nucleus

Nucleus after
neutron capture

Neutron binding
energy in MeV

E,

MeV

z s

A

Thorium

TIC

mi ::iit

Th 0«

5.2

7.0

34.8

Uranium I

U”“

u M *

03

5.2

5.9

35.4

Proto-

actinium

Pa 831

x in

Pa 2;,s

4 ** 01

5.4

5.5

35.7

Actino-

uranium

-r t23B

^ u a

u 2i,fl

W 03

6.4

5.4

35.8

Uranium II

u 2 * 4

v 03

u aao

v OS

5.4

5.2

36.0

94

NUCLEAR FISSION

Chap . IX

If these figures are correct, in the case of uranium II and actino-uranium
aiiy neutron captured, slow or fast, is capable of giving the necessary distor-
tion which preceeds fission. To bring about fission of protoactinium, the
bombarding neutrons must have an energy of at least 0.1 MeV; energies of
0.75 MeV or more are necessary in the case of uranium I, and in the case
of thorium neutrons of still higher energy are required.

By way of concluding our examination of this part of Bohr and Wheeler’s
paper, it is desirable to discuss briefly the likelihood of fission of a heavy
nucleus that has captured a neutron. We do this by considering an excited
nucleus and the way in which it disposes of its energy of excitation. Subse-
quently, in order to determine the consequences of neutron capture, we
consider the various important possibilities for a nucleus which has excitation
energy in the appropriate range. In the discussion that follows we shall
assume that the nucleus disposes of surplus energy by one or other of the
processes : emission of radiation, emission of a neutron, and fission.

Let us first assume that E x , the excitation energy which must be available if
fission is to occur, is large compared with E*, the neutron binding energy.
We now assume that the nucleus possesses a definite excess energy without
specifying the means by which it acquired it. Then for excitation energies
lower than E n , emission of radiation occurs in every case ; there is no other
way in which the nucleus can dispose of its excess energy. But once E n is
exceeded, alternative processes are possible. With energies of excitation only
a little greater than En, relatively few excited nuclei will emit radiation;
for although this process can still occur, it requires a longer time than does
neutron emission, which is so much quicker that it is almost the rule. The
fraction of excited nuclei radiating energy, and its dependence upon their
excitation energy, is shown in Fig. 29a.

For excitations higher than E r , fission also becomes possible. At these
high excitation energies, however, neutron emission occurs so rapidly that
there are relatively few cases in which fission actually occurs, rapid though
this process is. The fractions of the total number of excited nuclei disposing
of their energy by neutron emission and by fission are shown in Fig. 29b and c.
These sketches show that for excitations greater than E f , fission and neutron
emission are competing processes, and that fission is the less likely of the two.

We now consider the more important case in which E f is less than E n .
The dependence of radiative emission, neutron emission, and fission on
excitation energy are shown in Fig. 30a, b and c respectively. In this case,
also, fission occurs as soon as the excitation energy exceeds E f , and from here,
up to an excitation energy E n , fission increases in importance at the expense of
radiative emission. At excitations above E m fission and neutron emission

95

ATOMIC ENERGY

Chap . IX

Ef En

t3 Nuclear excitation Energy

2

u.

Fig. 29. The behaviour of a nucleus Fig. 30. The behaviour of a nucleus
possessing excitation energy. possessing excitation energy.

(Ef exceeds En.) (E n exceeds Ff.)

become the only important processes, and once again neutron emission is
the more likely. On this occasion, a reasonable fraction of highly excited
nuclei give rise to fission, in contrast to a much smaller fraction in the case
first discussed in which Ej was greater than En.

When the nuclear excitation results from neutron capture, it will exceed
En. If Ef is greater than E*, fission can result only for neutrons with kinetic
energies greater than Ef— En, and, as we have seen, even then fission occurs
much less frequently than does the emission of neutrons. On the other hand.

96

NUCLEAR FISSION

Chap. IX

if E n is greater than E x , the capture of a slow neutron will give sufficient
excitation to make fission possible. For these neutrons, which give an
excitation energy En, and for faster neutrons, fission is reasonably likely.

This discussion shows that fission is most readily achieved with substances
for which E f is less than the neutron binding energy, and from what has been
said, and from the data given in Table 1 we see that U 234 and U 235 are most
likely to exhibit fission on neutron bombardment. For both these elements,
but especially for U 236 , fission will take place on bombardment by slow
neutrons.

It now remains to consider some of the other topics treated by Bohr and
Wheeler. In discussing the total energy released in a fission process, they
point out that nuclei of mass number greater than 110 will yield energy if
they can be made to break into three nearly equal parts ; in the case of ura-
nium, calculation showed that the available energy in this hypothetical
process is actually greater than that released when the nucleus breaks into
two parts as in fission. Such calculations serve to remind us that a process
which theoretically will yield energy may or may not occur in practice.
Certainly fission is a process which releases energy and this is one reason for
its occurrence, but the most important factor is the possibility of producing
sufficient nuclear distortion to initiate the process that releases this energy.

The theories of energy release in fission show that the fission fragments
acquire the maximum total kinetic energy when the two fragments are of
nearly equal mass. They also show that for a given mass of one fragment
there is only a small range of nuclear charge numbers (atomic numbers)
which gives a release of kinetic energy at ail near this maximum value ;
outside this range of charge numbers, more of the energy of fission appears
as internal energy of the fission fragments— to be released subsequently in
radioactive (3 ray transformations — and less as kinetic energy. As has been
mentioned already, it appears that the fission process occurs in a wide variety
of ways, and that fission into two fragments with the same energy — in which
case they must also have the same mass — is unlikely, if indeed it ever happens.

Bohr and Wheeler have made estimates of the energies released in the (3 ray
emissions that transform the fission fragments into stable nuclei. The
results obtained give us the masses of the radioactive fission nuclei, and of
the substances produced from them by successive (3 ray transformations —
nuclei with mass numbers higher than the values appropriate to stable nuclei
carrying the same charge. In general, the energy released in successive (3 ray
transformations is believed to decrease uniformly as the nucleus nears its
final stable atomic state, but in detail only nuclei of odd mass number have [3
ray emission energies varying in this way. In the case of nuclei of even

G 97

ATOMIC ENERGY

Chap. XI

mass number, the energy of p ray emission is correctly given only after the
addition of a further quantity, the value of which depends on whether the
initial nucleus has an odd or even atomic number. The figures obtained
show that these p ray transformations release energies of up to 15 MeV and
that, although the average p ray emission energy is in the neighbourhood of
4 MeV, cases are not uncommon in which the energy of the p ray transfor-
mation considerably exceeds this value.

In the light of these theories, we have next to consider further some of the
available experimental data concerning nuclear fission. In particular, our
interest must be directed to the experimental values of the cross sections for
the various phenomena occurring when uranium is bombarded by neutrons.
Furthermore, we must examine, in some detail, the origin and properties of
the neutrons produced during and after uranium fission. These two matters,
both of the utmost importance from the point of view of the development of
atomic energy, are dealt with in the next chapter.

REFERENCES

1 Turner, L.A.,Rev. Mod. Phys., 12 , 1, 1940. This paper gives an account of the
discovery of nuclear fission and contains references covering the work on it up to
the beginning of 1940.

2 Bohr and Wheeler, Phys. Rev., 56 , 426 and 1065, 1939.

3 Booth, Dunning and Slack, Phys. Rev., 55 , 981, 1939.

98

CHAPTER X

RELEASE OF ATOMIC ENERGY: CHAIN REACTIONS

(1) The nature of a chain reaction .

The contents of the previous chapter are sufficient to stress the novelty of
the fission process. This new mode of atomic disintegration was of scientific
importance because it gave fresh information concerning the properties of the
nucleus and in addition provided many elements — the fission products— in
unusual radioactive forms ; furthermore, it was of great significance because
it provided a process which it was believed might permit use of nuclear
energy. The individual fission process was produced by a neutron ; the act
of fission yielded large amounts of energy and more neutrons, and in suitable
circumstances, some of these latter neutrons could bring about further
fissions. The available knowledge of fission suggested the possibility of a
“ chain reaction ” in which a single neutron would cause the nuclear fission
of a uranium atom, as a result of which a chain of fissions might be produced
throughout the mass of uranium.

Before we discuss such a reaction — it is called, as stated above, a chain
reaction— we should introduce a new term. This is k, the reproduction factor.
It represents the average number of neutrons which arise from one fission and
which themselves produce fission. If a million fissions produce two million
neutrons of which 999 000 produce further fissions, k is 0.999. If, on the
other hand, a million fissions give a million and a half neutrons of which
1 001 000 produce further fissions, the reproduction factor is 1.001.

To form a clear but simple picture of the chain reaction, we may assume a
reproduction factor of 2 so that each fission gives rise to two neutrons that
cause further fission. From these two fissions will arise four, and from these
eight ; at the tenth stage of the chain — it is sometimes useful to call this the
tenth generation — there are more than one thousand fissions produced and at
the twentieth more than a million.* This picture is too simple ; not only is
it improbable that our chain grows at the rate assumed, doubling itself at
every stage, but it is unlikely that every fission — or even every hundred
fissionsr— produces the same number of neutrons, or indeed that a given
number of neutrons produces a constant number of fissions. Nevertheless, if
it is arranged that, on the average, one fission is followed by just more than
one subsequent fission, we will have a chain reaction which is capable of

* The actual numbers are 2 10 and 2 80 respectively.

99

ATOMIC ENERGY

Chap. X

building up and of maintaining itself. Even if every hundred fissions is
followed, on the average, by only 101 fissions, corresponding to a reproduction
factor of 1.01, the chain will build up; after one thousand neutron
generations, the rate of fission will have increased in amount by a factor in
excess of 20,000. Such a chain reaction will build up in this way until other
factors, which we have not yet considered, come into play and diminish the
rate at which the reaction increases in intensity.

In the case of uranium it was believed that no more could be achieved than
a reproduction factor slightly greater than unity ; but as fission was believed
to occur almost instantaneously it was thought that the reproduction time
would be small and that a chain reaction might grow with tremendous
rapidity. Quite clearly, if this was achieved, enormous quantities of heat
energy would be produced, for if the fission of a single uranium atom yields
200 MeV, the fission of about 1 lb. of these atoms will yield 10 7 kWh, or over
two million times as much heat energy as is produced by burning 1 lb. of coal.
Considerations of this type prompt two questions. Will the process work, and
if it will, can it be controlled, or will the heat be yielded in such a way that
the reacting uranium and the apparatus associated with it are dissipated by
an explosion of unparalleled magnitude ? These questions were being
asked early in 1939 after the discovery of nuclear fission. Too little was then
known of the details of the process to enable an answer to be given. Further
experiments were needed to investigate the details of the reaction occurring
when a neutron brought about the fission of a uranium atom. Let us see
what conclusions were drawn from the experiments made.

(2) Substances capable of giving a chain reaction.

The substance of greatest interest is uranium, but as Bohr’s theories deal also
with thorium and protoactinium, it is desirable to mention first what is known
of their behaviour when they are subjected to neutron bombardment.

The case of thorium is simple ; the single natural isotope, Th 232 , exhibits
fission only when it is bombarded by high energy neutrons possessing energies
greater than 1.7 MeV. As the fission cross section is not very large, a fast
neutron which enters a mass of thorium is more likely to be slowed down
than to cause thorium fission, and for this reason a chain reaction is unlikely
to occur. According to published information, the organization for deve-
loping the atomic bomb gave little attention to the possibilities of making use
of thorium, despite the fact that this element is more plentiful in nature than
is uranium. In view of the way in which the atomic bomb organization
appeared to try every method that could conceivably work, it is to be inferred
that at the present state of knowledge it is not possible to produce a fission
chain reaction using thorium.

100

Chap, X RELEASE OF ATOMIC ENERGY

The case of protoactinium is somewhat different. According to Bohr’s
theories, this nucleus should exhibit fission on bombardment by neutrons
with energies in excess of 0.1 MeV. Experimentally it is found, according to
the Smyth report, 1 that this material gives fission only when bombarded by
fast neutrons of unspecified energy. On account of the relative scarcity of
protoactinium, it was not considered as a source of atomic energy, but even
if it had been available in quantity, its failure to react favourably to bombard-
ment by slow neutrons would have made its use relatively unattractive com-
pared with that of uranium.

Let us then consider the reactions of uranium when bombarded by neu-
trons. It should be remembered that there are three long-lived uranium
isotopes, U 238 , U 236 and U 234 , and that natural uranium consists of a mixture
of these three ; the commonest isotope is the heaviest which is 139 times as
plentiful as U 236 and about 16 000 times as plentiful as U 234 . In any reaction
involving natural uranium, we can usually neglect the effects of U 234 but we
must bear in mind that the amounts of U 235 , though small, are often sufficient
to make their presence felt.

Early experiments showed that uranium gives fission when bombarded by
either fast or slow neutrons. When fast neutrons are employed, fission
occurs, in the main, from U 238 , which forms U 23B on neutron capture. For
2.5 MeV neutrons, the cross section for this process 2 has been measured and
is about 5 x 10~ 25 cm. 2 , a figure that shows that these neutrons will have a
mean path length before causing fission of about 0.5 metre. In view of
this small fission cross section, and the fact that it falls in value with the
energy of the neutrons, it is necessary to consider alternative processes in
which fast neutrons may be involved, for if these processes have appreciable
probability, they may prevent the occurrence of any substantial numbers of
fissions. In fact this is what happens. For although a neutron loses only a
small fraction of its energy as a result of an elastic collision with a uranium
nucleus, such collisions will occur frequently and will result in the slowing
down of fast neutrons. Furthermore, every capture of a fast neutron does
not result in fission, especially in the case of neuiron capture by U 238 . In Ihe
majority of cases, neutron capture by such a nucleus is followed by the emission
of a neutron, usually with less energy than the one which was captured. When
account is taken of these interactions between a mass of uranium and fast
neutrons, it will be seen that few of these neutrons are likely to cause uranium
fission. From the point of view of causing a chain reaction with fast neutrons
in U 238 , there are negligible prospects unless it happens that each uranium
fission results in the production of many neutrons, each with sufficient
energy to cause further fissions of U 238 . And this does not occur.

101

ATOMIC ENERGY

Chap.X

Now that we have considered the consequences of bombarding uranium
with fast neutrons, let us consider the results when slower neutrons are used.
For neutrons with energies below about 0.6 MeV there are very few fissions
and almost all of these arise from neutron capture by U 285 nuclei. For quite
slow neutrons, however— those with energies close to 25 eV— theie is very
strong absorption by U 288 nuclei. The process is a resonance radiative capture
with a capture cross section 8 of 10 -21 cm. 2 corresponding to a mean path
before capture of only 0.2 mm.; the resulting nucleus is U 239 , a substance
which emits p rays and has a half life of 23 minutes. The capture process
which gives rise to U 289 has turned out to be of the greatest importance in the
development of the atomic bomb ; it arises at present because it absorbs
neutrons that would otherwise be reduced to thermal energies. Now neu-
trons of thermal energies have two possibilities ; either they are captured by
U 288 nuclei to form U 289 or they give rise to fission of U 285 nuclei. Despite
the fact that in natural uranium there is only one U 288 atom in every 140
uranium atoms, two U 288 fissions occur for every thermal neutron captured
by U 888 .

If then we bombard natural uranium with fast neutrons, there will be a
few fissions caused by fast neutrons which are not involved in other inter-
actions ; most neutrons will be slowed down and their fate must be considered
in the light of possible interactions between uranium nuclei and slower
neutrons. As the slowing down process occurs gradually as a result of
collisions with uranium nuclei, most neutrons will eventually be reduced in
energy to values sufficiently close to that of the resonance absorption level
of U 288 to be captured and to form U 239 . Those few neutrons which avoid
capture by U 288 cause fission of U 285 .

Although the numerical data are incomplete, it is apparent that in order to
achieve a single fission from natural uranium, some few fast neutrons must
fall upon it ; unless this fission results in the production of thermal neutrons
or of an appreciable number of fast neutrons, a chain reaction will not be
possible. The main difficulty in the way of achieving a chain reaction is the
presence of U 288 with its strong lesonance absorption level in the neighbour-
hood of 25 eV. Because of this interaction between slow neutrons and the
commonest uranium isotope, many neutrons are captured by it and not
enough are left to maintain a chain reaction depending principally on fission
of U 288 .

(3) Fission neutrons .

The last section has described the main properties of natural uranium relative
to its interactions with neutrons. Before we discuss other matters which

102

Chap. X

RELEASE OF ATOMIC ENERGY

determine the possibility of achieving a chain reaction, it is desirable to con-
sider the vague information available concerning the neutrons emitted in the
fission process. Accounts have been given of attempts to determine the
average number of neutrons emitted per fission ; it is not difficult to make
approximate measurements of this quantity, but accuracy is hard to achieve.
Some published measurements suggest that there are more than two neutrons
per fission but it is not possible to be definite upon this point. The Smyth
report 4 gives the number as being from 1 to 3, and does not appear to discuss
further a quantity which is of the utmost importance in any detailed considera-
tion of the possibility of achieving a chain reaction and of releasing atomic
energy on any appreciable scale. From the point of view of this book, the
number of neutrons emitted per fission is of general interest only, and we
shall assume, without any belief that the figure is correct, that there are
emitted on the average two neutrons per fission. We next require informa-
tion concerning the energy of these neutrons and the time in the fission process
at which they are released.

In view of the great variety of the fission products, it is not to be anticipated
that the fission neutrons will be released with uniform energy, and it is not
surprising to find that the energy of the neutrons is spread over a considerable
range. To make reliable detailed measurements of neutron energies is not
very difficult as long as neutrons of high energies only are involved ; it is
a much more troublesome experiment for neutrons with energies well below
1 MeV and for this reason the data available appear to be restricted to the
neutrons of high energies. It seems, however, that a few of the neutrons
emitted have energies up to 3 MeV and that from this point down to about 0.5
MeV there is a steady increase in the number of neutrons emitted as the
energy of emission decreases. Looking at this information from the point of
view of the possibility of obtaining a chain reaction with U 338 , it is apparent
that a small but appreciable fraction of the fission neutrons are emitted with
sufficient energy to cause fission of U 238 , but that the majority of the neutrons
have considerably lower energies. Quite apart from the fact that there is a
rather large chance that a fast neutron will not give rise to fission of U 338 , it
appears that a chain reaction depending on this material is not possible
because each fission does not yield one neutron with enough energy to cause
a further fission of U 238 . The prospects with this material are even less
favourable than with natural uranium where, as we found, a chain reaction
was not possible because of the radiative neutron capture by U 238 . The only
other possibility which is immediately obvious is to use U 235 ; as we shall see
later, a chain reaction is indeed possible with this material, but in order to
achieve it U 338 must be separated in some quantity from natural uranium.

The origin of the fission neutrons is a matter of some interest and impor-

103

ATOMIC ENERGY Chap . X

tance, and although there is some uncertainty of detail, it is known that most
of the neutrons are emitted at the instant of fission. If we again compare an
atomic nucleus with an electrified liquid drop, we see that some of the fission
neutrons may be a na logous to the small droplets which are found to be
produced when a drop of liquid divides into two major parts- Alternatively,
the neutrons may arise from the fission fragments themselves, probably
before they have lost much of the kinetic energy arising from their mutual
repulsion. It is to be remembered that a fission fragment of mass 100 and
energy 100 MeV has a velocity of 1.4 x 10 7 metres per second, or about 5%
of the velocity of light, and that even in air its path length is only of the order
of 3 cm. while its time of flight is less than 10' 8 sec. Usually, however, the
fragment loses its energy inside a piece of uranium, and in this case its path
length is of the order of 10“ 6 cm. while its energy will be lost in a time interval
of about 10- 13 sec. We have already seen that neutrons are emitted from an
excited nucleus in an interval of time of this order of magnitude, and it is to
be expected that if the fission fragments do indeed emit neutrons, they will do
so before they have lost much kinetic energy, and that the neutrons will
consequently carry with them their share of the initial kinetic energy of the
fission fragment. Investigations of the energy of emission of the fission
neutrons give support for the view that these are emitted from nuclei moving
at high speed, and this means that these neutrons must arise within a period
of about ,10" 12 sec. or less after the capture of the neutron which caused
fission. Not only is fission itself a rapidly occurring process ; the great
majority of the neutrons resulting from it arise so soon after its initiation that
their emission must be considered as part of the fission process itself. But
not all of the fission neutrons are in this position. Some few of them, little
more than 1% of the whole, are emitted a short time after fission ; they are
known as delayed neutrons.

These delayed neutrons have been studied in detail and it has been found
that after intense neutron bombardment of a mass of uranium, delayed
neutrons can be detected up to a period of 15 minutes after the termination
of the bombardment. The rate of emission of delayed neutrons gradually
becomes smaller throughout this period, and studies of this rate show that it
decreases with time in much the same way as does the activity of an ordinary
radioactive substance. It is found, however, that it is necessary to assume
that the delayed neutrons arise from a number of different kinds of nuclei, for
the observed neutron activity is best explained, as arising from four materials,
each of which has its appropriate rate of transformation, with half lives
ranging from 2.5 sec. to about 1 minute. At first sight one might suppose
that here was a new type of radioactivity in which neutrons were emitted
instead of the more usual oc or (3 particles ; a moment’s consideration of the

104

Chap.X RELEASE OF ATOMIC ENERGY

rapidity of emission of a neutron from an excited atom shows that some
alternative explanation is more probable. It will be remembered that the
primary fission products are radioactive substances of short half life, a fact
that suggests that the delayed neutrons arise from nuclei formed after radio-
active transformation of some of the fission products. On this view, the
relatively slow rate of release of these few neutrons occurs because of the
slow rate of formation of the nuclei from which they come. One doubt may
remain ; where do these product nuclei obtain sufficient surplus energy to
make possible the emission of a neutron ? If the neutron is emitted from
a nucleus formed after the radioactive emission of a p particle, the total
energy released in the radioactive transformation must be sufficient to provide
the (3 particle energy and to leave the product nucleus with an energy ex-
ceeding the neutron binding energy. It is apparent then that neutron emission
will be possible only after p particle transformations in which the maximum
available energy is very large ; furthermore, in every instance in which a
neutron is emitted from a nucleus, the p particle preceeding it must withdraw
only a small portion of this energy. Bohr’s calculations suggest that some of
the radioactive fission products release sufficient energy in p particle trans-
formations to make possible the emission of a neutron.

It may be imagined that these delayed neutrons, comprising only about
1% of those emitted in nuclear fission processes, are so few in number as to
be of no real significance. In some cases this is precisely the position, but
on the other hand, there are cases where the existence of these delayed
neutrons is a factor of great advantage and importance.

(4) Conditions for achieving a chain reaction .

Now that we have discussed the properties of the fission neutrons, we are in a
better position to complete our consideration of the conditions which deter-
mine the possibility of a chain reaction. The remarks already made are
sufficient to show that such a process will not be easy to achieve in practice,
and for this reason we shall discuss a hypothetical case in which we imagine
that there is available a supply of a material which has properties similar to
those of U a3B in that it has a large capture cross section for thermal neutrons
and that on capture of these neutrons fissions take place. It is convenient
to have a name for a material with these properties ; the term fissionable
material is appropriate. We shall suppose that this material is suitably
disposed in a substance— called a moderator — which quickly slows down fast
neutrons so as to ensure that they are captured as thermal neutrons by the
fissionable material. The mixture of this material and the moderator, from
which we hope to obtain atomic energy, we shall call the reacting mass. Let

105

ATOMIC ENERGY

Chap. X

us see how best to arrange these materials so as to encourage a chain reaction.

‘ We shall suppose that the fissionable material has a fission cross section
for thermal neutrons* of 3 x 10' 22 cm. 2 so that such neutrons have a free
path of about 0.7 mm. in the pure material. Because of the presence of the
moderator, any fast neutron produced as a result of a fission will quickly be
slowed down and will then be captured by an atom of the fissionable
material. If, then, a neutron once causes a fission, the resulting neutrons,
which we assume to be two in number, will be slowed down and will sub-
sequently cause the fission of two further atoms. On the basis of this simple
view, the chain reaction will multiply quickly, at a rate depending upon the
average time which elapses between the emission of a fission neutron and
the subsequent fission brought about by this neutron.

The view we have taken is unduly simple, a result of assuming that every
neutron produced brings about a further fission. In any practical system a
neutron may escape from the reacting system by passing through its boun-
dary; it may be absorbed in the moderator or in some impurity in the
reacting mass, or it may cause further fissions. Only the last process is
desired, but the others are inevitable and in some cases they will prevent the
occurrence of a chain reaction.

The likelihood of the escape of a neutron depends on a number of factors,
including the size and shape of the reacting mass and the position in it at
which the neutron originates. It also depends on the average distance a
neutron moves between its places of emission and absorption; for if this
distance is small, only those neutrons formed on the surface of the reacting
mass, or very near to it, will have any reasonable probability of escape.
Other things being equal, then, we should arrange that neutrons are absorbed
as close as possible to the place where they are released; this is best done by
slowing the neutrons to those energies for which the active material has a
very large fission cross section. Fast neutrons from an appreciable volume
of the reacting mass have a large chance of escape, but ones that are slowed
down will almost certainly be captured in the fissionable material and give
rise to fission. When the best arrangements have been made in this respect
— and they will involve some loss of neutrons because of absorption in the
moderator — there will still be other ways in which the loss of neutrons from
the reacting mass can be diminished.

In order to achieve a chain reaction we have to arrange that, on the average,
each fission is followed by a further fission. To determine whether this
happens we suppose that one neutron is produced in each cubic centimetre of

*The value chosen for this cross section is about that appropriate to pure U m
(Compare Bohr and Wheeler®).

106

Chap.X

RELEASE OF ATOMIC ENERGY

the reacting mass ; we then follow the fate of these neutrons in order to see
whether or not they result in an increase in the total number of neutrons. It
is clear that neutrons produced at the centre of the mass will have negligible
chance of escape from the surface ; they either cause fission or are lost because
of capture processes which do not result in fission. But a neutron formed
near the surface of the reacting mass has the same possibilities of fission or of
capture if it goes inwards, and the additional possibility of complete loss if it
goes outwards. Clearly no chain reaction can succeed unless a fission in the
centre of the reacting mass is able to produce enough neutrons to cause a
further fission ; even if this condition is just satisfied, a chain reaction can
only occur if there are no neutrons lost at the surface of the mass, a state of
affairs which can never be achieved. Nevertheless, if we find that in the
centre of the mass a single fission results in enough neutrons to ensure just
more than one fission, we can achieve a chain reaction if we make the reacting
mass of sufficient size, for it is only necessary to arrange that the excess of
neutrons produced in regions where they cannot escape from the mass is
large enough to make up for those that do escape. As has been mentioned
already, the only neutrons that are likely to escape are those formed near the
surface of the reacting mass ; if then we imagine that there is one neutron
produced in every cubic centimetre of the reacting mass, the number of
neutrons which escapes from the mass is proportional to its surface area, and the
total number of neutrons produced is proportional to its volume. Any
increase in dimensions of the reacting mass will increase the volume more
rapidly than the surface area, and so the volume in which excess neutrons are
produced increases by a greater amount than does the volume near the
boundary where the loss is excessive.

This discussion indicates immediately the most favourable shape for the
reacting mass. It should be a sphere, because this is the figure for which the
ratio of volume to surface area is greatest. If a reacting mass is made in
the form of a sphere, a chain reaction will be possible with a smaller amount
of fissionable material than is required to achieve a chain reaction in a mass
of any other shape, and for this reason any practical reacting mass is likely to
be made as nearly spherical as other conditions allow.

Before we leave this subject we should note that there is a device by which
we can reduce the loss of neutrons at the surface of the reacting mass. If it
is completely surrounded by a material which scatters neutrons, it is possible
to return to the reacting mass some neutrons which would otherwise be lost.
This shell of neutron-scatterer is called a reflector ; in some circumstances
carbon has been used for the purpose. It will be appreciated that the re-
flector can return only a fraction of the neutrons which fall upon it ; its

107

ATOMIC ENERGY

Chap. X

purpose is to scatter back into the reacting mass as many neutrons as possible,
and for this reason a reflector should possess a high scattering cross section
and a very s m a ll neutron capture cross section.

(5) Nuclear energy from the sun .

These considerations of size and shape of a chain reactor are illustrated by
the sun, where atomic energy is being produced on a very large scale. The
interior of the sun is believed to be at the very high temperature of 2 x 10 7 °C.,
and at this temperature the average kinetic energy of an atom is about 2,000
eV ; some small fraction of the atoms in the sun will have much greater
energies, and it is the nuclei of these atoms which are able to take part in a
series of nuclear reactions that results in the conversion of hydrogen into
helium, a process which liberates about 30 MeV for every helium atom formed.

If this simple picture is accurate, in every cubic centimetre of the sun
about 10,000 helium atoms are formed every second, and about 10 7 watt of
power is thereby developed ; when we determine the total amount of energy
produced throughout the sun, we find that it is sufficient to supply the enor-
mous quantities of heat that are radiated, and so it is able to maintain the
interior of the sun at a temperature at which these atomic transformations
can take place on a necessary scale. It is interesting to note that if the sun
were only half its present size, there would need to be double the present rate
of production of helium in every cubic centimetre in order to maintain its
surface at the present temperature ; if the surface layers of the sun did not
act as efficient reflectors of heat, it would not be possible for the interior of
the sun to maintain itself at a temperature at which there was any appreciable
liberation of atomic energy.

The size of the sun makes possible types of chain reactions that can hardly
occur on the earth, and it is for this reason that we have to depend on neutrons
in a manner which appears to be unnecessary in a tremendous body of matter
at a high temperature. It is nevertheless true that the same general principles
apply to chain reactions both on earth and in the remainder of the universe ;
in particular, large scale reactors can more readily give chain reactions than
can smaller ones.

REFERENCES

1 Smyth Report, 2.21.

2 Ladenburg et al., Phys. Rev., 56, 168, 1939.

* Meitner et al., Z. Phys. 106, 249, 1937.

4 Smyth Report, 1.57.

5 Bohr and Wheeler, Phys. Rev., 56, 426, 1939.

108

CHAPTER XI

THE REALIZATION OF AN ATOMIC CHAIN REACTION

(1) Administrative arrangements for atomic energy research .

Before we consider some of the practical results which have arisen from the
investigations into the possibility of releasing atomic energy, it is appropriate
to mention the organizations which were set up in Great Britain and in the
United States of America to determine the feasibility of making an atomic
bomb, and to give some account of the problems which were investigated.

In Great Britain research work on nuclear fission and its use in an atomic
bomb was carried out under a special division of the Department of Scientific
and Industrial Research called the Directorate of Tube Alloys.* The super-
vision of this directorate was in the hands of Sir John Anderson and a con-
sultative Council. In addition, under the chairmanship of the Director there
was a technical committee on which served a number of distinguished British
physicists who had great experience in nuclear investigations.

Some details of the British work are mentioned later, and at present it is
only necessary to say that by the beginning of 1942 it was clear that the
limited British resources available gave little prospect of producing an atomic
bomb in this country. Early in 1943, one section of the experimental work,
which till then had been carried out in Cambridge, was transferred to Canada,
and towards the close of that year arrangements were made for the closest
cooperation between the British and American work on the atomic bomb.
About that time, and during the course of 1944, a considerable number of
scientists engaged on Tube Alloys work in this country were moved to the
U.S.A. where it was believed that they could contribute more to the war effort
by helping with some of the problems which were arising in connection with
the realization of the atomic bomb.

Although the U.S.A. did not enter the war until the end of 1941, from 1939
onwards there was an appreciation of the potential value of atomic fission in
the production of a bomb, and early in 1940 arrangements were made for
restricting publication of important papers on this subject. When the
National Defense Research Committee was set up, an earlier government
committee on uranium research was brought under its control, but up to the
time of the American entry into the war, work was carried out on a relatively
small scale. In the meantime, there had been some interchange of infor-

* Tube Alloys work was a code name for Uranium research work.

109

ATOMIC ENERGY

Chap. XI

mation with the British, and towards the end of 1941 American physicists
visited Great Britain in order to obtain first-hand knowledge of what had
been done here. As a result of information obtained in Great Britain and
of independent investigations by American scientists, it was felt that there
was sufficient hope of achieving an atomic bomb to make it desirable to
enlarge the scale of the work in the U.S.A. Plans to do this were announced
to the Uranium Committee of the National Defense Research Committee a
few days before Pearl Harbour. In accordance with these plans the respon-
sibility for atomic energy research was transferred to the Office of Scientific
Research and Development.

During the course of 1942, a special group of the American Army Corps of
Engineers was formed to carry on work on atomic bombs, and in charge of
this group, which was known as the Manhattan District Engineers, was
General L. R. Groves. On 1st May, 1943, the Office of Scientific Research
and Development transferred all parts of the atomic bomb project to the
Manhattan District Engineers who remained in control of the work until
the end of the war.

(2) Requirements of the bomb and of the controlled release of atomic energy.

Viewed in the most general way, the problem was that of determining the
possibility of a chain reaction by the fission of uranium or of any other
material which possessed the necessary properties and which was available
in sufficient quantity. For use in a bomb it was necessary to have a chain
reaction with a reproduction factor considerably greater than unity and to
have circumstances in which a very short time elapsed between the occurrence
of one fission and those resulting from the neutrons thereby released ; in
other words a high reproduction factor and a small reproduction time* were
essential. But if, on the other hand, a chain reaction was to be used to yield
useful energy from nuclear fission processes, it was necessary to devise a
system in which the reproduction factor could be adjusted so as to have an
average value of unity ; furthermore, in this case, it was an advantage to
arrange that the time of a generation was long, for in such circumstances no
serious danger would arise if the reproduction factor rose temporarily above
unity, provided, of course, reasonably prompt action was taken to diminish
it. In view of the considerations outlined above, the research work divided
itself into two general investigations ; one directed towards achieving a
fast-growing chain reaction such as was required in an atomic bomb, and the
other for the realization of a large scale controllable chain reaction from

♦The average time between consecutive fissions in a chain. This time is
occasionally called the time of a generation (of neutrons).

110

ATOMIC CHAIN REACTION

Chap. XI

which energy would be released because of the continuous consumption of
the fissionable material.

Not only did these two lines of investigation have very different objects in
view ; they involved the use of fission on very different scales. For if we can
realize the whole of the energy available, the fission of 1 lb. of uranium-
yielding as much heat as is obtained on burning one thousand tons of coal—
if carried out in a reasonably short interval of time will produce an explosive
effect comparable with that arising from an ordinary bomb containing some
thousands of tons of high explosive. Clearly, if it were found possible to
construct an atomic bomb which used only a few pounds of fissionable
material, and if the whole of the energy of this material were released in an
explosive manner, the destructive effect would be on a very considerable scale.
A few hundred pounds of this atomic explosive would produce enough bombs
to convince an enemy of the futility of prolonging a war. And even if
conditions were less favourable than we assume, a few successful atomic
bombs, exploded so that the enemy was convinced of their effectiveness, were
likely to have so great a psychological effect that the war would be brought
to an end. However the matter was viewed it was clear that if a fast-growing
fission reaction could be achieved, and if something like a ton of the necessary
material could be.produced, the means would be at hand to achieve immediate
victory. Because only relatively small quantities of material were required,
it was quite reasonable to contemplate the use of materials such as U a3S , which
were difficult and extremely costly to prepare.

The requirements of the controlled chain reaction were quite different. If
such a reaction was to be used for large scale production of power, it was
essential that the necessary materials should be available on a corresponding
scale, for even if it proved possible to obtain by fission of one pound of
uranium as much heat energy as is yielded on burning two million pounds of
coal, it was clear that energy produced by such a process would be without
great significance unless it involved the annual consumption, by fission, of one
hundred tons of uranium. Such considerations made it desirable to examine
the possibility of achieving a chain reaction depending on the use of natural
uranium, and experiments to this end were carried out both in Great Britain
and in the United States of America.

(3) Plutonium : Mode of formation and properties.

However, the interest in a controlled chain reaction did not arise solely
because of the energy which it might be expected to release. Curiously
enough, because U 238 captures slow neutrons without fission, the controlled
chain reaction depending upon natural uranium was of the greatest importance

111

ATOMIC ENERGY

Chap. XI

in connection with the achievement of an atomic bomb. The reasons for
this are as follows. When U 288 captures a slow neutron it forms a
radioactive substance which emits P rays and has a half life of 23 minutes.
This material on p ray emission yields a nucleus of atomic number 93. The
element of this atomic number has been named neptunium, and the particular
nucleus formed in this case is Np“ a ®. Now neptunium is a radioactive
substance which emits p rays ; its half period is 2.3 days. After P ray emis-
sion there is formed from it an element of atomic number 94 ; this is plu-
tonium; in fact it is Pu a ”. This isotope is radioactive too, emitting
a particles and giving U 885 ; actually its half life is so long that from the
point of view of present considerations it can be regarded as a stable sub-
stance. Neptunium and plutonium are both of scientific interest because they
are trans-uranic elements, and because they have only recently been dis-
covered, but in view of the short fife of neptunium, it is unimportant compared
with plutonium. The importance of plutonium arose because the theories of
Bohr and Wheeler, 1 when applied to it, suggest that it is likely to be subject
to fission upon bombardment by slow neutrons. It will be remembered that
before fission can occur a certain amount of energy, denoted by E f , must be

Z 8

communicated to a nucleus ; on Bohr’s theory E* depends on and de-
creases as this quantity increases. Here we are interested in the energy
necessary to give fission of the nucleus formed after plutonium has captured

Z*

a neutron, that is of the nucleus Pu 2i0 , for which^ has the value of 36.8. On

comparing this with the other values in Table 1 we see that for Pu 240 , Ef must
be smaller than for any of the nuclei listed there ; it is not unreasonable to
expect that E, will have a value close to 4.5 MeV.* This low value of E, is
exceptionally favourable, but it does not in itself ensure that plutonium will
give fission on bombardment by slow neutrons ; this will not happen unless
the neutron binding energy of Pu 240 is greater than 4.5 MeV. Although all
the neutron binding energies listed in Table 1 are in excess of 4.5 MeV, it is
desirable to consider the matter somewhat further, in case Pu 240 has a small
neutron binding energy. This element is, however, an example of a nucleus
which contains an even number of protons and an even number of neutrons,
as is obvious from its even mass number and atomic number ; such nuclei are
known to have abnormally high neutron binding energies, t as is seen in the

* Turner 2 states that Ef for Pu 240 is about 4.0 MeV.

t This consideration of Bohr’s theory shows that U 233 should give fission upon
bombardment by thermal neutrons when U 234 is formed in an excited state. U 238
can be formed from thorium by reactions similar to those which produce Pu 289
from U 288 . (See Turner 2 and 4 ).

112

ATOMIC CHAIN REACTION

Chap. XI

case of U a8a , the only similar nucleus of those listed in Table 1 . From analogy
with this uranium nucleus, we might anticipate for Pu 240 a neutron binding
energy of about 6.5 MeV and unless this estimate is greatly in error, we may have
confidence in our conclusion that Pu 239 will exhibit fission when it is subjected
to bombardment by slow neutrons. The particularly high value of the neutron
binding energy, and the much lower value of E r , make it appear that when
Pu 239 captures a slow neutron fission is very likely. Furthermore, when this
substance captures a fast neutron, there will of course be the rival possibilities
of fission and of neutron emission ; but in the light of Bohr’s theories of
these alternative processes, one would expect to find that of those Pu 239
nuclei which capture a fast neutron, the majority will give rise to fission ;
whatever the actual magnitudes involved, the fraction of plutonium fissions
resulting from fast neutron capture is likely to be considerably greater than in
the most favourable case already discussed, that of actino-uranium, U 235 .

(4) Chain reaction with natural uranium .

Further discussion of plutonium is reserved for later chapters ; its mention
here is necessary in order to show why so much interest was taken, especially
in America, in the controlled chain reaction. If such a reaction were achieved,
it would yield large amounts of heat energy, and in addition it would slowly
manufacture the new element, plutonium, which would be very convenient to
use in atomic bombs. Nevertheless, the real problem was to achieve a chain
reaction using natural uranium, a problem which we have already seen to be
difficult because of the stiong resonance absorption of neutrons by U 238 .
Essentially, the realization of any chain reaction, even that involved in
lighting a coal fire, involves the same considerations ; if the chain reaction is
difficult to commence, every precaution must be taken to avoid loss of the
essential product of the reaction on which its spread depends. When lighting
a fire, as much heat as possible must be retained for communication to other
parts of the combustible material. When trying to arrange for a uranium
chain reaction, the ideal requirement is to consume neutrons only in the
capture process which gives rise to fission. From this point of view, any
other use of neutrons represents a loss. On the other hand, in the same way
that a coal fire which is only just capable of maintaining itself is of little use
for giving warmth, a hypothetical uranium chain reaction in which no neu-
trons are captured by U 23 8 nuclei will be of no use for the production of
plutonium. Whatever the outcome of plutonium production from uranium,
the first essential is to achieve a chain reaction which will sustain itself ; it
is safe to leave to the future the arrangements which will permit the maximum
production of plutonium as well as the maintenance of the chain reaction.

H 113

ATOMIC ENERGY

Chap . XI

And so the primary requirement was that of arranging to avoid capture of
neutrons by U 288 .

This problem was considered carefully both in Great Britain and in the
U.S.A. and although rather different solutions were proposed, both depended
upon the same mechanism and both were successful. Let us recall the details
of the problem. The fission neutrons are emitted with considerable energy
and some few cause fission of U 288 nuclei ; but most of the neutrons have
small chance of capture until they have lost most of their energy and then of
course there is the greatest likelihood of capture by U 288 nuclei. If this is
avoided there is a considerable chance of neutron capture by LJ S35 and the
occurrence of fission. The chance of loss of neutrons by U 238 capture is
greatest when the neutrons are gradually slowed down within a mass of
uranium; this chance is considerably reduced by slowing the neutrons
quickly in a medium which does not capture them. If it is arranged that
most of the neutrons are ejected into such a medium, and if they stay there
until they are reduced to thermal energies, there will be the best possible
chance of their causing fission of U 285 nuclei. With a view to achieving this
it was proposed that large masses of uranium, either in metallic form or as
the oxide, should be assembled in some regular way so that a considerable
distance separated each mass of uranium from the next ; around this struc-
ture,^ which was known as a lattice of uranium, was a neutron reflector and
within this, in the spaces between the uranium masses, was a suitable modera-
tor to slow down the neutrons. It was believed that such an arrangement
would operate as follows. From a single fission would arise two fast neutrons;
from one of these there might result the fission of a U 288 nucleus, but much
more likely they would leave the mass of uranium in which they were formed
and lose their energy in making collisions with the atoms of the moderator.
Before long the neutrons would attain thermal energies and would make
frequent collisions .with the moderator and move about in random directions.
Eventually it was hoped that the neutrons would enter a mass of uranium and
that one, and not too rarely two, would cause a further fission after being
captured by a U 285 nucleus.

If this arrangement is to succeed a number of requirements must be met.

^uT^ Il ^ maSS .T S shoidd COntain no absorbing impurities and

should be sufficiently small to give a reasonable chance of the escape of a

™ mUch energy ; distances between the uranium

masses should be such that a neutron has little chance of passing from one

Wlth ° Ut slowed down to thermal energies ; tte moderator

Sfv w m qmckly md ^ minimum of loss' by capture.
Finally, and m some ways this is the greatest difficulty, the structure must

114

Chap. XI ATOMIC CHAIN REACTION

be of sufficient magnitude to ensure that only a small fraction of the neutrons
are lost by leaving the structure. It is here that the lattice structure, and
the use of the moderator, have their most serious disadvantages For a
structure of given size, there is relatively little neutron-producing material-
U“*— and much too much surface area from which neutrons can escape, to
achieve the desired chain reaction a large structure containing a great deal of
uranium will be required ; furthermore, it is essential to arrange to keep
avoidable neutron losses at the lowest possible level.

The first big problem is that of obtaining a suitable moderator In order
to slow the neutrons quickly and in the smallest possible path distance, the
moderator must be a light element. Common hydrogen of mass uni ty is the
first choice, for as we have already seen some neutrons lose their total energy
as a result of a single collision with a hydrogen nucleus ; but hydrogen has a
capture cross section for slow neutrons which is too large to make it suitable.
Other light elements are deuterium (heavy hydrogen), helium, lithium, boron,
beryllium and carbon, but as carbon has a mass of 12 it is much less suitable
for slowing down neutrons than is hydrogen or heavy hydrogen with masses
of 1 and 2 respectively. Lithium and boron are both quite unsuitable because
of their large capture cross sections for thermal neutrons,* so that there
remain for consideration deuterium, helium, beryllium and carbon. Of
these, helium can be ruled out at once, for although its ability to slow neutrons
is entirely satisfactory, it is available only in gaseous form and consequently
the average path traversed by a neutron in being slowed down, even in high
pressure helium, is far too large to permit its use. Beryllium was not impos-
sible as a moderator but as no more than 700 lb. of this metal was produced
in the year 1940 in the U.S.A., it was considered that a major problem would
arise if it was necessary to obtain sufficient quantities for use as a moderator
in a controlled chain reaction. There remain, then, only heavy hydrogen
and carbon.

In Great Britain, where this controlled chain reaction was carefully con-
sidered, circumstances favoured studies of the use of heavy water as a modera-
tor. As has been told before, 3 just prior to the invasion of Norway, the
French Government purchased from the Norsk Hydro Company 165 litres
of heavy water. This heavy water, which represented almost the total world
stock, was brought to Britain at the time of the fall of France in 1940. Drs.
Halban and Kowarski, who brought it, had been instructed by Professor
Joliot to attempt to carry out in Britain an experiment which had been
planned in Paris and for which the heavy water had been acquired. Such an
experiment was carried out in Cambridge, and as a result it appeared that it

* Compare Chapter VIII, p. 78

115

ATOMIC ENERGY

Chap . XI

was possible to achieve a chain reaction if uranium oxide was used as the
active material and heavy water was used as a moderator. It appeared
further that if uranium metal was used in place of uranium oxide, the size
of the reacting mass could be considerably decreased and that not more than
a few tons of heavy water would be required for the construction of a workable
system. To achieve this reaction in Britain during the war was hardly
practicable, especially as a great effort would have been required to obtain
adequate quantities of heavy water, which has to be extracted by tedious
processes from ordinary water. For this reason the French physicists were
transferred to Canada to continue there the investigations of chain reactions
using heavy water as a moderator.

(5) Supply of materials for uranium chain reaction with carbon moderator.

In the U.S.A. the possibility of using heavy water as a moderator was also
considered, but in view of the necessity for providing much more heavy water
than was available or could be produced within a short period of time, it was
decided to attempt to make use of graphite. This material was one which
was already in large scale production, but this did not mean that the necessary
supplies were available ; for not only was there a heavy demand for the
available graphite, but the material being produced was of doubtful usefulness
because, when a beam of slow neutrons was passed through it, many of the
neutrons were absorbed. The graphite problem was thus mainly one of
punty, although priorities were also involved ; these difficulties were satis-
factorily overcome, and by the middle of 1942 large orders for graphite had
been placed with the manufacturers.

In the meantime serious difficulties had arisen in connection with the
necessaiy supplies of uranium metal. At the end of 1941 the only pure
mumum meta 1 m America was a few grams made on an experimental basis
S5? Wfmghouse Electric and Manufacturing Company and others ; in
addition there were a few pounds of metal containing much impurity As a

whk*Si n t ?H r 7 oT aS fZ a ^ able a commeric£d ^de of black uranium oxide
Vouch contained 2%— 5% impurity and which was found experimentally to

absorb neutrons too strongly to make possible a chain reaction Again the
EES"" '£*•?? by May 1942 black “■«» 3E of reSSaMy

3 ** 1542

116

ATOMIC CHAIN REACTION

Chap . XI

preparation were developed, and by the end of 1942 deliveries had exceeded
6000 lb. and were rising to more than half a ton a day. The purity of some of
the metal was good, and its cost had fallen to $22 a pound. Although for
some time the metal was rather less pure than was desired, more satisfactory
methods were developed, and by the middle of 1 943 new plants were in opera-
tion and were delivering uranium which satisfied requirements.

(6) Tests of materials for uranium-carbon pile .

In the meantime, of course, the necessary materials were not available to
make possible an experimental test of a chain reaction and in consequence
those who were responsible for the design of a reacting mass to give a con-
trolled chain reaction — such a mass is usually known as a pile— decided to
carry out experiments from which they could predict the reproduction factor
of a pile built from given materials. It is well to recall that a pile will not
give a chain reaction unless the reproduction factor is greater than unity, and
that this failure may arise either because too large a fraction of the neutrons
escapes from the surface of the pile or because the materials or their dis-
position in the pile, or both, are unsuited to the development of a chain
reaction. In the former case, a sufficiently large pile will develop a chain
reaction, but in the latter case an increase in the size of the pile will not cause
it to operate ; for even in the centre of such a pile, from which no neutrons
are lost by emission from the surface, the neutrons from one fission are not, on
the average, able to produce a further one. In this connection it is useful to
distinguish two reproduction factors, one k the reproduction factor for
a pile of given arrangement and of infinitely large size— where a negligible
fraction of the neutrons is lost at the surface — and k, the reproduction
factor for the given pile of finite size. In terms of these quantities, no pile
will operate unless k is at least unity ; if k w is greater than unity, a big
enough pile will have a reproduction factor of unity and will give a chain
reaction. When testing the suitability of materials for use in pile, one must
first determine whether they are capable of giving a reproduction factor
greater than unity for a pile of infinite size, that is one must measure k ^ to
determine whether it exceeds unity ; unless it does, no purpose is served by
building a pile.

During the course of 1942, experiments were designed and carried out to
determine whether it was possible to arrange a lattice of lumps of uranium
oxide in a mass of graphite in such a way that k ^ was greater than unity.
The experiments involved the construction of a small pile in which a proposed
disposition of uranium and graphite was employed ; below the pile was
placed a source of neutrons, and measurements were made of the number of

117

ATOMIC ENERGY

Chap. XI

neutrons inside the pile at different distances from the source; from a
knowledge of the way in which the number of neutrons would be expected to
decrease with increasing distance from the source, and of the influence on this
of the absorption and release of neutrons in the materials of the pile, it was
possible to determine k <*, for given materials and arrangement. The influence
of purity of materials was paramount, as was known from an experiment
which had been carried out a year earlier. On that occasion a graphite cube
with a volume of about 500 cub. ft. had been built ; within it some 7
tons of uranium oxide in iron containers was distributed throughout the mass.
The materials were not in a very pure state and the lattice arrangement was
probably not the optimum, so that there were reasons for supposing that the
performance indicated by this early experimental pile was considerably below
what could be achieved ; but the measurements showed then that success was
far off, for k was no more than 0.87. However large a pile was made with
those materials in the lattice form actually tried, no more than 87 neutrons
would be produced for every hundred introduced into the pile ; the possibility
of achieving a chain reaction had not at that time been shown.

In 1942 the materials available were much purer, and careful experiments
showed that with them a value of k M of 1.007 could be achieved. The
importance of this result can hardly be overestimated, for it showed beyond
doubt that a neutron chain reaction was possible. The size of a successful
pile cannot immediately be deduced from k^, but this can be determined
when additional data are available concerning neutron losses at the boundary
of the pile. The experiments showed that a self sustaining pile was large but
of practicable size if it employed the materials and arrangements which had
been tested.

(7) Method of control of the pile .

These experiments showed that a pile could be made in which the release of
atomic energy would occur. How was this energy release to be controlled?
This matter was a very serious one for it was clear that considerable damage
would result from" a pile which went out of control. As already mentioned,
the fission process occurs within a very short time after the moment at which
the neutron is captured by a uranium nucleus, and the fission process is
associated with the simultaneous emission of neutrons. Most of these neu-
trons pass into the moderator where they proceed to lose energy at such a
rate that half of it is lost in four collisions with the carbon atoms in a graphite
moderator ; after about one hundred collisions, an average neutron of 1 MeV
initial energy is reduced to thermal energies corresponding to 0.035 eV. Such
a neutron will have a velocity of about 2000 metres per sec. and on the average

118

Chap. XI ATOMIC CHAIN REACTION

it will make a further hundred collisions and move a distance of 2.5 metres
before it passes back into the uranium. When the neutron is fast, the col-
lision cross section of the carbon atoms will be' small so that the neutron
moves considerable distances between collisions ; but as it moves at high
speed we do not make a great error by assuming that the average time between
collisions is much the same whatever the speed of the neutron. On this
basis, no more than 2.5 x 10‘ 3 sec. elapses between one fission and the fission
produced by the neutrons it releases.

If, then, a pile is made with a reproduction factor of, say, 1.003, and the
period between successive neutron generations is 2.5 x 10 3 sec., one million
fissions at one moment will grow, in a second, to 3.3 milli on fissions, and
unless some action is taken the fission process will continue to increase at
this rate. A pile will operate at constant level only if the reproduction factor
is exactly unity ; if it is lower than this value, the neutron density and the
reaction rate will diminish, but if it is higher than unity, the reaction rate will
increase until it brings about such a disturbance of the conditions in the pile
that the reaction rate becomes steady. Naturally, it is likely to be difficult to
maintain the reproduction factor at the desired value of unity, and as it turns
out this is not necessary ; satisfactory operation will occur if k is held very
slightly above unity until a predetermined increase of reaction rate has
occurred, when it can be reduced to a value at which the reaction rate slowly
diminishes. When this diminution has proceeded sufficiently, the value of k
can be increased and this cycle of fluctuations can be repeated indefinitely.
Such an arrangement is quite practicable. The overall value of k for a pile
can readily be reduced by introducing into the pile a substance like cadmium
which strongly absorbs slow neutrons. Automatic means can be provided to
move absorbing strips of cadmium-containing material, or of boron steel, in
or out of the pile according as the rate of reaction is above or below its desired
value. Our calculation of the time between successive generations of fissions
suggests that this control mechanism should operate rapidly, but fortunately
this is not necessary for not all the neutrons are emitted at the moment of
fission ; the existence of the delayed neutrons plays its part in making a pile
easy to control. We can understand this by regarding the reproduction fac-
tor as arising in part from the neutrons emitted at the instant of fission and
in part from the delayed neutrons ; if we arrange that the first portion is
made just less than unity and that the sum of the two exceeds unity, the build
up of the chain process will then depend on the release of the delayed neutrons
and will occur quite gradually. It is still necessary to move absorbing strips
to positions where k is very close to unity, but even if this adjustment is made
slowly, very satisfactory control of the chain reaction can be achieved.

119

ATOMIC ENERGY

Chap. XI

(8) The first successful uranium chain reaction.

When a pile is built, provision must be made for the introduction into the
pile of the rods that control the reproduction factor ; furthermore, as a
precaution, it is desirable to make tests to determine the reproduction factor
of the pile at a number of stages in its construction. From these tests it is
possible to estimate the size of the pile at which the reproduction factor will
just attain the value of unity. It will be appreciated that even though this
factor is less than unity, any neutron within the pile will be almost certain to
give rise to further neutrons. This chain of reactions does not maintain
itself, but it is easy to show that if the reproduction factor is k, and is less than

k

unity, each neutron will, on the average, produce a further (fZ£) neutrons. If

a source of neutrons is used, this phenomenon enables a determination to be
made of the reproduction factor even though it is less than unity.

The first reacting pile was erected in the autumn of 1942. By this time
some uranium metal was available and nearly six tons was included, although
apparently the bulk of the uranium was in the form of lumps of pressed
uranium oxide. This pile was known as the West Stands pile and was
originally built in the grounds of the University of Chicago. It was planned
to build die pile in a form which was approximately spherical, but in fact the
critical size that at which the reproduction factor became unity — was
reached before the sphere was complete and the shape of the pile was some-
what modified ; when all the neutron absorbers were removed from the pile
the reproduction factor was found to be about 1.0006. This pile first
opiated on 2nd December, 1942, when it liberated atomic energy at the rate
of 0.5 watt, a power yield which is so small that it produced a negligible

taSnn t°Jr^ e ?i tenal f 1116 pde : The ener sy liberated was in fact calcu-
5fJ “ f “ eutrons "to* were Produced in the pile ; these amoun-
Sec ? nd ’ corresponding to some 10 neutrons per
centunetre of material of the pile. Ten days later the rate
to 200 watts ; this figure was not exceeded
f { t U - ? • ° raise further P owe r output would produce
SSofthfpil? mity aS t0 endanger pe °P le working in the neighbour-

waShirfh? i ? 42 •* W “ prOVed ** 46 sIow neutron chain reaction

2 S2 % omC eDergy . could be released from uranium. There

was tittle doubt that the uranium chain reaction could be carried out m a

mudi large: scale, when perhaps it could release energy

22K a to produce Soffit

unis, it will be realized that the operation of a pile involves the occur-

120

Chap . XI

ATOMIC CHAIN REACTION

9 Neutron
• Impurity
® U 1 "

@ U 3M
© IP*

(a)

|a) and (b) : Two
slow neutrons
about to enter
each lump of
uranium.

(a) : One neutron has been cap-
tured by a U 888 nucleus and a U 230
nucleus results. The other neu-
tron gives fission with a U 235

nucleus.

(b) : One neutron is captured ty
an impurity. The other gives

fission.

(a) : Fission neutrons make
elastic collisions with nuc-
lei of the moderator.

(b) : One of the fission
neutrons gives fission with

a U 238 nucleus.

(a) and (b) : The fission neutrons make frequent collisions with
the moderator. One is lost. Of the four remaining one is about
to enter a lump of uranium.

Two lumps of uranium (a) and (b), in a carbon moderator.

Fig. 31. Some processes in a slow neutron chain reacting pile.

121

ATOMIC ENERGY

Chap. XI

rence of a number of different nuclear reactions, some of which are shown in
Fig. 31 ; the successful achievement of a controlled chain reacting pile is
evidence for the correctness of our ideas about the nuclear processes occur-
ring within it.

(9) The Clinton pile at Oak Ridge , Tennessee .

The next problem was that of devising a uranium-carbon pile which would
liberate energy at a much greater rate, for only by actual experience could
information be obtained concerning a number of doubtful points ; in addition
such a pile could be expected to give considerable information about the
possibility of preparing plutonium on a large scale. It was therefore decided
to construct a uranium-carbon pile near Clinton, Tennessee ; this pile was to
be air cooled and was designed to be capable of liberating atomic power at
the rate of 1000 kW. Although this pile was originally intended as a pilot
plant for some much greater piles which were being designed, it did not in
fact serve this purpose, but it did provide information on problems relating
to the control of a pile and, much more important, it gave essential experience
in the handling of plutonium.

The Clinton pile was cubical in shape and used a graphite moderator ;
within the graphite mass were horizontal channels in which were placed
gas-tight aluminium cans containing cylinders, or “ slugs,” of uranium metal.
Sufficient space was available to permit adequate flow of cooling air past the
aluminium cans, and arrangements were made by which they could be pushed
out of the pile when this was desired. The pile was of course provided with
additional channels for the control rods and for various instruments which
were used to make measurements of the operating characteristics of the pile.

This pile was put into operation on 4th November, 1943, and within a few
days of this time the power liberation was brought up to 500 kW, in which
condition the surface of the uranium slug containers reached 110°C. Im-
provements in the air cooling system allowed the power level to be raised to
800 kW, although this involved a can temperature of 150°C. As a result of
further improvements, including a redistribution of the uranium and improved
techniques for sealing the aluminium cans which contained the slugs, it was
possible to operate the pile at power levels in excess of 1800 kW, the figure
attained in May of 1944. By this time the pile was liberating nearly twice
the energy for which it was designed, and generally its performance exceeded
expectations. It was easy to run, it was steady in operation, and it could be
controlled without risk to the operators. The pile was provided with nu-
merous measuring instruments and safety devices and was to all appearances
a very complicated piece of mechanism. In fact, however, its most striking

122

Chap. XI ATOMIC CHAIN REACTION

feature was simplicity of operation ; most of the time the operators had
nothing more to do than to record the readings of the indicating meters.

(10) Preparation of heavy water for uranium-heavy water pile .

It is appropriate to conclude this chapter by describing the work that was
carried out in connection with a pile using heavy water as a moderator. We
have already seen that heavy water is a better moderator than carbon, if
only because, on the average, more energy is lost when a neutron collides with
a deuterium atom than when it collides with a carbon atom. This advantage
is somewhat reduced because 5 cm. 8 of carbon contains as many atoms as
9 cm. 8 of heavy water, but it remains ti ue that heavy water slows the neutrons
more quickly than does carbon in the form of graphite. Furthermore, as
heavy water has a smaller capture cross section for slow neutrons than
graphite, there is an additional advantage in using it. The main reason for
using graphite in the American experiments was the absence of any consider-
able supply of heavy water ; the decision to use graphite involved the risk
that a pile depending upon it might fail to operate, and for this reason the
work of preparing large quantities of heavy water was undertaken.

Two methods of preparation were used. The first and simplest was the
fractional distillation of water. The separation produced by this method
depends on the fact that the boiling point of heavy water is somewhat different
from that of ordinary water ; when water is distilled the steam which first
comes off is somewhat poorer in heavy water than are later fractions. Un-
fortunately the boiling points are so close together — the boiling point of
heavy water is only 1.4°C. higher than that of water — that a great deal of
water must be boiled in order to concentrate appreciable quantities of heavy
water, and although this method was successful and required only simple and
well understood equipment, it was wasteful.

The second method of preparation depended upon the exchange of deute-
rium between hydrogen gas and steam or water in the presence of a catalyst.
When equilibrium is established the concentration of the deuterium in the
water is greater than in the gas by a factor of about three. In principle,
hydrogen is mixed with steam, passed over beds of catalyst and then bubbled
through down-flowing water. Part of the deuterium originally in the
hydrogen exchanges with hydrogen in the steam and increases the deuterium
content of the steam ; the steam is then absorbed in the down-flowing water
which is subsequently electrolysed so that the hydrogen may be used again
in a continuous process. The scheme involves the handling and rehandling of
immense quantities of material, but despite this the process was found to be
economical in operation. A plant using this method for preparing heavy

123

ATOMIC ENERGY

Chap. XI

^ T ra *?’ British Columbia, Canada, this site being chosen

^ cessity for . ^ving available large amounts of electric power
for the electrolytic preparation of hydrogen.

(1 1) Performance of uranium-heavy water pile.

flf’ ^hiring 1 944, a uranium pile with heavy water as a moderator
^ I th * Argonne Laboratory outside Chicago ; by 15th May this
, y i , 1 ^h® 11 aB fhe uranium was in place, the moderator

. . _8radually added and all the time measurements were made of neutron
order to determine the moment at which the reproduction factor
of rvnircp. X Va ^ Ue ^ u ^ aty ‘ hio real difficulty or danger was anticipated, for
* usual f afet / arrangements were provided, and rods of neutron
Wefe S0 11 pkced as t0 ^ readily inserted into the pile. The pile as
«®aU compared with a uranium-carbon pile, but the designers
were astonished to find that, by the time three-fifths of the estimated require-
f,^ y wa * er had been added, a chain reaction commenced. Had the

haw V of bea . vy water been added at one time, the value of k would

, appreciably greater than unity and the neutron absorbing rods,

“ 1Ser ^ d “ to P Ue > would not have brought the repro-
a i a ? v * lue ‘ But when only a portion of the moderator
added, and the cham reaction commenced, these rods had sufficient
Cnab e fije reaction to be stopped. Subsequently some of the

* T£ V6d f r T * e p0e > extra neuiron absorbing control rods
were inserted and the calculated amount of heavy water moderator was added.

Snt p ^sfactonly and on 8th August, 1944, it was developing

in the pile power ’ ad which came from nuclear reactions occurring

references

* Tnmw^T Y he SL er ’ ^ ys ' Rev -> 56 . 426, and 1065, 1939.

, Tu^er. L-A., Phys. Rev., 57 , 950, 1939.

No. m5. reIatU18 t0 tte Atomic Bomb > H - M - Stationery Office, S.O. Code

4 Turner, L.A., Rev. Mod. Phys., 17, 296, 1945.

124

CHAPTER XII

THE PRODUCTION OF PLUTONIUM

(1) Discovery and preparation of first small supplies .

The possible importance of plutonium was discussed in the previous chapter
where it was explained that this substance resulted from two short period
radioactive processes occurring after a radiative neutron capture by U a3B . It
was apparent, however, that plutonium would be used in atomic bombs only
if it were prepared in relatively large quantities, and to achieve this required
an effort of great magnitude. The belief that plutonium was suitable for
atomic bombs arose initially from Bohr’s theories and from a general considera-
tion of the precise masses of the elements, particularly of the radioactive
elements ; initially there was no direct evidence to support the prediction that
plutonium, like U 23B , was subject to fission on bombardment by slow neutrons;
there was not even an appreciable quantity of plutonium in existence.

Plutonium was first discovered as Pu 238 , a rather short-lived radioactive
substance which on emitting oc rays becomes uranium II (U 33 *). The dis-
covery was made in the following circumstances. A cyclotron in the Radia-
tion Laboratory of the University of California at Berkeley was used to bom-
bard uranium with fast deuterons. From the bombarded uranium neptun-
ium, Np 238 , was separated, the first true trans-uranic element to be isolated.*
Early experiments showed that Np 288 emitted p rays, but the nature of the
product substance was not then ■ determined. Subsequently, when larger
quantities of Np 238 had been prepared, the methods of tracer chemistry! were
employed to determine the chemical properties of the substance produced by
radioactive decay of Np 238 , an element which we now call plutonium, the
isotope formed being Pu 238 .

In the summer of 1940, the nuclear physics group at Berkeley was urged to
use the neutrons produced by bombarding deuterium with deuterons from
its cyclotron for the purpose of producing Pu 239 , with a view to separating it
from uranium and determining its fission properties. The mode of formation
of this isotope, by two p ray emissions following radiative capture of a
neutron by U 238 , has already been discussed, but although the likelihood of
such a reaction was widely accepted, it was not verified until late in 1940. In
1941, Lawrence, of the University of California, reported that experiments in

* The reaction is U” H +H;==Np 8 0 a H H-2ni.

t See Appendix II.

125

ATOMIC ENERGY

Chap. XII

Berkeley had indicated that plutonium was formed in the manner we have
described and that it underwent fission when it was bombarded by slow
neutrons. Lawrence pointed out that a controlled chain reaction with natural
uranium might be used for the production of plutonium, that this substance
could probably be separated from uranium by ordinary chemical methods,
and that it might then replace U 235 as a possible fissionable material for use in
an atomic bomb.

By the end of 1941, when more information was available concerning
plutonium, it had been ascertained by using the methods of tracer chemistry
that satisfactory processes could probably be devised for separating pluto-
nium from uranium. There was little doubt about the general soundness of
the proposals to manufacture plutonium, but there was much uncertainty on
a number of specific points and in particular on matters relating to the ade-
quacy of the proposed methods of chemical separation. To settle some of
these doubts, cyclotrons in Berkeley and in St. Louis were used for the pro-
duction of plutonium. Although several hundred pounds of uranium salt
was subjected to neutron bombardment, it was not until the end of 1942 that
the product was available in sufficient quantity ; the yield consisted of 0.5 mg.
of plutonium— less than would be needed to make the head of a pin. Small
as was this amount of material, it was enough to permit microchemical
methods to furnish much reliable information about the chemistry of
plutonium.

On this subject few details are available ; from the position of element 94
in the atomic table, plutonium might be expected to be similar to the rare
earths or to uranium, thorium or osmium. 1 According to the Smyth report,
from which the information in this paragraph is taken, plutonium is more like
uranium than any of the other elements named and it may be regarded as a
member of a new rare earth group which commences with uranium. How-
ever this may be, by the end of 1942, plutonium, which was not known prior
to 1940, and even then was available only in microscopic amounts, was an
element whose main chemical and physical properties were well established.

(2) Possibility of large scale production of plutonium .

And yet the feasibility of using chain reactions to prepare large amounts of
plutonium was at the end of 1942 subject to doubt. At this time, it will be
remembered, the first pile — the West Stands pile — had operated. This pile
gave little help in laying doubts to rest, for although it did work, the uranium
was arranged in a way which was very favourable for achieving a chain
reaction but which was quite unfavourable for permitting the extraction of
plutonium. It was essential to arrange the uranium so that it could readily

126

THE PRODUCTION OF PLUTONIUM

Chap. XII

be removed from the pile, and for this reason it was proposed to build the
mass of carbon moderator so that it contained longitudinal holes into which
the uranium could be placed, as has been desciibed in the last chapter ;
such an arrangement made it easily possible to push portions of the uranium
out of the pile, but as it was less favourable than that used in the West Stands
pile from the point of view of the development of a chain reaction, there was
some doubt as to whether such a pile would work. Subsequent analysis and
experiment showed that it was possible to construct a pile which would work
and permit the removal of uranium for the extraction of the plutonium in it,
and these conclusions were verified by the operation of the Clinton pile at
Oak Ridge during the winter of 1943-44. But even when it was realized that
a suitable pile could be devised, a number of outstanding problems remained.

These included the following questions. How much power will be released
by a pile which manufactures plutonium at the rate of 1kg. per day, and how
is this power to be removed ? How much radiation is emitted, how dangerous
is this radiation and how can the operation of a pile be made safe for the
necessary personnel ? What dangers have to be anticipated from the chemi-
cal processes involved in handling the uranium that has taken part in a chain
reaction and how can the necessary chemical processes be carried out without
danger to the operators ? In addition there was the necessity of testing and
improving the proposed chemical processes and of finding experimentally the
materials which were able to exist, without deterioration, in the intense
streams of radiation which arise within an operating pile.

(3) Yield of heat and plutonium .

Let us examine these problems ; we commence by considering some of the
characteristics of a pile which is capable of pioducing 1 g. of plutonium per
day. The size of the pile must be large enough to allow a chain reaction to
occur but not so large that the removal of the heat generated in the uranium
becomes a major problem. Linear dimensions are kept a close secret and as
they depend on the purity of available materials as well as on their actual
airangement, it is not very profitable to speculate about them. It is useful,
however, to determine the order of magnitude of the energy liberated during
the production of 1 g. of plutonium. Since the atomic weight of plutonium
is 239, 1 g. will contain about 2.5 x 10 21 atoms and its production will require
the liberation of 2.5 x 10 ai neutrons for resonance capture by U a88 , a require-
ment that is approximately met by 2.5 x 1CP fissions, each releasing two
neutrons and about 200 MeV. Hence these fissions liberate about 5 x 10 23
MeV or in terms of larger units about 24 000 kWh, and to produce 1 g. of
plutonium a day a pile will liberate power at the rate of 1000 kW. If we are
more ambitious, and wish to provide for the production of 1 kg. of plutonium

127

ATOMIC ENERGY

Chap. XII

a day, we must arrange to remove heat from the pile at the rate of about 1
million kilowatts. These figures are surprising ; they serve to show that even
though we have discovered the means of transmuting elements the processes
are difficult, for they involve the liberation of heat on a scale that far trans-
cends that produced in ordinary chemical processes. It may be possible to
manufacture plutonium at the rate of 1 kg. a day, but if so a very large and
elaborate plant is required.

(4) Cooling the pile .

To remove heat energy amounting to a million kW is an undertaking of
some magnitude in the simplest of circumstances but in a pile circumstances
are not simple. In order to avoid the use of piles of undue size, it was
necessary to operate with higher neutron densities and to employ more
effective cooling than had been used with the Clinton pile, and air cooling was
not considered to be adequate. It will be remembered that almost all the
heat is developed in the uranium whence it must be withdrawn without
absorbing an unduly large number of neutrons. The uranium then must be
in good contact with an efficient cooling fluid of such a nature that few
neutrons are captured by it. There are not many fluids which are at all
suitable ; helium, water and molten bismuth were all considered, and for a
time it was intended to use helium cooling, but finally water cooling was
decided upon and this was successfully employed.

The problems of cooling the pile were not of course immediately solved when
the decision to use water cooling had been reached. It was necessary to
provide a large flow of water, the actual amount depending upon the rise in
water temperature which was allowable ; when it is remembered that with a
temperature rise of 60°C. a water flow of 4 tons of clean water a second is
needed to remove heat energy at a rate of 1 million kW, it can be seen that
very extensive water purifying and circulating systems were required. It was
originally intended to erect the large production piles at Oak Ridge, but
subsequently it was felt that even this part of Tennessee was not sufficiently
isolated from centres of population, and finally an area of about 1000 square
miles was acquired on the Columbia River near Pasco in Washington State.
The situation of this region, the absence of nearby centres of population, the
availability of cool, pure water supplies from the Columbia River, and the
possibility of drawing large amounts of electric power from the Grand Coulee
Dam, about 140 miles to the north, made the Hanford site a favourable one.
It was necessary to provide water pumping plant on a scale such as is required
for a fair sized city, a need that was met by engineering along well established
lines. It was also essential to ensure that any water returned to the Columbia
River was free from appreciable radioactivity arising from its passage through

128

THE PRODUCTION OF PLUTONIUM

Chap. XII

a pile, but this was not difficult to arrange ; and calculation showed that the
operation of the projected piles at Hanford would not raise the temperature
of the Columbia River by an important amount so that in no possible way
could these piles have any effect on the fish life of the river.

(5) Canning : The problem of a jacket to prevent corrosion of the uranium

slugs .

Although these aspects of the removal of the heat from the pile presented a
task of considerable magnitude, the problems involved were straightforward
compared with those of arranging satisfactorily to remove the heat from the
uranium in which it was chiefly produced. Now hot water attacks uranium
and so the proposal was to enclose the uranium in a sealed jacket which would
prevent corrosion by the cooling water and would also ensure that the fission
products released in the uranium were retained within the jacket. In view of
the large amounts of heat which were to be liberated within the uranium, it
was essential to ensure good thermal contact between the uranium and the
protective can ; furthermore, the only available materials which could be
considered for jackets were those which imposed little restriction on the free
passage of neutrons. The various requirements are satisfactorily met by an
aluminium can, provided that it is arranged that good thermal contact is made
between it and the uranium. This condition, and that of ensuring that the
can was gas tight during the period it was in the pile, were very troublesome
to satisfy, and yet the provision of absolutely reliable cans was essential if
the pile was to operate safely and continuously. Apparently the solution of
this problem— known as the canning problem — was in doubt until a very
short time before it was necessary to load the uranium into the first Hanford
pile, and in fact a minor modification of the method of canning was necessary
after this pile had commenced operation. Despite the difficulties and un-
certainties which were associated with this problem, the methods used proved
satisfactory, and up to the summer of 1945 no can failure had been reported.

(6) Radiations from a pile .

The next problem to consider is the effect of the radiations produced by the
pile. It will be remembered that uranium and plutonium arc both radio-
active substances emitting a rays, that U 239 and Np 230 are both p ray emitters,
and that the fission products emit p rays and in some cases y rays as well ;
furthermore, the fission process results in the emission of neutrons which
maintain the operation of the pile. There is little need to consider the effects
of the a and p particles at any point outside the pile ; their paths in dense
materials are so short that they are easily confined to the interior of the pile.
Ideally, of course, no neutrons should be allowed to escape from the pile,

129

I

ATOMIC ENERGY

Chap . XII

but despite the use of a carbon reflector around the pile, this ideal cannot be
achieved and a pile in operation emits a very considerable number of neutrons
in a second. The y rays emitted, either in the fission process itself, or after
the emission of p lays by the fission products, are of no benefit to the opera-
tion of the pile, but they too are likely to make their presence felt outside the
pile. It is desirable to estimate the magnitude of the radiations escaping from
the pile, for otherwise it will be impossible to prescribe adequate screens to
protect those who are to operate it.

s When we attempt to calculate the rate of emission of y rays or of neutrons
from an operating pile, we are faced with a number of difficulties, of which
only one is the lack of published information. If we consider a pile producing
1 g. of plutonium a day — and this of course must be regarded as a small
yield— we see that there occur within it about 3 xlO 16 fissions per second ;
as a result of each fission there are about 10 p ray transformations and it is
not unreasonable to guess that each fission yields high energy y rays, which
will be able to penetrate considerable thicknesses of matter, and which will
produce ionization comparable with that produced by the y rays from the
disintegration of 1 atom of radium and its products. Of the neutrons formed
per fission only a small fraction will escape, but as the physiological effect of
one neutron is considerably more serious than that produced by the penetra-
ting y rays from one radioactive emission process, it may be assumed that
the radiation per fission is equivalent to the y rays from 2 atoms of radium.
Thus in every second the pile produces radiation comparable with that
arising from the decay of 5 x 10 16 radium atoms ; some part of this radiation
is absorbed in the pile itself. In order to appreciate the seriousness of its
effects we compare it with the radiation produced by 1 g. of radium and its
short-lived products. Here we have occurring about 4 x 10 10 disintegrations
per second, so that, on this basis, the pile previously discussed, which evolved
heat at the rate of about lOOOkW, will produce radiation which is of the same
order of magnitude as the y rays from 1 ton of radium.

Now it is considered that the human body can tolerate for an indefinite
period a daily dose of X radiation or of y radiation which produces 2 x 10 8
ion pairs in a volume of 1 cm. 3 of air. The amount of radiation which
produces 2 x 10 9 ion pairs in 1 cm. 3 of air is known as the Rontgen unit, and
is written as the “ r unit 99 ; the statement above is therefore equivalent to
saying that a human being can tolerate a daily dose of radiation of 0.1 r unit.
Isolated doses of larger amounts of radiation can be tolerated, but a dose of
about 500 r units, given in a short time, is almost certainly fatal.

At a distance of 1 metre the y rays from 1 g. of radium produce about
4 xlO 5 ion pairs per cm. 8 per sec., so that a man could work safely at this

130

Chap. XII

THE PRODUCTION OF PLUTONIUM

distance from 1 g. of radium for only about 8 minutes a day, whereas if he
kept at a distance of 3 metres from the radium, he could safely work there
for an hour and a quarter a day. The radium may be surrounded by some
material which absorbs y rays ; it will then be safe for a worker to remain for
a longer period in its vicinity ; but as ten inches or so of concrete is required
to reduce the y rays to 0,1 of their original intensity, it is obvious that
considerable amounts of such material are required to give adequate pro-
tection from large sources of y rays.

Returning to the consideration of the pile, we see, first of all, that a pile
liberating 1 watt emits y rays and neutrons which are comparable in effect
with the penetrating radiation arising from 1 g. of radium. Furthermore, if
absorbing material is relied upon to reduce the intensity of the radiations
from an operating pile, this material must be chosen to absorb neutrons and
y rays. The figures given above show that the intense radiations from a pile
liberating lOOOkW will be capable of giving dangerous intensities after passing
through a number of feet of concrete, a material which absorbs both neutrons
and y rays. In fact, if a large pile is to be safe in operation it is best buried
as completely as possible ; exposed parts should be completely enclosed in a
thick layer of concrete and all operations should be carried out by remote
control in such a way that no workers are at any time near the pile when it is
emitting radiations. Naturally the whole of the pile cannot be enclosed in
thick permanent shields ; arrangements must be made for the introduction
and the removal of the uranium. This necessitates shields that can be
removed, and these shields, as well as being sufficiently massive to provide
adequate reduction of radiation intensity, must also be equipped to permit
the flow of cooling water into the pile and at the same time must be air tight
so as to prevent the escape from the pile of air which has been made radio-
active by neutron capture processes.

(7) Effects of radiation on materials within the pile.

It must be remembered that any material within a pile is exposed to the full
strength of these very intense radiations which we have been discussing, and it
is natural to expect that they may eventually cause the deterioration or even
failure of materials which are quite stable under the other conditions existing
in the pile. This difficulty arises frequently in the engineering of a pile. The*
pipes carrying the cooling water in the pile must capture very few of the
neutrons passing through them and they must not fail because of extended
periods of irradiation by neutrons or y rays ; they must be good pipes and
so they must not leak, warp or corrode. As it turned out, aluminium pipes
were satisfactory, but uncertainty on this point only disappeared, after they

131

ATOMIC ENERGY

Chap. XII

had been successfully used in an operating pile. Again, these problems arise
when making a choice of an electrical insulator to be used in the pile ; such
insulators are needed for various probes which are placed there and which
convey information to the operators or to automatic controls which keep the
pile working at a constant output level. Where the need for reliability and
freedom from deterioration is great, almost any trouble is warranted if it
leads to the discovery of a material which is really suited to the purpose
being considered. Although the effects of prolonged neutron bombardment
may be serious, there are not in fact a great many neutrons at any one time
in unit volume of the pile. If we consider the case of a pile liberating 1000 kW
of power, there are within it about 3 x 10 16 fissions a second, each of which
gives two neutrons ; as these neutrons have an existence of only about 0.0025
sec., there are only 10 14 neutrons in the pile at one time and the actual number
per cm. 3 must lie between 10 4 and 10 7 . Lest this number should sound
large, it is to be remembered that in what is regarded as a very good vacuum
there are about 10 10 atoms per cm. 3 ; the effects produced by the neutrons
arise then, from their ability to interact with the matter through which they
pass, rather than because there are so many neutrons present. In the course
of time, incessant neutron bombardment is able to bring about changes in the
physical — as distinct from nuclear — properties of materials. It is reported,
for example, that the electrical resistance, the elasticity and heat conductivity
of graphite are all changed by prolonged neutron bombardment.

(8) The operation of a pile .

In order to see what is the state of the uranium slugs when they are with-
drawn from the pile after a prolonged period of operation, it is useful to
follow briefly the chain of events that occurs when a pile is first put into
operation. We can imagine the uranium slugs to be in place and the control
rods to be slowly withdrawn so as to permit the starting up of the pile. The
initiation of a chain reaction might be carried out by having a neutron source
within the pile, but in practice it commences spontaneously either upon the
arrival of a stray neutron, of which there are about 6 per hour falling on every
cm. a of the outside of the pile, or from the spontaneous fission of a U 835
nucleus within the pile. 2 The chain reaction will build up relatively slowly,
at a rate which depends on the reproduction constant of the pile and on the
life time of a generation of neutrons. During the operation of the pile U 239
will be formed, but as this is a short-lived radioactive substance it will never
exist in any quantity ; in a matter of a few hours the amount present will
reach its equilibrium value so that after this it will decay to Np 239 just as
rapidly as it is formed. In a similar way the quantity of neptunium will
build up to an equilibrium value which is more than 100 times that of the

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THE PRODUCTION OF PLUTONIUM

equilibrium amount of U 230 and after a week or two, when this state has been
reached, the rates of formation of U 239 , of Np 239 and of plutonium will all be
equal. Pu 339 is a substance of such slow decay that it will continue to
accumulate in the uranium at a steady rate during the period it is kept in the
operating pile. In addition to these reactions there occur the rather rare
fissions of U 238 nuclei after the capture of fast neutrons, and the much more
frequent fissions of U 336 nuclei formed by neutron capture from U 23B . From
these processes there arises the great variety of radioactive fission products,
and eventually these materials reach equilibrium values in which the rate of
production of any one of them is just equal to the rate of its decay.* For
fission products which are derived from a common fission nucleus, the equi-
librium amounts will be proportional to their half lives, so that there will be
only small amounts of the short-lived fission products and much larger
amounts of the long-lived ones. When a piece of uranium is within the pile,
it becomes permeated with a variety of materials, most of which are radio-
active ; the main part of the radiations arising within this uranium comes
from the fission products, although there are also appreciable contributions
from the presence of U 230 and Np 239 .

(9) Extraction of plutonium .

Immediately the uranium slug is removed from the pile, the radioactive
substances will commence to decrease in amount and in the case of some
short-lived ones this change will be rapid. Nevertheless, as it is impracticable
to wait for the disappearance of the whole of the short-period radioactivity
of the fission products, it is necessary to arrange to handle the uranium while
it still contains highly radioactive substances. In this state, the uranium slug
is emitting y rays on such a scale that it cannot safely be approached by
human beings ; furthermore, the plutonium within the uranium is an intense
poison, as are also the radioactive fission products. It is therefore essential
that the uranium should be handled by remote control. The general scheme
adopted has been described by Smyth. 3 A 44 canyon ” was built coasisting
of a line of compartments having heavy concrete walls ; this was almost
completely underground. Each compartment contained chemical equipment
for treating the uranium and for extracting the plutonium from it. Uranium
entered the line from the pile at one end of the canyon, where it was dissolved ;
it then went through various chemical processes and from time to time was
pumped from one compartment to the next until eventually there came from
the last compartment a solution of a plutonium salt which was free from both
uranium and from fission products. The processes involved were similar to

* In practice it is unlikely that the uranium slugs remain in the pile for long
enough to achieve equilibrium amongst the fission products.

133

ATOMIC ENERGY

Chap. XII

ordinary chemical processes but they were rather complicated and were made
more so by the necessity for controlling them from distant points above
ground.

Very little information has been given about the actual chemical processes
used, but it is worth recalling the nature of the problem and recounting what
has been revealed. In the case of the Clinton pile, uranium went to the
treatment plant at the rate of about 300 kg. a day. Now this pile, operating
so that 1000 kW is liberated as heat, produces about 1 g. of plutonium a day
in a mass of uranium that probably lies between ten and one hundred tons.
It is neither possible nor necessary to extract daily the whole of the plutonium
produced ; it is more satisfactory to treat each day a fraction of the uranium
in the pile, for in this way there is a welcome increase in the concentration of
plutonium in the uranium slugs. If the uranium is handled systematically so
that each slug spends the same period in the pile, the plutonium in the uranium
which is withdrawn daily from the pile will be equal to the whole daily
production of plutonium within the pile. Consequently in the 300 kg. of
uranium withdrawn daily from the Oak Ridge pile there was about 1 g. of
plutonium with the addition of a similar amount of fission products, much of
which was in the form of highly dangerous radioactive substances. Thus the
concentration of plutonium in uranium is in this case comparable with the
concentration of gold in gold-bearing minerals, but the process of separation
is much more difficult here because of the chemical similarity of plutonium
and uranium and the presence of the fission products. It must be remem-
bered, too, that when the Clinton pile was first put into operation at Oak
Ridge, the chemical studies of plutonium had been made in the laboratory
when only very small quantities of material were available. Nevertheless the
actual experience with plutonium extraction at Oak Ridge was very favour-
able. By 1st February, 1944, after the Clinton pile had been in operation at
a low reaction level for a period of nearly three months, only 0.190 g. of pluto-
nium had been delivered, but a month later several grams had been separated.
From the very first it was found possible to excract 50% of the plutonium
within the uranium slugs going into treatment, and by the middle of 1944 this
recovery efficiency had been raised to between 80 and 90%. The chemical
methods, though very successful, were expensive and complicated, and the
work at Oak Ridge gave opportunities for making the improvements which were
needed for the much larger scheme at Hanford. In this way the Clinton pile
was invaluable ; it also assisted progress generally by providing an example
of a pile of moderate size in operation, for on this pile operators could be
trained and experiments could be carried out with a view to determining the
procedure to be adopted for the projected piles at Hanford. Finally it

134

THE PRODUCTION OF PLUTONIUM

Chap. XII

provided appreciable quantities of plutonium from which physical constants,
and particularly nuclear constants, could be determined with accuracy.

The following information has been published concerning the nature of
the chemical processes used to separate plutonium from uranium and the
fission products. It appears that plutonium has four states of oxidation,
corresponding to positive valencies of 3, 4, 5 and 6 and that the separation
processes make use of this fact. It is possible to prepare a solution of
uranium and plutonium in which the plutonium is in oxidation state 4, to add
a suitable carrier and then to precipitate the plutonium and the carrier ; with
the precipitate is a part only of the fission products. After dissolving the
precipitate, the plutonium is brought into oxidation state 6 and the carrier
compound is then precipitated in such a way that the plutonium remains in
solution. When suitable carriers are used, fission products which precipitate
with the carrier in the first stage also precipitate with it in the second. By
carrying out a sufficient number of cycles of this type — and apparently it is
advantageous in different cycles to use different reagents according to whether
it is more important to eliminate uranium or fission products — a very efficient
and satisfactory separation process is achieved ; this process was available in
time to be put into operation when the Hanford piles commenced to deliver
plutonium.

(10) Depletion of U- u in a reacting pile .

It will be realized that a pile operates and is able to produce plutonium by
virtue of the presence of the small quantities of U 236 in the natural uranium
which forms the active material of the pile. What happens as U 33C is con-
sumed ? In the long run, of course, if the pile can continue to operate, all
the U 236 will be used up and the pile will continue to run only as long as there
is sufficient Pu 230 to ensuie that the reproduction factor can be maintained at
the value of unity. In practice, however, the U 335 is consumed quite slowly
as can be seen by remembering that plutonium is produced at about the same
rate as U 235 is consumed. In the case of the Oak Ridge pile, where the plu-
tonium content of the uranium slugs going into solution was 3 parts in 1
million, the consumption of U 336 had reduced its concentration by only about
0.05% ; this reduction in U 235 content occurs during the period ihe uranium
slug remains in the pile, and as this period probably exceeded a month, the
daily reduction in U 33C content was very small indeed. At Hanford, where the
plutonium concentrations were considerably greater than those at Oak Ridge,
the daily consumption of U a3C amounted to a few grams for every ton of ura-
nium in the pile. The consumption of U 23C tends to lower the reproduction
factor of the pile but, on the other hand, the production of Pu 289 , which gives

135

ATOMIC ENERGY

Chap. XU

fission when bombarded by slow neutrons, makes good some of the loss of U 285 ,
the precise change in reproduction factor depending upon the relative amounts
of U 285 consumed and of Pu 839 produced. There is also the possibility of a fall
of reproduction factor arising from the presence of fission products in the
pile. Some of these materials have appreciable neutron capture cross sec-
tions and if they are present in great enough quantity the neutron consump-
tion they cause will prevent the operation of the pile. This phenomenon is
known as poisoning and no precise information is available about the stage in
the operation of a pile at which it becomes significant ; in piles which are oper-
ated for the plutonium they produce, the uranium slugs are removed from the
pile before the depletion of the U 28B , or the accumulation of excessive amounts
of neutron absorbing fission products, has occurred to any great extent. These
factors, as well as others, must be considered when a decision is being made
concerning the time for which a given uranium slug should remain within a
reacting pile.

Uranium which has taken part for a long time in a chain reaction in a pile
contains a smaller concentration of U 235 than occurs in natural uranium, and
for this reason uranium, from which plutonium has been extracted, is of
relatively little use at present for the purposes of releasing atomic energy. A
pile which has a reproduction factor greater than unity when natural uranium
is used as active material, may be able to operate with uranium having
slightly subnormal concentrations of U 235 , but it seems unlikely that simple
arrangements can be made to use up the whole U 235 content of natural ura-
nium, let alone the whole available quantity of U 238 . If this is the case, as
it would appear to be in a uranium pile being run for the production of
plutonium, one of the most important by-products is uranium which is
substandard from the point of view of U 235 . It may well be that this uranium
is of use in industry, but for the production of atomic energy its value has
been seriously diminished.

(11) Atomic transmutation in a pile.

Very little information has been released about the performance of the
Hanford piles, and relatively little about the operation of controlled reacting
piles in general ; for this reason it is impossible to give precise details of
many features of the operation of a pile which is being run for the plutonium
it yields. The details which have been discussed give some impression of the
magnitude of what has been achieved. In 1938 neither uranium fission nor
plutonium was known ; less than six years later, after a scientific effort of
unprecedented magnitude, the first of the giant Hanford piles was brought
into action and the transmutation of matter was carried out on such a scale

136

Chap. XII THE PRODUCTION OF PLUTONIUM

that a new element, which had been discovered about four years earlier, was
being made at a rate which perhaps exceeded 100 g. a day. Not only were
the substances and the processes novel ; they involved the production of
vast amounts of very penetrating and very deadly radiations and the treatment
of substances which were intensely poisonous. That this work was carried
to a successful conclusion is a tribute to the efforts of the many technicians
who were employed directly on this project, and also to the soundness of the
fundamental researches which were carried out in nuclear physics during the
1930’s. Without these and the experimental techniques which grew around
them, the manufacture of plutonium could not have been undertaken.

REFERENCES

1 Smyth Report, 6.35.

2 Smyth Report, 8.8.

3 Smyth Report, 8.41.

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THE ATOMIC BOMB

(1) The bomb as a chain reactor .

The most spectacular achievement in the field of atomic energy has been the
successful use of the atomic bomb. Naturally, this device is regarded as a
military weapon, and no detailed information has been released concerning
it ; regarding the most interesting question of the actual means employed in
detonating the bomb, the published accounts are either extremely vague or
totally unmindful of the widespread desire for information and explanations.

Nevertheless, there is a certain amount of information which can be given,
and on matteis which are secret some speculation is possible. In the first
place, it must be realized that the atomic bomb is only a chain reactor. It
differs from a uranium pile in that it is small and is designed to give rise to a
chain reaction in which the reproduction factor is as great as can be achieved ;
furthermore, in the atomic bomb the life time of a generation of neutrons is
as small as possible.

(2) Explosions .

Let us consider briefly the mechanism of an explosion and the properties of
a good explosive. In order to make an explosion, it is necessary to have some
mechanism by which the volume of a piece of matter is suddenly increased.
An effective explosive is one in which there is a very large increase in volume
within a very small interval of time. An explosion may be achieved by the
use of an unstable liquid or solid which suddenly liberates a large volume of
gas, but most explosives liberate heat in addition to gas. The process of
explosion is often very similar to that of combustion ; this is illustrated when
liquid oxygen comes into intimate contact with powdered charcoal and an
explosion results because the charcoal and the oxygen form carbon dioxide
and liberate large quantities of heat. Similarly the explosion of gunpowder
involves the combustion of carbon and sulphur. The evolution of heat by
an explosive is by no means essential, but as it gives rise to an increase of
pressure of the released gas, the effectiveness of an explosive is closely related
to the heat liberated in the reaction ; other factors are also important and will
require consideration when an explosive is being chosen for a particular
purpose. Nevertheless, an explosive that delivers a large amount of heat
energy per unit volume of material is likely to be very effective provided the
delivery of heat occurs sufficiently quickly. The heat energy raises to a high

138

THE ATOMIC BOMB

Chap. XIII

temperature the material of the explosive and temporarily a localized region
of high pressure is produced ; the sharp boundary of this spreads as does a
sound wave, and regions near the centre of explosion experience a sudden
rise in pressure from which much destruction may ensue. Unless the ex-
plosion occurs rapidly, it is not complete before the hot products of explosion
extend over a rather large volume and this, and the fact that they are diluted
with cool air, diminishes the intensity of the explosive wave. We have
already seen that nuclear fission is capable of yielding very large amounts of
heat energy ; if this process can be carried out quickly, and on a vast enough
scale, a terrible explosion must occur. In principle, then, a nuclear fission
chain reaction which is rapid and which grows to a sufficient magnitude to
result in the fission of some pounds of material will provide an atomic bomb.

( 3) Requirements of an atomic bomb.

We have already mentioned that the energy released in the fission of 1 lb. of
uranium exceeds that liberated when two million pounds of coal are burned ;
the same amount of energy may be produced from the explosion of nearly
10,000 tons of T.N.T. The real problem was that of arranging a bomb in
which a reasonable portion of the fissionable material present was caused to
yield its energy before the bomb and the products of explosion began to
disperse themselves ; it was further desirable that the bomb should not be too
large and that it should not contain an undue quantity of very rare material ;
finally it was essential that the bomb should not detonate by accident, and
that its instant of detonation should be subject to reliable control. The task
of devising an atomic bomb involved the determination of an arrangement
which would give rise to a chain reaction of the desired type and the perfecting
of a suitable mechanism for commencing the chain reaction at the desired
moment.

Let us consider the necessary means for achieving an atomic bomb. We
shall imagine that supplies of suitable fissionable material are available, and
we shall suppose that we have a number of small bricks of this material ;
from them we commence to build a cube. Because of the existence of stray
neutrons, on occasion there will occur the fission of an atom within the
structure we arc building, and this fission will give rise to fast neutrons. Now
all materials have small capture cross sections for fast neutrons so that before
neutron capture occurs the neutrons released will travel some considerable
distance, in which they may lose energy as a result of interactions with the
matter through which they pass. It may happen of course that a neutron
escapes from the structure before it is captured, and in that case it will have
no further influence unless it is reflected back again. Even if a neutron is

139

ATOMIC ENERGY

Chap. XIII

captured before it leaves the structure, it will not necessarily give rise to
fission, not even if the material used is free from neutron absorbers like U 888 ,
for even though a nucleus is excited with sufficient energy to give the defor-
mation which is followed by fission, cases will occur in which the excess
energy results in neu f ron or y ray emission rather than in fission. In the
most favourable circumstances, then, an atomic bomb will be made from a
substance in which the neutron binding energy exceeds Ef — the energy which
is sufficient to give the deformation from which fission arises — by so much
that the capture of a neutron is almost certainly followed by fission. This
requires that the atomic bomb is made from a material which gives fission on
the capture of a slow neutron, not because slow neutrons are of significance in
the explosion of an atomic bomb, but because this requirement gives the best
possible chance that fission will result from the capture of a fast neutron ;
in fact it ensures that fission is highly probable upon the capture of a neutron
of any energy. In terms of present knowledge, the best materials for an
atomic bomb are U 285 and Pu 289 ; it is probable that U 233 is also suitable.*

It will be appreciated from earlier discussions that the size of the structure
being built will determine whether or not one fission results, on the average,
in a further fission, and that size determines whether the chain of fissions
grows or dies. If the structure is just smaller than the size at which the
reproduction factor is unity, the structure is said to be below the critical size,
and in this condition, if k is the reproduction factor, a single fission will be

k

followed on the average by further fissions. As explained earlier,!

from observations of the number of neutrons released in the structure when
a beam of neutrons falls on it, k may be determined ; if desired further bricks
may be added in order to bring the reproduction factor up to unity. If the
reproduction factor is made just greater than unity by increasing sufficiently
the size of the structure, a chain reaction will be initiated by a single fission
and the spontaneous reaction of the structure will commence ; fissions will
occur at a steadily increasing rate, but there will be no large explosion,
because if k is not much greater than unity the growth of the fission rate will
depend upon the emission of delayed neutrons and it will occur relatively
slowly. At this stage, however, it is desirable that steps be taken to stop the
growth of the chain reaction, for otherwise the fission rate will increase so far
that at the least there will be emitted excessive and unsafe amounts of radia-
tion.

Let us consider some of the details of a chain reaction with a view to making
an estimate of the critical size of an atomic bomb. In the interests of

* U 283 may be derived from thorium. (See footnote, Chap. XI, p. 112.)

t Compare Chap. XI, p. 120

140

THE ATOMIC BOMB

Chap. XIII

simplicity, (and as we cannot hope to achieve accuracy we can afford large
sacrifices in aid of simplicity) we shall assume that every fission results in the
release of two neutrons. We shall assume, further, that our atomic bomb is
a sphere, and that the neutrons released upon fission have a certain path
length in the sphere before they cause fission. We are interested first of all
in determining the critical size, when the reproduction factor just attains the
value of unity. If the radius of the sphere is just equal to the free path of
the neutron, and if the neutron path is a straight line, more than half of the
neutrons will escape without making a further fission, so that if two neutrons
arise per fission a chain reaction will not be possible unless an adequate
reflector encloses the fissionable material. If the size of the sphere is somewhat
increased, neutrons formed near the centre will rarely escape and the advan-
tage arising here may compensate for the excessive losses occurring in other
regions of the sphere. Without the use of a reflector, the critical radius is
somewhat larger than the distance the neutron moves in a straight line ;
with it, the critical radius will be smaller, perhaps considerably smaller, if the
reflector returns an appreciable fraction of the neutrons which would other-
wise leave the reacting system. It will be understood that the critical size
depends on the shape of the fissionable material ; the shape considered here
is spherical, but the conclusions are sufficiently vague to be applicable to
shapes which do not depart very far from the spherical.

To make further progress in this consideration of the critical size, we need
to know what figure to use for the path length. We take for this quantity
the mean path length between the emission of a neutron and the fission
produced by it. This latter quantity is secret and we can do no more than
estimate it from other data. It is likely that the capture cross sections for
fast neutrons of given energy in U 238 , U 235 and Pu 239 are very much the same,
so that if we knew the correct value for U 238 we would have a useful figure
to employ for whatever fissionable material is used in an atomic bomb. As
the capture cross section of U 23 8 for fast neutrons does not appear to have been
published, we must base our estimate on the fission cross section of this
nucleus 1 ; for 2.5 MeV neutrons it is 5 x 10 -25 cm 8 . Now when U 238 captures
a fast neutron, it is more likely to release surplus energy by neutron emission
than by fission, and as every capture does not result in fission, the capture
cross section is considerably greater than the value quoted for the fission cross
section. For the capture cross section of U 238 we guess the value of 1 .5 x 10 -24
cm. 2 In the case of U 23C the capture of a neutron most probably results in
fission, so that for this nucleus capture and fission cross sections are almost
identical. This leads to the conclusion that the fission cross section for U 235
is about 1.5 x 10 -34 cm. 2 for 2.5 MeV neutrons ; for slower ones it is likely to
be still greater. The same arguments apply to plutonium, although in view

141

ATOMIC ENERGY

Chap. XIII

of the large amount by which the neutron binding energy exceeds that
required to initiate fission, in this case the capture of a fast neutron is almost
certain to result in fission, and consequently the fission cross section of
plutonium may be somewhat higher than that of U m .

If the densities of these fissionable materials are about 20 g. per cm. 3 each
cm. 8 will contain about 5 x 10 aa atoms ; consequently the path of a neutron
win average about 13 cm. Now a sphere of uranium of radius 13 cm. has a
volume of about 9 litres and a mass of 180 kg., and in view of our estimates
of critical size, the bomb would exceed this mass. Although the Smyth
report is very vague about the mass of material required to make an atomic
bomb, it gives the limits of between 1 and 100 kg. It will be appreciated that
the estimates given above are based on the crudest assumptions, and that the
mass of the bomb is very sensitive to the value chosen for the critical radius.
Furthermore, no account has been taken of the effect of surrounding the bomb
by a reflector, of the favourable effects of non-capture collisions between
neutrons and file material of the bomb,* or of the possibility that the average
number of neutrons emitted per fission is sufficiently in excess of two to cause
an appreciable decrease in the critical size and mass. Even if the estimate of
critical mass had been in closer accord with expectations, great uncertainties
would still have existed ; the only value of an estimate is to help to present
the factors on which the critical size depends.

Let us now discuss the factors which determine the life time of a generation
of neutrons. A neutron emitted with an energy of 2 MeV moves with an
initial velocity of 2x10 7 metres per second, so that such a neutron takes
about 6 x 10' 9 sec. to move the distance of 13 cm. which we estimate as the
average path length between the place of emission of a neutron and the fission
caused by it. For somewhat slower neutrons, the fission cross section will be
somewhat larger, the path length will be shorter and fission will occur in
about the same average lapse of time. This gives an approximation to the
life time of a generation of neutrons, for the time between neutron capture
and the occurrence of fission is quite negligible compared with the average
time which elapses between the emission of a neutron and its subsequent
capture. In addition to the life time of a generation of neutrons, we require
to know for how long the explosion can continue without loss of catastrophic
effect. Perhaps no precise limit can be determined ; doubtless the matter has
been carefully considered by those who were concerned with the design of the
bomb, but no official information has been released concerning it. At a
guess it seems reasonable to assume that the explosion should be completed

* Such collisions deflect the neutron and increase the distance it travels before
it escapes from the bomb.

142

THE ATOMIC BOMB

Chap. XIII

within a period of 1 /x sec. (10“ 6 sec.) ; to achieve so rapid an explosion will
not be reasonably possible if the neutron generation life time appreciably
exceeds our estimate of 6 x 10-® sec.

In order to make clear a number of points, let us assume that we have an
atomic bomb for which the reproduction factor is 1.2 and the neutron gene-
ration life time is 6 x 10“ 9 sec. We suppose that a chain reaction commences
with a single fission. One microsecond* later, in the 167th generation of
neutrons, there will be about 16 x 10 u fissions, and altogether in this period
of 1 /xsec. there will have been a total of 8 x 10 18 fissions. Nevertheless, as
this number of fissions corresponds to about 3 x 10“ 8 g. of uranium, it releases
insufficient energy to cause a marked rise in the temperature of the bomb, let
alone an explosion. At first sight this is a disappointing result ; it appears
that the circumstances assumed — and they looked reasonably favourable — are
such that the chain reaction grows too slowly to produce a serious explosion.
In fact, however, the process is just starting up, and the period that has
elapsed, although apparently wasted, has involved no detrimental effect to
the subsequent performance of the bomb. In the next interval of 1 fx sec.,
there are 12 x 10 26 fissions, provided, of course, that the necessary uranium
is still available ; the. quantity consumed would amount in this case to 500 kg.

Let us see what appear to be the minimum requirements for a successful
atomic bomb. An adequate explosion is likely to be produced by the fission
of a few pounds of uranium, and to achieve this 10 24 or more fissions must
take place within a period which should be less than 1 /xsec. ; as it is hardly
likely that a bomb can be made in which one fission gives rise to 10 24 fissions
within a period of 1 /xsec., we are faced with the problem of deciding on the
maximum allowable number of fissions before the explosion is said to begin.
If we assume that the bomb contains 20 kg. of fissionable material and that
the explosion begins when the uranium temperature has risen to 150°C., we
find that this state of affairs has been reached after 10 16 fissions. The ex-
plosion then occurs in the period in which the number of neutrons in a
generation increases by a factor of 10 8 or more. If the reproduction factor
is 1.2 this will require at least 100 neutron generations, if it is 1.4 about 55
generations will be required, and if it is 1.6 an adequate explosion will occur
after 40 neutron generations. In practice, then, the period of the explosion
depends upon the attainable value of the reproduction factor and on the
neutron generation life lime. To assume that the reproduction factor
exceeds 1.2 would seem optimistic ; it likewise appears unreasonable to sup-
pose that the life time of a neutron generation is very much less than the
value of 6 x 10-° sec. already assumed. Unless these figures are much in

* 1 microsecond may be written as 1 /x sec. It is 10"° seconds.

143

ATOMIC ENERGY

Chap. XIII

error, the explosion, as we have defined it, requires a period of at least 0.6
jLLsec. It is to be observed, however, that we assume a chain reaction that
grows steadily throughout the explosion, and as a result in the last period
of 0.1 jusec. there is liberated about 95% of the total energy of the explosion.
The results of these calculations do not agree with a statement in One World
or None 8 to the effect that the time of explosion of the atomic bomb is about
10‘ 7 sec. ; as it is uncertain whether the estimate is made on the basis used
here, the value is mentioned only in view of the authority behind it.

The figures derived here serve to show how necessary it is to achieve a high
reproduction factor and the minimum possible neutron generation life time.
In the case of a 20 kg. bomb the fission of 10 24 uranium atoms involves the
consumption of only about 2% of the fissionable material of the bomb ; never-
theless, if uranium had its usual specific heat at all temperatures the heat
equivalent of the energy released in 10 24 fissions is enough to raise the tem-
perature of the uranium in the bomb to 10 10 °C.

It will be realized that although a high reproduction factor helps to give a
very rapid explosion, high reproduction factors can be achieved only by
using large bombs. A larger bomb may be more destructive, but it will
certainly require greater amounts of fissionable material and on balance the
more effective explosion may not compensate for the greater consumption of
this material. Whatever the size of the bomb, it seems desirable to arrange
it so as to make as large as possible the reproduction factor and the period
during which the chain reaction can usefully take place.

From the point of view of a short generation life time, a neutron reflector
around the bomb is a doubtful advantage. It will certainly return neutrons,
but if it is of real service it must return these neutrons quickly ; time that a
neutron spends in the reflector represents lost opportunities for causing
fissions, and unless the neutron returns quickly to the fissionable material, its
contribution to the fission process will be so long delayed that it will not give
adequate assistance to the rapid build up of the chain reaction. On the other
hand, the reflector, which should be made of heavy material, has a consider-
able mass and its inertia tends to prevent the spread of the materials of the
bomb in the earlier stages of the explosion.

. the development of the chain reaction there is liberated a vast quan-

of energy some of which is in the form of penetrating v rays ; much
of this energy escapes immediately from the system. The kinetic energy of
the fission products and of the fission neutrons is communicated as heat
energy to the material of the bomb, and once the chain reaction is proceeding
at high intensity the bomb rises rapidly in temperature. This temperature
rise, which gives to uranium atoms velocities which are not negligible corn-

144

Chap. XIII

THE ATOMIC BOMB

pared with the velocities of some fission neutrons mav u
in the probability of neutron capture and hence in th y J eu J 1,0 - 110 * chan 8«
the bomb ; but the main consequence of the liberation * pr ? du ® ,on factor
high pressures and temperatures and the emission of liehf 6 w* 0 p / 0< ?“ cc
violet rays appropriate to the temperature of the material*^ *
in these radiations quite appreciable amounts of enerev w • b< *J? b '
vicinity. In the bomb itself the high pressii S 2 t ,mmed l ate
value of 10 ,a atmospheres, tend to cause its material to flv ara n t °/^ lcb a
the early parts of the explosion the force, devetog ^^gS^g
ttag the external portiom of the bomb. Any resulting eSStnent of tte
bomb will cause a diminution of uranium density and an increase of the neu-
tron path length by more than the increase of linear dimensions of the bomb ■
on this account the reproduction factor will decrease and at the same time
there will be an increase in the neutron generation life time. Furthermore
uranium is being consumed and is replaced by fission products Each of
these changes causes a reduction in the rate of build up of the chain reaction
and eventually the expansion of the bomb and the conversion of the materials
within it will proceed sufficiently to reduce the reproduction factor to values
less than unity, at which the chain reaction dies down. The explosion will
be most effective if the expansion can be delayed until the bulk of the uranium
has been subjected to fission, and the neutron reflector around the bomb
serves to provide a heavy mass which must be removed by the forces of
explosion and the presence of which materially delays the expansion. Never-
theless, within a few microseconds at the most the explosion is over and the
atomic bomb has become an incandescent mass which consists of unused
fissionable material, the fission products and all apparatus which was in
close proximity to it.

The high temperature of this material results in a great upward air current
and the fission products and the fissionable material, all of which are poison-
ous, are carried to a great height in the atmosphere and are eventually
deposited very thinly over a vast area of the earth. There was reason to
suppose that in the immediate neighbourhood of an exploding atomic bomb
the earth would be strewn with radioactive fission products which would
make human existence impossible, but if the bomb is exploded at some
considerable height above the earth there is no undue concentration of radio-
active substances at points near the explosion. This does not mean, of course,
that there is any chance of safety in the vicinity of an exploding atomic bomb,
for not only is there a most intense explosion wave, but the bomb emits large
quantities of y rays. These y rays are rather less in amount than might be
expected from the calculations relating to an operating pile, because during
the explosion of the atomic bomb there is only a small amount of radiation

K 145

ATOMIC ENERGY

Chap. XIII

from the fission products, which are so quickly carried away by the upward
stream of hot air. Most of the y rays emitted come from the excitation
energy of the primary fission nuclei. As has already been stated, 1 g. of
radium gives y rays from 4 x 10 10 disintegrations per second, and at 1 metre
distance these give an ionization of 4 x 10 5 ion pairs per cm. 3 per sec., i.e.,

2 x 10 -4 r units per sec. Now we believe that a successful atomic bomb should
involve 10 24 fissions at least, so that the y rays emitted may produce 10 18 ions
pairs per cm. 8 or 5 x 10 8 r units at 1 metre. It may be that on many occasions
the primary fission nuclei do not emit y rays, but even if this view is accepted
the total y radiation at a distance of 1 metre can hardly be less than 10® r
units. At 1 km. from the bomb there has been considerable y ray absorption
by the air, and the dose of radiation might be about 5 r units ; at half this
distance the total radiation is much larger and might reach 300 r units, an
antount which will often be fatal. These figures are only approximate, but
they serve to show that even at considerable distances from an atomic bomb
death may result from y radiations as well as from the effects of the explosion
wave.

It is probable that the most difficult problem connected with the atomic
bomb was that of arranging a satisfactory method of detonation . A piece of
U m or of plutonium is quite safe as long as it is smaller than the critical size,
but when this size is exceeded the onset of a chain reaction will not be long
delayed ; there are stray neutrons passing through the atmosphere, a neutron
may be formed as a result of a collision between an a particle emitted by U 286
or plutonium and an atom of impurity, or a nuclear fission may take place
spontaneously, a process which though infrequent is occurring once every few
seconds in a kilogram of U 235 or Pu 282 . It is imperative that the bomb should
be built from two or more masses of fissionable material, each less than the
critical size and so separated from one another that a chain reaction is im-
possible. When detonation is required, these masses are brought into close
contact ; precautions must be taken to avoid the commencement of the chain
reaction before contact is established, and to initiate it immediately the
component parts of the bomb are united. At this stage the material of the
bomb must be exposed to the neutrons from a neutron source, for only in
this way can the commencement of the chain reaction be made to occur close
to the moment of contact. The example of the rate of neutron growth,
already considered, shows that there is no utility in commencing the chain
reaction by trying to introduce many neutrons simultaneously into the fission-
able material, for the number of neutrons which exist, 1 jusec. after a single
fission initiates a quickly growing chain reaction, is much greater than the
number of neutrons arising even in one second from any neutron source of
convenient size. For this reason the chain reaction begins at the moment of

146

THE ATOMIC BOMB

Chap. XUI

the first fission and neutrons entering the system a fraction of a microsecond
later produce only negligible effects.

Fig. 32 gives a representation of the paths of neutrons in the initial stages
of a chain reaction in a bomb. Within the inner circle is fissionable material
and surrounding it is a neutron reflector. The chain commenced with fission
(1), brought about by a neutron which started at 0 in the centre of the bomb.
This fission gave two neutrons, of which one was lost. The consequences of
other fissions are readily seen. This diagram shows a case in which the
reflector makes an important contribution to the build up of the chain re-
action. Non-capture collisions are frequent ; without their effects the fraction
of neutrons escaping would be too large to permit the growth of the chain
reaction.

147

atomic energy

Chap, XIII

Fig- 33- The New Mexico atomic bomb explosion. 0.016 sec. after detonation.

(Reproduced by courtesy of the Directorate of Atomic Energy, Ministry of Supply.)

With reference to the means adopted for the detonation of the bomb* it is
clear that one part of the fissionable material may be a projectile which is
shot from a kind of gun into another portion of the bomb ; the speed ol
projection must be high enough to ensure that there is no danger of the onset
of a chain reaction before the two parts are close enough to allow it to grow
quickly to a high intensity. Although this means of detonation is obvious,
and is discussed briefly in the Smyth report , 3 it is by no means simple, in
de tail and from the remarks that Smyth makes it is clear that alternative
methods of detonation were considered. As there is hardly any information
available on this interesting matter, it is not profitable to discuss it . further.

It is worthy of note, however, that the task of devising an atomic bomb
involved a difficulty which is most unusual in engineering experience : there
was no possibility of trying out the bomb or the means of detonation by the
use of a small model. Difficulties of a similar nature arose throughout the
work on the atomic bomb ; the first experiments were handicapped by lack
of fissionable material, but even when this was available in quantity it was
still necessary to base the design of the atomic bomb on the results of studies

148

Chap. XIII

THE ATOMIC Q:>MB

Fig. 34. The New Mexico atomic bomb explosion. 0.053 sec. after detonation

(Reproduced by courtesy of the Directorate of Atomic Energy, Minis' ry of Supply •

which could not include a chain reaction such as was to be used in the actual
bomb.

In ordinary engineering, it would be regarded as difficult to design a bomb
to make efficient use of a material which was said to be explosive but which,
for some reason, could not be detonated before it was assembled in a bomb ;
the task would be made more difficult if the problems of detonation imposed
similar restrictions to those arising from the use of fissionable material. It
was only incidental that the bomb depended on the use of materials which
were many times rarer and more costly than gold, but it made it essential that
the bomb should succeed on the first attempt. Above all, when it is remem-
bered that the action of the bomb depended on the use of a recently discovered
nuclear process which had never before been used to give an explosion, it
will be realized that the successful construction of the atomic bomb was a
feat of the greatest difficulty and one which perhaps has never been surpassed
in the history of science or engineering. The success of this work lends
powerful support to the statement that “ the end of 1944 found an extra-

149

ATOMIC ENERGY

a

Fig 35. Aerial photograph of the site of the New Mexico atomic bomb «
28 hours after detonation.

(Reproduced by courtesy of the Directorate of Atomic Energy, Ministry of Supply

ordinary galaxy of scientific stars gathered on this New Mexico mesa
in reference to the personnel at Los Alamos in New Mexico where tl
bomb was designed, constructed and assembled.

On 16th July, 1945, at 5.30 a.m., the first atomic bomb, mounted
steel tower, was detonated. There was a blinding flash which illumii
surrounding country more brightly than the brightest day, the ma*
the bomb were raised to a temperature exceeding that of die inter!
sun, and very soon afterwards a huge many-coloured cloud, conta
products of explosion, had risen to a height of 40,000 ft. Where

150

THE ATOMIC BOMB

Chap . XIII

tower had stood was a large shallow crater on the surface of which was a jade-
like substance which had previously been grains of desert sand. Figs. 33
and 34 are photographs taken within a tenth of a second of the instant of
detonation of the bomb. Fig. 35 gives an aerial view of the bomb site after
the explosion ; the region within which the sand was fused surrounds the
site of the bomb and appears as a rather irregular dark patch.

Such were some of the results of the explosion of an atomic bomb in the
waste lands of New Mexico. Words fail to describe the consequences of
atomic bomb explosions over densely populated regions of Japan*; even
to-day I find it difficult to understand the inhumanity of the man or men who
decided to reveal the atomic bomb to the world by using it in such a way.

* A description of the effects of the Hiroshima bomb is given in One World or
None 5 . See also The Effects of the Atomic Bombs at Hiroshima and Nagasaki 5 .

REFERENCES

1 Ladenburg et al., Phys. Rev., 56 , 168, 1939.

3 One World or None , McGraw-Hill, 1946 : p. 14.

3 Smyth Report, 12.19 and 12.20.

1 Smyth Report, 12.5.

6 One World or None , McGraw-Hill, 1946 : p. 1.

6 H.M. Stationery Office, S.O Code No. 34-312.* (1946).

151

CHAPTER XIV

THE SEPARATION OF THE URANIUM ISOTOPES

(1) General considerations .

In our discussion of atomic energy, the use and properties of U a35 have
frequently been mentioned, but nothing has yet been said about the process
of separating it from natural uranium, in which it occurs to the extent of 0.7% .
When the existence of isotopes was established, it was realized that they could
not be separated by any chemical process, but from time to time experiments
were made with a view to separating them by making use of some physical
difference between them. Isotopes differ in mass and of course in properties
which are connected with their mass ; nevertheless, it is difficult to find such
a property which gives good prospects of separating isotopes in any quantity,
and prior to 1940 in the case of heavy hydrogen only had it proved possible
to separate isotopes on any considerable scale. Because the mass of heavy
hydrogen was double that of the common isotope, separation was relatively
easy and could be effected by the electrolysis of water ; it was realized that
success in this instance afforded no promise of success in cases like that of
uranium in which the isotopic masses differed only by a few percent., and that
for such cases electrolysis was unlikely to be useful.

(2) Porous barrier method of separation .

In a mixture of gases in temperature equilibrium, every kind of molecule has
the same average kinetic energy, although individual energies are spread over
some considerable range ; this means, on the average, that light molecules
move faster than heavier ones, and it also means that in a mixture of equal
numbers of light and heavy molecules the former make more collisions with
the walls of the containing vessel than do the latter. If we arrange that the
containing vessel is made of a porous material with very small holes in it,
fast light molecules will more frequently enter these holes than heavy slow
ones. If every atom or molecule which enters a hole is able to leave the
vessel through the porous wall, we shall find that the gas issuing is richer in
light molecules than was the original gas. The process by which gas mole-
cules pass through a porous membrane is known as diffusion. It is not
necessary to restrict ourselves to mixtures of equal numbers of light and heavy
molecules, for diffusion produces a similar change in concentration whatever
the initial proportions. It has long been known that this process is capable

152

Chap. XIV the separation of uranium isotopes

of separating ^ light gas from a heavy one ; thus in this way hydrogery**F a
been separated from oxygen or carbon dioxide.

Two points connected with the process are worth further consideration.
The gas that goes through the membrane should be prevented from diffusing
back again, for if this happens, the initial increase in concentration of the
light molecules on one side of the membrane will eventually disappear. To
retain the advantage achieved, the gas must be pumped away immediately it
diffuses from the membrane. The other point is equally obvious. If there
is an increased concentration of light molecules on one side of the membrane,
there must be a decreased concentration on the other side, so that as the
diffusion proceeds the gas in the first container becomes impoverished in
light molecules and there is a steadily decreasing advantage in continuing the
process. If the most rapid increase in concentration is to be achieved, it is
necessary to allow the diffusion of only a small poition of the available gas ;
this, however, is not practicable, because the relatively rapid increase in
concentration is associated with a very small yield. In practice a consider-
able fraction of the gas must pass through the membrane even though this
involves more diffusion stages to achieve a given separation of light and
heavy molecules.

The feasibility of an isotope separation process depends on many factors,
but of these one is of paramount interest and importance : it is a ratio which
we call the enrichment factor. The value of this quantity is obtained by
comparing the concentration ratio of wanted to unwanted components at
two stages of the separation process ; the enrichment factor is defined as the
higher concentration ratio divided by the lower. * An example helps to clarify
the meaning of this term. In natural uranium, the ratio U 236 : U 238 is about
1 : 139. If it is desired to obtain 90% U 23B , the final ratio U 235 : U 238 is 9 : 1
and the necessary overall enrichment factor is 139 x9, i.e., 1251. Or, again,
an enrichment factor of 139 will give 50% U 235 from natural uranium. An
advantage of using this enrichment factor arises when different stages in a
separation plant involve different enrichment factors, for in such a case the
overall enrichment factor, from which the nature of the output product is
determined, is simply the product of the enrichment factors for the various
stages.

Let us determine what enrichment factor can be achieved by the diffusion
method when the isotopes of uranium have to be separated. Unfortunately
it is necessary to make use of uranium hexafluoride, UFa, a substance which

* This quantity is what Smyth 1 calls the separation factor ; his enrichment
factor is obtained by subtracting unity from the quantity used here. As there is no
separation it appeared well to avoid the use of the term “ separation factor.

153

atomic energy Chap

is a solid at normal temperature and pressure, but which vaporizes read
temperatures not inconveniently high. As fluorine consists of a single isc
UF« contains two different types of molecules, U a88 F« and U m F e .* t
difficult to handle because of its corrosive properties, and apart froi
advantages arising because of its low vaporization temperature an
existence of only a single isotope of fluorine, it appears to have few attr;
properties ; it would certainly not have been used in the diffusion proces
a more satisfactory alternative compound been available. As the additi
six fluorine atoms to an atom of uranium increases the mass by 114
the masses of the two types of UF e molecules are 352 and 349, and the
sion process has to be used to distinguish these two molecules, which
in mass by less than 1% and in. average velocity by only 0.43%. Wh<
consider the theoretical enrichment factor in a diffusion process, we fin<
it is equal to the ratio of the mean velocities of the two gases, so that
plant using uranium hexafluoride to separate the uranium isotopes it is 1 .

If wc wish to attain an overall enrichment factor of about 1200 it w
necessary to put the gas through about 1700 stages.

(3) Theory of diffusion separation .

A simple theory of diffusion may be derived by assuming that the numl
molecules diffusing in unit time is proportional to the number of moh
striking the porous membrane. One then finds that each isotope diffu
a rate which is proportional to the velocity of the molecules and to
5 gas passing through the membrane is enriched in the
> a corresponding impoverishment of the gas which ha
entually the diffusing gas is no richer— and might ev<
nat with which the process commenced. In practice i
DU'/o or the gas in each stage was diffused through ihe porous memb
the theoretical enrichment factor for the first fraction of gas is 1.0043, bt
factor falls steadily as the gas diffuses, and by the time half the gas has p
through the membrane it is only 1.0013. The enrichment factor for a
gas which passes through the membrane is theoretically 1.0030. In
experiments, diffusion backwards through the membrane and imp
mixing of the gas to be diffused were found to make the enrichment 1
considerably less than the theoretical value ; the enrichment achieve<
only 1.0014. Apparently this figure was improved upon, for it is cer
not sufficient to give a yield of 99% pure U a38 F« in 4000 stages, a perforr.
which Smyth considers to be possible if each stage has a “ reason*
enrichment factor. This official statement need not be interpreted as me

* Throughout this chapter we take no account of the presence of U 884 c

154

Chap. XIV THE SEPARATION OF URANIUM ISOTOPES

that there were 4000 stages in the diffusion plant or that it produced U M5 F e
of 99% purity.

Let us consider the general arrangement of a uranium diffusion plant. It
is evident that a cyclic process must be used in which the output from one
stage is passed on to other stages ; such a process is often referred to as a
cascade process. It will be appreciated that it is not normally desirable to
discard the impoverished output material from any stage, for this material is
in practice very little poorer than the enriched output of the same stage. It
was considered advantageous to have the impoverished output from one stage
as rich as the input to the stage below, and it was then arranged that this
impoverished output was fed into the stage below that from which it was
produced. For a plant which gives a very small enrichment factor per stage,
this is achieved by passing nearly half the material to the next higher stage and
returning the remainder to the next lower stage. Unless the raw material is
so cheap that the impoverished gas from the first stage can be thrown away, it
is necessary to have a number of stages set aside for handling impoverished
material only. These stages form what is known as the “ stripping ” cascade ;
in practice some hundreds of stages may be required, but the actual number
cannot be determined without knowing the point at which it is more easily
practicable to obtain further supplies of uranium hexafluoride than to add and
operate further stages in the stripping cascade.

The difficulty of the diffusion separation method can only be appreciated
by considering the sizes of the various stages of the plant ; we shall assume
that the size of a stage is equal to the volume of gas handled by that stage in
order to obtain unit volume of output from the plant. To simplify the
discussion we shall first suppose that the concentrating cascade delivers pure
U a38 F 6 , and that the stripping cascade delivers gas in which there is no trace
of U 285 F 6 , even though no plant could be made to achieve such a separation.

We imagine a unit volume of gas introduced at the first stage ; about half
this gas constitutes the enriched output of the first stage and goes through the
rest of the concentrating stages ; the net result of these stages is to remove
sufficient U a88 F« to reduce the enriched output from the first stage to the
concentration at which it entered the stage. In a similar way the stripping
stage removes a quantity of U 238 F 6 sufficient to bring the impoverished
material from the first stage to the concentration at which it entered that
stage. Numerical values show how small are the amounts of U a88 F 0 and
U 285 F e removed, and what a large fraction of the gas is returned to the first
stage for recycling. Suppose that we admit 280 cm. 3 of gas containing 2 cm. 8
of U a88 F 6 . If the enrichment factor per stage is 1.003, we find that after this
gas has gone through the first stage we have nearly 140 cm. 8 of enriched gas

155

ATOMIC ENERGY

Chap. XIV

containing 1.003 cm.® of U a85 F fl and 140 cm.® of impoverished gas containing
0.997 cm.® of U 285 F e . From the enriched gas 0.003 cm. 8 of U 285 F a is removed
by the rest of the concentrating cascade ; from the impoverished gas the
stripping cascade removes 139x0.003 cm. 8 of U a88 F a . Consequently, the
passage of 280 cm. 8 of gas through the first stage yields 0.003 cm. 8 of U 285 F a ;
to yield 1 cm. 8 of U 288 F 6 and 139 cm. 8 of U a88 F a there must pass through the
first stage about 93 000 cm. 8 of natural uranium hexafluoride, and of this
only 140 cm. 8 is new material. Later stages of a diffusion plant are smaller
than the first stage, but the decrease in size depends on the value of the
enrichment factor per stage, and for the case considered above it is about 0.3%
per stage. The smallest stages of the stripping cascade are those handling the
most impoverished material, but in the case of a stripping cascade with an
output of pure U a88 F 8 , or even of very highly impoverished material, the
decrease in size is much slower than for the concentrating cascade.

In practice, of course, the material is withdrawn from the diffusion plant
either enriched or impoverished and not as we have assumed as perfectly
separated products. It turns out that the presence of the stripping cascade
has no effect upon the relative sizes of the stages in the concentrating cascade,
for clearly the stripping cascade is only a device for bringing impoverished
material to the same concentration as in natural uranium so that it may be
acrain, instead of new UF e , as working material for the concentrating
On the other hand, the concentration of U 28fi F a in the output
discarded from the stripping cascade has a great influence on the
of new input material required for a unit output of U 235 F 6 of given

he sizes and number of the concentrating stages are determined mainly
by n, the enrichment factor per stage. For a given volume of output, the
capacities of the individual stages are somewhat affected by the concentration
at which the enriched material is withdrawn from the diffusion plant. If the
overall enrichment is 100 or more, the output of 1 litre of U 235 F« necessitates
280

the passage of litres of natural UF 6 through the first stage, so that for

n — 1

an enrichment per stage of 1.003, the passage of about 93 000 litres through
the first stage still yields 1 litre of U a86 F a . It is vital that n should be as close
as possible to its theoretical value ; any increase in n results in a reduction
in the number of stages and a decrease in their size.

If a diffusion plant is arranged to give an overall enrichment factor of 139,
the output will consist of material containing 50% U 28H F a . In this case,
supposing again that the enrichment per stage is 1.003, the passage of 93,000
litres through the first stage will yield 2 litres of material at this concentration.

156

Chap. XIV THE SEPARATION OP URANIUM ISOTOPES

If then the size of each stage is expressed in terms of the volume of output
material,* the absolute volumes at the early stages will depend on the concen-
tration at which the enriched material is withdrawn from the mn^ntrating
cascade. In the case of overall enrichments in excess of 100, the sizes of the

early stages form a geometric series with a common ratio close to - .

Many features of an ideal diffusion plant can be appreciated by considering
the way in which the volume of circulating gas varies from stage to stage. In
order to make the matter clear, some figures have been obtained for the case
of a plant with an enrichment factor of 1.003 per stage. It is assumed that
there are seventeen hundred stages in the concentrating cascade, sufficient to
give an overall enrichment of 163 and to delivei U 2S5 F, at 54% purity. The
stripping cascade is assumed to contain about 232 stages, so that the impover-
ished UF, contains just half the U m concentration of natural ur anium in
Fig. 36 are shown the first few stages of the stripping and concentrating
cascades. Each stage is represented by a circle ; the horizontal line to the
right of each circle carries enriched material to the next higher stage and that
going to the left carries impoverished material to the stage below. The
vertical lines carry the input material either after being enriched by the stage
below or impoverished by the stage above. Inside the circle repr esentin g

New Material Input

* Smyth® stated yield in terms of the U Ma F« content of the output.

157

ATOMIC ENERGY

Chap. XIV

each stage is a number which gives, as do similar numbers on each supply or
output line, the number of litres of gas passing through it for 1 litre of output.
The values given are those which satisfy the condition that the impoverished
output from one stage has the same U 2SB F e concentration as the supply
material to the stage below. The diagram shows how large is the gas circu-
lation in the early stages. It will be noticed that in the concentrating cascade
the net flow of material from any stage to the one above it is just 1 litre, as
it must be, because of course gas is not accumulating in any part of the cascade.

The new material admitted to the system is 151 litres of which is

U 2SB F«. The output of enriched material is 1 litre containing 0.54 litres of
U 286 F 6 ; the balance of the U 23B F e , amounting very nearly to 0.54 litres, is
discarded from the stripping cascade.

Fig. 37 depicts the last few stages in the concentrating cascade, the begin-
ning of which was illustrated in Fig. 36 ; the only notable features of these
stages aie their small size and the rapidity with which it decreases.

In Fig. 38 is a graph showing the stage size throughout the assumed ideal
diffusion plant, again in terms of one volume of output material containing
54% U 285 F e . This shows that nearly half the stages handle more than 4000
times the volume of the output material and, as may be estimated from the
graph, the total circulation of material through all stages of this concentrating
cascade exceeds ten million times the volume of ouiput. In Fig. 38 there

Fig. 37. Output stages of an ideal uranium diffusion plant.

158

STAGE SIZE

Chap. XIV

THE SEPARATION OF URANIUM ISOTOPES

STAGE NUMBER

Fig. 38. Enrichment and stage size throughout uranium diffusion plant.

159

enrichment

ATOMIC ENERGY Chap, XIV

is also a curve showing the enrichment of the material used in any stage of
the plant.

It will be realized that the numerical values are theoretical ones, appro-
priate to an ideal diffusion plant. In actual practice, adjustments must be
made to allow for the properties of the apparatus which is to be employed.
It is to be expected, however, that such changes will not require any great
departure from these general conclusions relating to an ideal diffusion cascade.

(4) Some features of a diffusion plant .

It is of interest to consider briefly some practical details of a diffusion plant
and to examine, in particular, the type of porous membrane required an d the
apparatus needed to pass the gas from stage to stage. According to the
information published, it was proposed to take gas at atmospheric pressure
and to allow it to diffuse through a porous membrane into a region where
the pressure was maintained at about 0. 1 atmosphere. To obtain the highest
possible enrichment factor per stage, it was necessary to use a membrane with
very small holes in it, and in order to diffuse gas rapidly through this mem-
brane very many holes were required. It was necessary to use me mbranes
which were not attacked by the diffusing gas and in which the tiny holes of
less than 10~ fl cm. diameter neither clogged nor enlarged with use. Added to
these very severe requirements was the need for using a membrane structure
with sufficient strength to withstand a pressure difference of 1 atmosphere.
For a large scale plant many acres of this type of porous membrane are
required. The plant requires many pumps, not only to compress the diffused
gas from 0.1 atmosphere to 1 atmosphere at which pressure it enters the next
higher stage, but also to raise the pressure of the impoverished ga g and to
convey it to the stage below. It was essential that these pumps, numbering
some thousands, should neither leak nor corrode, and this also was a re-
quirement of the whole of the gas circulating system. The problem of
connecting miles of piping in such a way that there are no leaks, is one to
which there is no simple solution. It is necessary to have reliable workmen
to connect the pipes, using the best possible methods of making joints, and
then to ascertain whether any leaks exist and if so to find them. To-day,
this is practicable, even on a large scale ; the task of finding leaks has been
made much easier by a new method of leak detection in which a simple mass
spectrograph is used to look for the presence, inside the apparatus, of a
suitable testing gas to which a suspected leak is exposed. When the diffusion
plant is free from leaks, U 285 will be lost only because of chemical action
between the working gas and materials within the system, or because discarded
impoverished material contains appreciable quantities of U a8S . The structure
of the plant was such as to avoid corrosion of the metal forming the gas

160

THE SEPARATION OF URANIUM ISOTOPES

Chap. XIV

circulating system, and to provide negligible opportunities for reactions
between uranium hexafluoride and materials which were used to make vacuum
tight seals in various parts of the equipment ; consequently the m ain loss
arose because of the U a3B content of the output from the stripping cascade.

The diagram of the diffusion cascade process shows the equilibrium state
when the material taken into the plant is equal to the output. When the
plant is started up, however, the only material available is UF e made from
natural uranium, and of necessity the operation of the plant commences with
the use of only the input stage. Each stage of the plant requires a finite
amount of gas to enable operation to occur at all, and for this reason the
plant must work for a long period before all the stages are in operation. Only
after the elapse of a considerable time has enough enriched material accumu-
lated to allow the operation of the higher stages of the plant, and for this
reason there is a start up period in which there is no output although material
is continuously entering the diffusion plant. Another aspect of this property
of the diffusion plant is the necessity for having locked up within it large
quantities of uranium hexafluoride, some small fraction of which is very
considerably enriched. The provision of this working material is an essential
requirement, and during a continuous process it represents a stock of uranium
hexafluoride from which no IP 35 is obtained. The disadvantages of having
a large stock of working material in the early stages of the plant are not par-
ticularly serious, for, although the bulk of the locked up material is actually
in these stages, it has not been greatly enriched. On the other hand, in a
plant using 4000 stages to prepare 99.3% U- 36 , 2000 stages are required to
convert 50% U 235 into the desired product, and the holding up of such valuable
working material within these stages is a great disadvantage. Despite the
suitability of the diffusion plant for the large scale handling of material
containing low concentrations of U 230 , it is possible that a different method,
involving the holding up of smaller quantities of enriched material, is desirable
for the final concentration processes. The inconvenience of the delay in
obtaining output and the large stock of material held inside the plant are
necessary consequences of a process in which there is only a small enrichment
factor per stage. To minimize these disadvantages, the diffusion plant must
be designed so as to reduce, as far as practicable, the amount of material
required for the operation of a single unit of the plant.

This brief description of the diffusion plant gives an inadequate picture of
the difficulties of putting it into operation. Construction of the plant at
Oak Ridge, Tennessee, was commenced in the summer of 1943 but it was not
until early in 1945 that the immense plant was in successful operation. A
photograph of the exterior of the plant is shown in Fig. 39. Rumour had it
that the Manhattan District Engineers had great faith in the diffusion plant,

161

L

ATOMIC ENERGY

Chap. XIV

Fig. 39. The porous barrier diffusion plant at Oak Ridge, Tennessee.

(Reproduced by courtesy of the War Department, U.S.A.)

that an eminent scientist had given his opinion that the plant would not work,
and that in fact there were superhuman difficulties to be overcome before it
would work. At length the rumours ceased. It was known that the diffu-
sion plant was working, although, of course, no details were available. From
official statements made since the end of the war, it is apparent that the diffu-
sion plant is the most satisfactory and economical means of separating the
isotopes of uranium, and that this separation plant alone is to be kept in
operation in times of peace. Its performance justifies the confidence of the
Manhattan District Engineers and of those British physicists who also were
convinced of the feasibility of using a diffusion plant to separate the uranium
isotopes.

(5) Electromagnetic separation method.

Although the diffusion process has been so successful, the first supplies of
fissionable material were produced by a different method which in principle
and in operation is just a mass spectrograph. As has long been realized, if

162

Chap, XIV THE SEPARATION OF URANIUM ISOTOPES

a mass spectrograph will distinguish isotopes and give their masses, it will also
permit their separation. This method was used many years ago by Oliphant 8
to separate the lithium isotopes Li° and Li 7 , and it was used more recently by
Nier 4 to separate the uranium isotopes. The main difficulty in using it, even
for small scale separations, is that of devising a satisfactory means for trans-
forming the material being handled into atoms carrying single positive
charges, or, as they would normally be described, into singly charged or
monovalent ions. In previous isotope separations using the electromagnetic
method, the ion beams were minute and the yield of pure isotopes was
measured in micrograms (10"°g.).

The Faraday, the amount of electricity which in electrolysis transports 1 g.
equivalent of a substance, is the rather large charge of 9.65 x 10 4 coulombs.
This means that if we can readily produce uranium ions in a mass spectro-
graph, we shall require to pass, for example, an ion current of 1 ampere for
27 hours in order to transport 238 g. of uranium, and of this only about 1 .7
g. is U 236 . A mass spectrograph, kept working continuously with a current
of 1 amp. of mixed uranium monovalent ions would require a period of
nearly two years to separate 1 kg. of U 835 . A calculation of this type shows
that this method of isotope separation is impracticable on any adequate scale
unless it is possible to build mass spectrographs of such size or in such
numbers that they provide a total uranium ion current of about 100 amp. In
Nier’s experiments, in which he used a mass spectrograph to obtain small
quantities of U 23C , the ion current was less than 1 microamp.

(6) General arrangements of the electromagnetic method .

In Berkeley, California, the small cyclotron was dismantled in the autumn of
1941 and the magnet, which gave a uniform field between 37" diameter pole
pieces, was used for experiments on the separation of uranium ions. It was
proposed to arrange a strong electron beam passing in the direction of the
magnetic field. Through this beam was to diffuse the vapour of a salt of
uranium so that there was decomposition and ionization of the vapour ; ac-
celerating electrodes in the neighbourhood of the electron beam were to be
maintained at a high negative potential with respect to the beam so as to
accelerate positive ions which diffused from the region traversed by the
electrons. Although success was finally achieved, there were at first some
obvious sources of difficulty. Would it prove possible to obtain strong
beams of uranium ions, and if so would the electrostatic forces of repulsion
between the ions in the beam be strong enough to disperse the beam and
make it impossible to obtain a separation of the uranium isotopes ? Further-

163

ATOMIC ENERGY Chap. XIV

more, was it possible to arrange that a reasonable fraction of the ions drawn
from the ion source consisted of monovalent uranium ions ?

Let us consider some of these points briefly and in doing so examine some
general features of the method. In Fig. 40 is a plan of the arrangements
between the poles of the magnet ; it is assumed that the magnetic flux is
upwards and at right angles to the plane of the diagram. The ions from uie
source S, which was of the nature mentioned above, are accelerated by suitable

Fig. 40. Plan showing the arrangement for electromagnetic separation.

potentials and pass through slits S x and S 2 ; the methods of electron focussing
of beams for cathode ray tubes indicate the arrangements of distances and.
potentials which are likely to give a well focussed beam. Suppose that ions
of mass m, carrying the electronic charge e, fall through a total poten-
tial V. Then their velocity is /^— and the radius of curvature of the path

V m __

they describe in a magnetic field of induction B is *. In practice

the ions are allowed to describe semicircles ; the diameters of these will be
proportional to the square roots of the masses of the ions ; in the case of the
isotopes of uranium the diameter of the U 236 ion path is about 0.6% less than
that of the U 288 ions. If these paths are described in the field of an electro-
magnet with a pole diameter of 37*, the greatest possible separation of the
two beams is less than 6 mm.

This shows that the separation of uranium isotopes will be possible only
* These relations are easily derived. This is done in Appendix I, p. 182.

164

Chap. XIV THE SEPARATION OF URANIUM ISOTOPES

with beams which can be brought to a focus with a width of a few millimetres,
and, as may be shown from theory, or indirectly from experience with the
beams of cathode ray tubes, it does not appear possible to obtain good focus
with a beam 1*5 metres in length unless it carries only a small current. It
was considered, however, that conditions might be made more favourable by
the magnetic field which seriously restricts the motion of slow ions or electrons,
and it was found in fact that in some circumstances positive ion beams in a
magnetic field are not subject to undue spread from mutual repulsion of the
ions in them, a result that must be attributed to the presence of negatively
charged particles within the region traversed by the beam, and to the conse-
quent existence of attractive forces which hold the beam together. Because,
of this fortunate circumstance, it proved possible to obtain well focussed ion
beams of much greater current densities than had been anticipated, but in
order to achieve the best results it was necessary to use high potentials for
accelerating the ions.

The final choice of accelerating voltage will depend upon many factors,
of which some are economic, but it seems reasonable to say that voltages
should not be lower than 20 kV and will not be much higher than 50 kV.
Uranium ions which have been accelerated by 20 kV describe a circle of
radius 0.5 metres in a field of about 0.6 webers per metre 2 (6000 gauss), a field
which though high is not to be considered unreasonably difficult to provide.
Nevertheless, this simple calculation gives some indication of the magnitude
of the problem which was to be solved, for even if all the ions from the ion
source were uranium ions — and actual experience was far less favourable than
this— it was necessary to make available apparatus to deliver the order of
100 amperes at a potential of 20 kV or more and to provide strong magnetic
fields in large evacuated tanks in which these beams described their paths.
If the separation method was to be successful, it was further necessary to
arrange a high degree of constancy of both the magnetic field and the accelera-
ting voltage ; deviations of more than a very few parts in one thousand could
not be tolerated.

These difficulties were in fact rather more serious than can be indicated
here, but they were far less troublesome than those arising from attempts to
obtain ion beams carrying large currents. It was necessary, among other
things, to arrange the apparatus so as to make use of rather divergent beams
from the ion source, but it was essential that the use of wider beams should
not cause any marked deterioration of the focus. Fortunately, a device
employing a localized ion source to produce ions which have a semicircular
path in a magnetic field is well adapted to the use of wide beams ; this can
be shown by drawing several circles of the same radius with neighbouring

165

ATOMIC ENERGY

Chap. XIV

p

Fig. 41. A divergent beam from O des-
cribes a circular path of constant diameter
OP and focusses close to P.

centres and with one point O in com-
mon. This has been done in Fig. 41
where it is seen that all these circles
cut the line OX at points which are
quite close together. If these circles
represent ion paths, a receiver placed
near the point P will collect almost
all the ions from the rather divergent
beam arising from the point O. The
quality of focus can be somewhat
improved, for a given beam diver-

gence, by using a magnetic field which, instead of being uniform.

has spatial variations of the correct form. Although the use of such

a field is of real advantage, it is still the case, just as is seen in Fig. 41, that some

ions meet the line OX rather closer to O than is desired. This is particularly

unfortunate, for if the diagram represents the paths of U 238 ions the U 230
collector is on the side of P nearer O just where unwanted ions, that form
the tail of the U 888 beam, will fall into it. Clearly, the divergence of the beam
can be reduced if desired, and if this is done, the product U 235 will be purer
in quality and smaller in amount ; it is essential to preserve the proper
balance between large yield and high purity. The enrichment factor achieved
by this method is very high, but as it is certainly not sufficiently high to give
a suitable product in one stage, it is possible to arrange to obtain large yields
in the first stage and high purity in the subsequent one.

(7) Advantages and disadvantages of the electromagnetic ?nethod .

The electromagnetic method has many desirable features, particularly that of
making use of a considerable number of independent units, each of which
consists of a high voltage supply and control unit, together with a source of
ions and a collector in a vacuum tank through which passed the necessary
magnetic field. The operating plant was set up in Oak Ridge, Tennessee,
and made use of ion sources and collectors developed in the Radiation
Laboratory of the University of CaUfomia. Fig. 42 is a photograph of a
portion of the electromagnetic separation plant. Because of the smallness of
the units into which the plant was divided, it was possible to continue develop-
ment of the separation processes during the running of the plant ; improve-
ments which were decided upon were thus available from time to time, and
when conditions suited these improvements were quickly put into use. These
features of the apparatus used in the electromagnetic plant were of the greatest
advantage in the circumstances which existed at the beginning of 1944, when
it was urgently necessary to obtain appreciable supplies of reasonably pureU 885 .

166

Chap. XJV

THE SEPARATION OF URANIUM ISOTOPES

On the other hand, the apparatus was complicated and expensive, and
required skilled personnel for its operation. The most serious objection to
the method arises because only a small fraction of the uranium in the ion

Fig. 42. A portion of the electromagnetic separation plant at Oak Ridge, Tennessee*
(Reproduced by courtesy of the War Department, U.S.A.)

source actually finds its way into the ion beam ; the remainder, which
deposits itself on various parts of the vacuum system within which the separa-
tion process is carried out, has to be collected from time to time and re-treated
chemically for subsequent use. This feature of the process, and the compli-
cation of the necessary chemical treatments, bring about a greater hold up of
material than might have been anticipated; in addition, it is essential,
especially when using material with high U a3G concentrations, to take the
greatest precautions to avoid loss. It is probable that the electromagnetic

167

ATOMIC ENERGY

Chap. XW

separation method is best suited for small amounts of material ; if its use is
justified in the process of separating the uranium isotopes, it will be in con-
junction with the diffusion process which is best suited for handling large
amounts of material and for achieving an initial enrichment which provides
a suitable material for final treatment by the electromagnetic method.

Of the atomic bombs which were dropped on Japan, the Hiroshima bomb,
it is said, made use of U 23B . The separation of the necessary material de-
pended upon both the diffusion plant and the electromagnetic method ; it
is reasonable to suppose that the existence of the necessary quantity of U 23B
depended in no small measure upon the success of the electromagnetic
separation method. Whatever the truth of this surmise, it is certain that the
electromagnetic method made available the first substantial supplies of fission-
able material. In view of the very small yields obtained from pre-war
attempts to separate isotopes by the electromagnetic method, the successes
achieved in Berkeley and in large scale operation in Oak Ridge, Tennessee,
are most remarkable. They serve to remind us again of what scientists can
accomplish by team work where the leadership is of high quality and adequate
facilities are available for the tasks in hand.

REFERENCES

1 Smyth Report, 9.8.

2 Smyth Report, 9.9.

3 Oliphant, Shire and Crowther, Proc. Roy. Soc., A 146 , 922, 1934.

4 Smyth Report, 11.14 and Nier, A.O., Phys. Rev., 55 , 150, 1939.

168

CHAPTER XV

ATOMIC ENERGY AND THE FUTURE

(1) Future organization of scientific research work .

It is natural to contrast the manner in which scientific problems have been
solved during peace and war. In peace time, fundamental scientific dis-
coveries originated partly from the efforts of a few leaders and their assistants
and partly from very small scale experiments which were carried out elsewhere
by a relatively large number of individuals. It had always been maintained
that the most fertile soil in which fundamental scientific theories grow is
that of freedom for the individual to investigate what interests him. It is
true that the problems of the atomic bomb were concerned only in part with
fundamentals, but it is certain that these problems were solved, not by many
individuals investigating whatever interested them, but by wise leadership
which directed the work of very large teams of capable scientists. They
worked hard because they were convinced of the value and importance of
their work, and success was achieved because every effort was directed
towards a single goal.

In normal circumstances the scientist is a cooperative individual, for he likes
to discuss with others his ideas and his experiments ; in the abnormal cir-
cumstances of war time research on atomic energy, cooperation was greatly
extended by frequent discussion meetings in which day to day results were
set forth by the individual workers who were carrying out experiments. Good
suggestions were welcome from whatever source. The scientist had not
forgotten his individualism ; success in his own problem was still a spur to
his efforts but he realized, too, that the success of the atomic bomb was of
greater importance. If his work was not making a positive contribution to
the atomic bomb he realized that there was every justification for stopping it.
If ever the truth is told it will be found that in the atomic bomb project
much work was wasted ; investigations were stopped, not because they were
leading nowhere, but because they were unlikely to contribute much to the
immediate objective, that of making an atomic bomb.

Success itself must not delude us into the belief that the organization of the
atomic bomb project is representative of the correct way to do all research
work, nor should the novelty of the organization prejudice us against it. If
we consider the Los Alamos group alone, we find that its successes arose in
part because there existed there a physics research laboratory which Smyth

169

ATOMIC ENERGY

Chap. XV

claims, apparently with justice, to have been the best equipped in the world.
In addition, in the laboratory were grouped together some of the ablest
scientists in the world. Success was achieved because of the enthusiasm and
ability of the workers and the facilities at their disposal. It would appear
likely that in similar conditions science can achieve in peace time just as much
as has been achieved in atomic bomb research during the war. Scientific
research work in the near future must, similarly, be carried out by teams of
enthusiastic workers, well led and having at their disposal adequate facilities
for their work. This will cost money, but money spent on investigating the
right problems may return dividends which are enormous in proportion to the
expenditure made. The development of atomic energy is a case in point ;
in peace time this can hardly hope to develop at quite the rate achieved
during war, but it can be developed rapidly if the countries interested are
prepared to devote the necessary resources to the work. Expensive appara-
tus and a considerable staff of competent scientists will be required, but the
mere spending of money on these things will not achieve results quickly. Even
the scientist is human, and he will not work with the enthusiasm that can be
so productive unless the support his work receives is such as to convince him
that the Government for which he works is in real earnest in its desire to push
ahead with the development of atomic energy. If the proper steps are taken
we may see great progress in this field during the next five to ten years.

(2) Atomic bombs in war.

Unfortunately, however, there are other possibilities. Without the slightest
doubt, the atomic bomb is an ideal weapon of aggression. A few bombs,
discharged on vital places in Britain, would give rise to such destruction that
this country would have little or no prospect of waging a successful war. It
is sometimes assumed that in the next war atomic bombs will not be used
because of their great destructive power ; this view is supported by the argu-
ment that in somewhat similar circumstances poison gas was not used in the
recent war. It is probable, however, that possessors of atomic bombs will
use them if there appears, on balance, to be real advantage in doing so,
especially since the Allies used them against Japan ; it is hardly to be expected
that any future enemy of ours will hesitate before raining atomic bombs on
this country or even on the United States of America if by doing so the success
of his arms seems likely to be more quickly assured. Thus, the most sensible
assumption is that atomic bombs are certain to be used in any future war
efforts of statesmen must be directed towards preventing war
rather than towards making international laws which, even if observed, would
only make wars a little less destructive and unpleasant. The only possible

170

Chap. XV ATOMIC ENERGY AND THE FUTURE

alternative — and in fact this is not practicable — is that of ensuring that no
possible enemy possesses atomic bombs.

Now unfortunately, there is no real hope that the present state of affairs, in
which the U.S.A. is the sole possessor of atomic bombs or of fissionable
material, can continue for long. Great Britain, which has cooperated with
the U.S.A. in the development of the atomic bomb, intends to carry out
investigations of atomic energy, and for this purpose it will be necessary to
manufacture plutonium and perhaps also U 235 ; the experiments carried out
will make available supplies of the materials which are suitable for producing
atomic bombs and so it will be very difficult for other countries to be certain
whether atomic energy experiments are directed primarily towards the deve-
lopment of sources of industrial power or towards the accumulation of atomic
bombs or of the material from which to make them. This country would
show an undue confidence in the prospects of avoiding future war if it failed
to take reasonable precautions for securing a supply of the material from
which atomic bombs may be made.

What is reasonable for us is just as reasonable for others, and there can
be no doubt that many powers, great and not so great, will consider that
they can only insure future freedom to develop as they wish if they too possess
supplies of atomic bombs. It is doubtful whether the countries of the world
would agree not to make atomic bombs, but even if they did so the menace of
the atomic bomb would be but slightly reduced, for as long as a country can
make or separate fissionable material for experiments on atomic energy, that
country will not have much difficulty in making atomic bombs.

Now the technical processes used in separating uranium isotopes or in
arranging for the manufacture and extraction of plutonium are costly and
difficult, and it is true that the Americans, with perhaps the British and the
Canadians, have knowledge and experience of these methods that is denied to
other nations ; in this respect the U.S.A. particularly has a favourable posi-
tion. Nevertheless, as the Allied atomic bomb project was successful in
achieving the atomic bomb without prior experimental proof of its practi-
cability, other nations who wish to make atomic bombs or to develop atomic
energy will at the worst be more favourably situated than were the Allies in
1939, and for this reason the present Allied or American monopoly must be
regarded as unlikely to endure. There is no use in an agreement not to make
atomic bombs, unless there is also an agreement to make no fissionable
material ; but then the development of atomic energy would be tremendously
retarded if such an agreement were observed, and doubtless a proposal for it
would receive negligible support. Progress in the development of atomic
energy is likely to mean progress in the size and destructiveness of atomic

171

ATOMIC ENERGY

Chap. XV

bombs, and the only real hope for civilization lies in appreciating that technical
progress in this and in other spheres makes war much more destructive ; the
only way of avoiding destruction is to have no war, and this endeavour, not
the making of rules in an attempt to control the use of atomic bombs, must
be the ultimate purpose of statesmanship to-day.

There is another difficulty of a more obvious type. If it proves possible
to use plutonium or U 285 as a source of power in engines, it means that these
materials will find their way into the hands of an appreciable number of
people. Can precautions be taken to prevent some of these people pooling
their supplies to make an atomic bomb ? This matter has recently been
discussed publicly, and it has been made clear that a safeguard is easily
available. It will be appreciated that although nearly pure U 386 is essential
for an atomic bomb, even natural uranium can be used in a very large pile
and so samples of uranium with about 50% U 235 would make possible the
release of atomic energy in a controlled reacting pile of reasonable size, even
though this material would be quite unsuitable for use in an atomic bomb.
Doubtless it could be made to explode, but as the material would not permit
the development of a fast-growing chain reaction the explosion would only
be comparable with those produced by ordinary means. Consequently, for
such atomic energy processes as may prove feasible, uranium in which the
proportion of U 235 is ten to one hundred times that occurring in natural
uranium may be entirely satisfactory for every possible process except that
of making atomic bombs. There would then be no objection to the wide-
spread distribution of such material, unless it was thought that it was likely
to be used as the raw material for a plant that was preparing pure U 235 . From
the statements which have been made, it is apparent that it is also possible
to combine with Pu 289 a plutonium isotope which ensures that the mixture is
useless for making atomic bombs. Details of the source or mass number of
this isotope do not appear to have been released. It is clear, however, that,
in the same way as in the case of uranium, such a mixture of plutonium
isotopes may be eminently satisfactory for the production of atomic power
in a controlled chain reaction, despite its inability to give a fast-growing chain
reaction in an atomic bomb.

(3) Atomic energy for small power plants.

Let us try to decide what peaceful uses can now be made of atomic energy.
There is no doubt that U 23c and Pu 289 are capable of being used to develop
heat energy as a result of a controlled chain reaction. The arrangements
required to achieve this are fairly clear, at any rate in outline ; the active
material should be used with a moderator so as to lengthen the life time of a
generation of neutrons and to slow them down to speeds at which they are

172

Chap. XV ATOMIC ENERGY AND THE FUTURE

most likely to be captured. Provision must be made for the use of neutron-
absorbing rods so as to make it possible to maintain the reaction, and the
power output, at the desired level, and these should be automatically con-
trolled. In very many respects the unit which develops atomic energy from
U 235 or from Pu 23fl is like an atomic pile designed for the use of natural
uranium, although, of course, it is not essential here to use a lattice structure
in which the uranium is concentrated in a number of discrete masses immersed
in a large volume of moderator ; furthermore the structure will be much
smaller than the type of atomic pile used for the manufacture of plutonium.
It seems likely, however, that it will be larger than an atomic bomb, even
though it contains less active material.

Many people have been led to believe that the day may come when pluto-
nium power units will be built into motor cars, but if present estimates are
at all accurate this is most unlikely. If such an arrangement were possible
it would present the fuel problem in a novel form ; for the fuel would be
purchased with the car and it is likely that what remained of it would still be
of great value after the car was mechanically useless. If we estimate the
running life of a car as being 5000 hours and assume that it develops 40 kW,
we find that in all it develops 2 x 10 6 kWh, the amount of energy which is
released by the fission of 8 g. of uranium ; hence this is the quantity of Pu aa ®
or U 235 which would be consumed during the life of the car and small though
this amount is, it is likely to be expensive. It is probable, too, that many
times this quantity of material will have to be carried in order to achieve the
necessary liberation of atomic energy. Now although these difficulties may
prove to involve serious financial problems, there are technical difficulties
which are even more troublesome. In the first place there is the emission of
radiation which accompanies the operation of a pile ; although a motor car
power unit is a small one, the assumed power production level is associated
with radiation comparable with that from 40 kg. of radium, and provision
must be made to protect the driver and his passengers from such intense
radiations. This can be achieved by surrounding the source of atomic power
by a sufficient thickness of concrete, the actual thickness depending upon the
precise properties of the radiations emitted ; but unless these radiations are
much less penetrating than those from radium, it appears that the necessary
thickness of concrete is not less than 6ft. The advantages of an atomic energy
motor car fade away when it is found that its use involves encasing the source
of powei in so large a sphere of concrete, the inconvenient shape and size of
which are more acceptable than the mass, which exceeds 50 tons.

If atomic energy units are not suitable for driving motor cars, can they be
used in railway locomotives or on board ships ? Here the prospects are

173

ATOMIC ENERGY

Chap. XV

better. In the case of a railway locomotive, weight within reason is an actual
advantage, and the possibility of placing the power unit at a considerable
distance from the engine driver and of surrounding it with a large mass of
concrete or of other absorber of radiation does not seem to be unreasonable.
Even here, however, there are problems to be overcome. The fission products
must not be allowed to escape, or theie will be serious dangers of radioactive
poisoning from these materials. Furthermore the satisfactory performance
of this source of atomic power depends on the effects, on the controlled
chain reaction, of the fission products which are produced as atomic power
is released. If these materials absorb neutrons, and are produced in sufficient
quantities, there will be difficulties in maintaining the chain reaction, and the
liberation of power may cease.

This brief review of the feasibility of using plutonium in relatively small
scale power units is speculative and it is subject to modification as more
information becomes available. It does seem reasonable to suppose, however ,
that a locomotive or a steamship could be driven by heat from a small atomic
energy unit, but the means for achieving this will require to be examined and
it will be necessary to test and perfect any arrangement that appears to have
good prospects of success. The technical problem is not by any means the
only one ; atomic energy will not be used widely in the way suggested unless
it is economically attractive, but this cannot finally be determined until the
relevant technical problems have been solved.

(4) Atomic energy for large electrical generating stations .

It will be appreciated that atomic piles like those at Hanford liberate very *
large amounts of heat energy, and it appears possible that use can be made of
some of it. It will be remembered that this heat is liberated in the uianium
slugs from which it is conducted to some cooling fluid ; in the case of a pile
operated for the production of plutonium it has been arranged to keep the
ura n iu m slugs at a relatively low temperature. On the other hand, the
requirements of a pile operated for power production are those dictated by
the thermodynamics of heat engines ; considerations which are well known
and which arise indirectly from the second law of thermodynamics, show that
the greatest efficiency results if the source of heat is at the highest possible
temperature. Hence, if the atomic pile is to liberate energy to be used in
heat engines for the production, for example, of electrical power, the uranium
slugs must be operated at a high temperature and the heat developed within
them must be transferred at a comparable temperature to the working fluid
of the heat engine. When account is taken of the processes occurring within
a pile, it is evident that the problem of making efficient use of the heat energy
liberated is one that may not be simple to solve, although, in view of the

174

Chap. XV ATOMIC ENERGY AND THE FUTURE

difficulties which have already been overcome in connection with the develop-
ment of atomic energy, it is likely that a satisfactory arrangement will even-
tually be devised.

It would appear also that the possibility of using an atomic pile as a source
of heat will depend largely on the time for which the pile will run without
replacing the uranium slugs. If it turns out that the fission products soon
accumulate to a sufficient extent to absorb many neutrons and stop the
operation of the pile, it will be necessary to remove the uranium and extract
the fission products by chemical treatment long before the fissionable material
within the uranium is so greatly depleted as to make it useless for the liberation
of atomic energy. This may prove a serious disadvantage, in view of the
difficult nature of the necessary chemical processes. It is rather unfortunate
that we cannot see any way of using atomic energy except by allowing the
fission energy to be converted into heat and then using it in relatively inefficient
heat engines. Initially the greater part of the fission energy exists in the
electrical repulsion of the two fission fragments ; subsequently it is trans-
formed into heat energy, and of this only a portion can be converted into
mechanical or electrical energy for industrial uses.

What has been written already in this chapter assumes that the separation
of U 235 from natural uranium will continue to be a difficult and expensive
process. Although such an assumption appears to be justified, we should not
overlook the consequences that would arise if a simple, cheap and efficient
method of isotope separation were devised. On the one hand, the difficulty
of producing atomic bombs would largely disappear ; if the necessary raw
material was available, they might be no more troublesome to produce than
motor cars, and any nation which was favoured by the possession of uranium
supplies would be able to build up stocks of atomic bombs. On the other
hand, the liberation of atomic power could then be effected by using uranium
which had been enriched in U 235 as described in the section above, with advan-
tages of economy and convenience over the alternative of using larger piles
operating on natural uranium. In some cases the use of puie U 235 might be
advantageous, although it will be appreciated that some admixture of U 288 is
usually desirable. Not only does this prevent the occurrence of a fast-
growing chain reaction, but it results in conversion of U 238 into fissionable
material ; for reasons of economy it is better to capture neutrons in U 238 — or
in Th 232 *— than to allow them to leave the pile or be absorbed uselessly.

(5) Uranium supplies .

In connection with the future of atomic energy a very important question is
the availability of uranium. In terms of present knowledge, it will not be

* See footnote, Chap. XI, p. n z.

175

ATOMIC EMERGY

Chap, XV

useful to contemplate the large scale use of atomic energy unless there are
large supplies of uranium which can readily be obtained. The magnitude of
workable uranium deposits is a matter of some doubt. In order to obtain
some idea of the quantities required annually, let us consider what would be
involved if the whole electrical supply of Great Britain was generated from
heat liberated in uranium fission. The public supply of electricity provides, on
the average, 5 million kW, or 120 million kWh daily. This is the amount of
energy liberated on the fission of about 12 lb. of uranium ; of course this
heat energy would not yield so much electrical power ; losses, and the low
thermodynamic efficiency of a heat engine, would result in giving in the form
of electrical energy only about i of that liberated in fission. Nevertheless,
the amount of U 236 necessary to produce the total electrical supply for this
country is amazingly small, for it requires the consumption of some six tons
of fissionable uranium annually. In practice, it is not likely to be economi-
cally profitable to extract U 285 from natural uranium, and it is consequently
necessary to contemplate making use of natural uranium ; however this may
be, the natural uranium requirement is found to be about 1000 tons a year,
provided that use is made of the whole U 235 content of uranium. To achieve
so much is unlikely, so that we estimate the uranium requirements at a few
thousand tons annually for the production of the electric power at present
generated by the public supply, and perhaps a few tens of thousands of tons
annually for the amount of electric power that must be used here if we are to
remain a great manufacturing nation. Regarded even from the point of view
of world consumption, the amounts required are small compared with world
consumptions of coal, steel, and many metals of commerce. The mining of
this uranium is not a major task, provided that it occurs in sufficient amount
in rich deposits.

Estimates based on knowledge of the size of known high grade uranium
deposits appear to discourage the belief that there is sufficient uranium
available for long term power production on a large scale,* but against this
we must remember that uranium has not heretofore been regarded as a valuable
mineral for which intensive prospecting was justified. Uranium is widely
distributed in small amounts throughout the rocks found on the surface of
the earth, and it may well be that the new interest in uranium will lead to
the discovery of large new sources of supply. Indeed, this may have occurred
already ; information concerning new uranium deposits is regarded as a
military secret, and details of success or failure in locating useful deposits are
not at present available.

It is clear that there are important problems— technical, geological and eco-
natuMu^w^ Pli ° r t0 1939 haVe 136611 estimated to amount to 50,000 tons of

176

Chap. XV ATOMIC ENERGY AND THE FUTURE i .

01

nomio— to be solved before atomic energy can be used on any , Jverc*'inin>j
providing industrial power. There seem to be good prospect* fly quickly it
the difficulties they present and possibly this can be done i" 11 ! j|n* licKl til
sufficient effort is applied. Although this country was early 1,1 |,^c led to
the development of atomic energy, the circumstances of the lai ge

such a great relative advancement in the U.S.A. that a P tt l (he dctelop
effort will be required here if British inventiveness is to play. '" Lpahililie-.
ment of atomic energy, the part which is commensurate with
Unfortunately, the development of nuclear physics, which 'fJIL.d h> the
to advances in methods of using atomic energy, is greatly huuvJ 109 ™ urittfi the
lack of information concerning experimental work carried <nl . n(i that tlw*
wax, principally in the Los Alamos laboratories. Smyth Nuclear

store of knowledge accumulated by the Los Alamos I’xperi |t,(:l ! .hjiikifift on
Physics Division forms an integral and invaluable part of sl L;, r y sccuiitv
nuclear problems 8 ; it is to be regretted that considerations ol' n' 1 ' 1 ,i 0 f ,uitui e
should delay the free publication of such material. The kno^ , u ntil these
contained in the reports of this division cannot long bo secret, l ,ll | aJul miu j tf
reports are published or the data they contain are redelernti , ' c ‘* IiecC s.surily

sss of nuclear physics lS 11

radioactive

making ar/if 11 1

a source of

. , — —1 — -- — n-ivumv vuvi ir>y ” ji* enemy is

industrial power, there is one respect in which progress in 111,1 f- the nature
almost certain to have most beneficial results. In the discussin" l ’‘ « u Hicient
of an atomic pile, it was pointed out that within a pile there Vl ® which
neutrons to bring about alterations in the properties of nui licr . lis nor UI j if
subjected to their bombardment. Although the number of nc l » ir ‘ ‘ ,

volume in a pile is very small compared with the number number of
volume of a gas at normal temperature and pressure, yet l * lC ;i„ nuu ,t,
neutrons passing per second through a cm . 8 of the area of 'L,.,' smirw .
greater than the number released by any possible laboratory nci ,
and consequently, in some cases, the uranium pile makes p‘ ,sS ,. tunnies or
experiments that cannot be carried out in the laboratory Sn iaI, J u" lit,*,

material, placed within a pile, are subject to most intense nortion « r

ment, and m certain cases where neutron capture occurs, a sl ’ .. crnl Heim,
these sutetoncM will be transformed into an isotope of the ,n fr a pile S
bombarded. We see an example of the advantage of the u* c .. Pu i» Usil .„
such a purpose, when we compare the rate of production <’* ™ rsc is in
neutrons from a cyclotron and using those in a pile. This c> ^ * * n

177

known to the scientific world, the progress
impeded

(6) The use of atomic enei-gy processes for
substances .

Whatever success is achieved in attempts to use atomic energy aS

M

ATOMIC ENERGY

Chap. XV

extreme case, but it is generally true that nuclear processes which are brought
about by neutron bombardment can be performed, on a far larger scale by the
use of a pile than by using any neutron source.

Now the importance of these neutron-induced nuclear transformations lies
in the field of medicine. A simple example is provided by an experiment in
which animals— in the case considered they were rats — were given food
containing artificial radioactive phosphorus. From the point of view of the
animal accepting the food, radio-phosphorus does not differ from ordinary
phosphorus, P 81 ; it is true that radio-phosphorus has mass number 32 , but
this makes no appreciable difference to its chemical properties, to its taste
or ease of digestion ; it is also true that the phosphorus is radioactive, but
by the time it has exhibited this property it is no longer phosphorus. Now
^3 ^ ias the convenient half life of 14.5 days ; if an animal is given a meal con-
taining some radio-phosphorus, it can be killed subsequently and the various
parts of its body subjected to analysis. The point of interest in such an
experiment is the general problem of phosphorus metabolism ; how much of
the phosphorus of the meal was retained in the body structure of the animal
and of this portion what fraction entered the teeth, the bones and other
phosphorus-containing organs ? Naturally, as the radio-phosphorus behaves
just like ordinary phosphorus, the history of the phosphorus of that particular
meal is shown by the location of the radio-phosphorus. This phosphorus is
distinguishable from ordinary phosphorus because of its higher mass number,
and if it had been absorbed in some quantity it could be detected even if it
were not radioactive. But as this isotope is radioactive, it is possible to
detect it even though it is present only in minute amounts, and in practice a
relatively small dose of radioactive phosphorus is sufficient to allow its fate to
be followed with adequate accuracy. Experiments of this type have shown
timt the phosphorus of a rat’s teeth is slowly but regularly replaced by some

nnA in daily ’ This discover which was a surprising

one, could hardly have been made without the use of radioactive phosphorus,

< f n h® P roduced “ several ways, including the bombard-
ment of P S1 by neutrons.

me S£° rUS t ii 0Illy °°? of elements w hich play an important part in
auantinf^iH 5“^ 0th ?£ elements which are needed in some considerable

2S wh£h ?“,^ ere are elements such “ koa > manganese and

^ essential but are required only in small amounts. Infor-
te * eir 1 metabolism h of considerable interest, and can best

ffiSS a T ml ^Periments using food which contains small quan-
ta SSSTSr elem ® nts - * most cases adequate quanti-

ties of radioactive forms of common elements can readily be produced by

178

APPENDIX I

METHODS FOR ACCELERATING CHARGED PARTICLES

From about 1925 onwards there was a growing realization that nuclear
physics would make a notable advance if it were possible to devise means of
accelerating charged particles. Up to that time the only fast particles avail-
able were a particles with energies of up to about 8 MeV ; such particles
were useful but they were not available in sufficient numbers or indeed with
sufficient energy. It was not usually possible to employ a source of particles
which supplied more than 3 xlO® a particles a second and as each of these
carries two positive charges its ability to approach closely to a nucleus is
seriously limited. Nevertheless it was difficult to find any practicable alter-
native. There was the possibility of using the positive ions that are present
in a discharge tube ; these exist in vast numbers, but in the discharge tube
itself they have very low energies and it is necessary to devise means for
accelerating them if they are to be of use in effecting nuclear transformations.

It should be realized that the generation and use of high electrical potentials
is a most difficult problem. Potential differences of 10 kV are very easy to
generate, a potential of 100 kV is much more difficult, and one of lOOOkV or
more can be generated and employed only when very elaborate precautions
arc taken. Such voltages will spark over long distances because under the
influence of very powerful electric fields air is no longer an insulator. It was
apparent that although these high voltages would provide direct means of
accelerating positive ions, it was not likely that they could be used to provide
ions with energies in excess of a very few MeV.

. w alton »d this direct method for accelerating hydrogen

r Ith 11 *ey succeeded in disintegrating lithium. This nuclear
3Zt’if d \? W oth . er V nduding the D on D action, can be
^Smional a J T ener ^ ^ SS than 1 MeV > but these reactions are
a - and U . S J uaUy much kgher energies are required. There is little

detaas °U these direct methods Of accelerating
SZ^’ 316 * ose of obtaining the necessary steady

hesnrSw f 80 accelerating tube to which they can safely

‘SJ?* sFZf r * 11 "j”” 10 ” w “ ch ■»>*• a. SSK

Mcsl of tk tadkec. methods of accetaadng particle, make use of hioh

180

Chap. XV ATOMIC ENERGY AND THE FUTURE

making use of neutrons within a reacting pile ; with these radioactive sub-
stances biological knowledge of great importance may be obtained. It is
probable that the first benefits to arise from experiments on atomic energy
will be in the form of a better understanding, first of animal, and then of
human metabolism with corresponding benefits to all mankind.

(7) Conclusion.

He is rash who attempts to tell the future, especially in this novel field of
atomic energy where there are no historical parallels to guide us. Naturally,
there is some uncertainty in the accuracy of present-day estimates of the
consequences to the world of the discovery of means for releasing atomic
energy. If we realize the seriousness of the threat to our civilization that
arises from the atomic bomb and take the steps which are needed to prevent
war, we may in this way alone achieve benefits of the greatest value. If, in
addition, it proves possible to use atomic energy for the supply of cheap
power and especially if, as would then seem likely, coal mining becomes an
occupation of diminishing importance, the discoveries in nuclear physics made
during and after 1939 may give rise, in a few decades, to more material
progress than has been achieved since man came to this earth. The discovery
of atomic energy may be compared with the discovery of the steam engine ;
if this comparison is apt and if the development of atomic energy is carried
out on an adequate scale, a new industrial revolution will follow quickly on
the heels of these discoveries. The future is full of hope and promise, but
only if we see to it that never again are these new powers used for killing and
destruction.

REFERENCES

1 One World or None , McGraw-Hill (1946), p. 21.

2 Smyth Report, 12.33.

179

APPENDIX I

Appendix I

frequency alternating potentials. If arrangements are made whereby the
particles being accelerated pass many times through the applied voltage, it is
possible to impart to them an energy of say 10 MeV when the accelerating
potential is only 200 kV. The simplest arrangement employing this principle
is the linear accelerator. A diagram showing the principle of this device is
given in Fig. 43. Within an evacuated tube are a number of cylindrical
electrodes which have lengths depending upon their positions in the tube.

To high frequency

Fig. 43. The arrangement of the electrodes In a linear accelerator.

Alternate cylinders are connected together and between the two sets so formed
a high frequency electric potential is applied. A beam of positive ions moves
down the tube. Let us fix our attention on those ions which cross from
cylinder A to cylinder B at a moment when the electric fields are momentarily
maximum and directed as shown by the arrows drawn above the electrodes.
These ions will be accelerated and their speed when within B will be greater
than it was when they were within A. During the time the particles are
moving inside B, the field falls and reverses, and if cylinder B is of the correct
length these ions will cross from B to C when the electric fields are as indicated
by the arrows below the electrodes ; the particles, now between B and C, are
again accelerated. Clearly, the ions are accelerated at both gaps because it
takes them one half cycle of the high frequency potential to pass from one
gap to the next. This can take place as many times as is desired, and provided
that the length of each cylinder is such that the accelerated ions take one half
cycle to pass from one gap to the next the ions are accelerated each time they
cross a gap. Practical limitations are quite serious ; the apparatus is very
long and in consequence there is a difficulty in preventing ions from drifting
sideways and being caught on the electrodes. This method has been success-
fully employed, but it is described here not because of its importance but be-
cause it provides a useful introduction to a description of the cyclotron.

In the cyclotron the ion paths are made circular because of the presence of
a strong magnetic field. This addition causes some considerable simplifi-
cations for then there are required only two accelerating electrodes which the

181

APPENDIX I

Appendix I

ions traverse very many times. Ions must traverse the gaps between the
electrodes at the appropriate instants, and this is achieved by using the correct
value for the magnetic field.

The behaviour of ions in a magnetic field is so simple that it is worth
deriving the formulae on which the principle of the cyclotron depends. When
ions of mass m carrying the electronic charge e move with velocity v in a
magnetic field of strength B they experience a force Bev. This force is at
right angles both to the magnetic field and to the direction of motion of the
particle ; consequently the speed of the particle is unaltered but its direction
of motion is continually changing and it describes a circle such that the
centrifugal force balances the force arising from the magnetic field.

Hence Bev = — , or Ber = mv.

t r

We use this relation to determine firs the time taken for the ion to complete
one circle in the magnetic field. In doing so it travels a distance 2ttt at a

velocity v; this takes a time ,i.e.,

This time does npt depend on the velocity of the ion and as long as m and B
remain constant the particle describes a complete circle in the field in a time
which is independent of its speed.

We do need another relation : that between the energy of the particle and
the radius of its orbit. If V is the energy of the ion in electron volts we know

that Ye = imv 3 , or v

Hence Ber

V2Vem, i.e., r = ^ or V

BVe
' 2m •

For deuterons

’ Q

— = 5 x 10 7 coulombs per
.m

when B = 1 .4 weber per sq. m

(14 000 gauss) and r— 1 metre we find that V=5 x 10 7 electron volts. For
reasons which will be given below the cyclotron is not able to give quite this
much energy to deuterons.

The following is a description of the cyclotron. A metal box, which can
be evacuated, is placed between the poles of a large electromagnet. Within
the box are two hollow electrodes. These electrodes and their position in the
magnetic field are shown in Fig. 44 and in a plan of the arrangement shown
in Fig. 45. Here it is seen that the hollow electrodes are D-shaped ; they are
known as the D’s. Between the D’s, and at their common centre, is a device
for producing an intense electron stream through which a slow current of

182

APPENDIX I

A&pendix I

Pig. 44. A section showing the disposition of apparatus between the poles of a

cyclotron magnet.

Fig. 45. A plan of cyclotron electrodes showing the ion paths.
183

APPENDIX I

Appendix t

sas is led into the highly evacuated box. This arrangement forms an ion
source very cimiiar to that used in the electromagnetic separation method as
j- j in Chanter 14 It provides a copious supply of positive ions near
£^nt?e”f *e D system. Now between the D’s a large radio-frequency
voltage is applied which causes many ions to be drawn mto one °r ?ther
the ITs ; in the presence of the magnetic field the ions describe cycles. A
long as an ion is within a D it is uninfluenced by any change ' ° f inwards
the D, but eventually it wiU leave one D and travel across the gap towards
the other one. If the frequency of the applied voltage is correct, the potentia
between the D’s will be such as to accelerate the ion and inconsequence on
entering the other D it will have a higher velocity, and within this D it WiU
describe a semicircle of larger diameter than the previous one. The greater
circumference of this circle compensates for the greater velocity of the particle
—our formula shows that the time of description of a circle does not depend
on the velocity— and when the electric potential has reversed again the ion is
passing from one D to the other and is being accelerated. As long as the ion
keeps in step with the high frequency field it will continue to gain energy each
time it crosses from one D to the other. This will happen if the magnetic
field is constant and if the energy of the ion does not become great enough to
bring about an appreciable increase of its mass. In practice; when the
particle has been given an energy of between perhaps 10 and 20 MeV its
mass has increased so much that it can no longer keep in step with the changes
in the electric field. It might be thought that the disadvantages of this
increase of mass could be overcome by using a magnetic field which is strongest
near the edge where the mass of the ion is greatest, but this is not practicable.
The cyclotron is able to produce large numbers of high energy particles
because ions do not drift to the D’s ; it is for this reason that ions are able
to describe perhaps 100 circles and that some ions can pass 200 times through
the maximum potential between the D’s. And this is only possible when the
magnetic field is stronger at the centre than in the regions near the outside
where high energy particles move. Thus although the cyclotron will give
particles of very high energy, there is a limit imposed by the increase of mass
predicted by the theory of relativity.

It remains to mention the means used for deflecting the high speed ions
from their circular paths within the D’s. This is done by providing in one D>
a curved metal plate connected to a source of high steady negative potential.
When ions describe a circle large enough to bring them near this deflector
plate, they are forced out of their normal paths and pass through an opening
in the D. Thereafter they may take a path which causes them to fall upon a
target that is to be bombarded, or they may be used in any other manner
desired.

184

Appendix I APPENDIX I

The ion beams obtainable from a cyclotron carry a current of the order
of 10“ 5 amp., corresponding to 6 x 10 13 ions per second. Thus even these
small currents of high energy ions provide fast particles in very much greater
number and of higher energy than those available from any radioactive
source.

Detailed information concerning cyclotrons is given in “Cyclotrons”,
W. B. Mann, (Methuen).

185

APPENDIX II

TRACER CHEMISTRY

In the study and applications of radioactivity special chemical methods are
often employed with great advantage. Let us consider, as a case in point, the
separation of radium from uranium and its products. The radium content
of geologically old uranium ores is rather less than one part of radium to a
million of uranium, so that if the uranium and radium are brought into
solution, there will be a large amount of solution for a very small amount of
dissolved radium. In these circumstances, attempts to precipitate the radium
as insoluble sulphate may be unsuccessful, for the minute amount of radium
may remain in solution in the very much larger amount of water. This
precipitation can be achieved if a soluble salt of barium is present in the
solution or is added to it. The precipitate of insoluble sulphates contains
barium mixed with radium ; after the removal of other impurities, the radium
and barium are converted into chlorides ; in order to obtain the radium
which was originally mixed with the uranium, it is only necessary to work up
the chlorides to separate the radium from barium.

This procedure is frequently advantageous. Another case, which shows the
process in a slightly different form, arises when artificial radio-phosphorus is
made by bombarding aluminium with a particles. This form of phosphorus,
which emits positrons, was one of the artificial radioactive substances dis-
covered in the pioneer work of the Joliots. They showed that bombarded
aluminium was radioactive and emitted positrons. On bringing the alumi-
nium into solution, adding a soluble phosphorus compound and precipitating
he phosphorus, it was found that the positron activity was in the precipitate

^h a ?i solu 5 011, .™ s j? bservation > together with experiments which
showed thst the radioactivity did not precipitate with aluminium or magne-

"2* for example, served to show the chemical nature of the radioactive
^ t ?-\ t0tal amount available was far less than
c ? ses 111 whlcl1 thh process has been invaluable have
va F ous . parts of book - Here it is sufficient to recall
“^tfsations of the chemical properties

natm^ ^fThat trr^^ results-in the investigations of the

nature ot what were believed to be trans-uranic elemen ts but were renilv
fission fragments and the products of their radioaS dSy *

Further information on this subject will be found in “ Radioactivitv ”
Hevesy and Paneth, (Oxford University Press), Chap. 1 ^ n Radl0actlvIt y ’

186

APPENDIX III

PROBABILITY IN RADIOACTIVITY

In the realm of dynamics, the motion of a body is described in terms of the
motion of the particles of which it is made. It was at one time felt that if
it were possible to specify the position and velocity of every particle in a
body and in any other bodies with which it came in contact, the complete
motion of the body would be determined and its position at any given moment
could be predicted. It has not been possible to use any such idea so that it
gives results which agree with observations of radioactivity in particular and
of nuclear processes in general.

The simplest type of process to discuss is the radioactive decay of a sub-
stance like radium. Considered in bulk, radium has a half life of about
1600 years ; that is 1 g. of radium to-day will 1600 years hence be emitting
a particles and y rays at a rate which shows that only 0.5 g. of radium re-
mains. This remaining half gram will exhibit the same behaviour, and in the
next period of 1600 years half of it will go through a radioactive transforma-
tion and the other half will remain. The regularity and predictability of
this radioactive decay is in marked contrast to what is observed when a
more detailed view is taken. In a sample of radium containing 7 x 10 10
radium atoms, 1 radium atom, on the average, decays every second. Hence
in a day nearly 10 5 atoms of radium have emitted a particles and have
changed their chemical nature. What is it that makes these atoms decay now
when nearly 2 x 10 10 atoms within the sample will live for a further period
of over 3200 years ? To this question no answer has been found ; perhaps
there is no answer. The observation of the behaviour of radium, however,
makes it necessary to direct attention to average behaviour, rather than to
the behaviour of individual atoms. For although it is true that amongst
7 x 10 10 radium atoms there is, on the average, one atom decaying every
second, there will be occasions when a period of 3 or 4 seconds will elapse
without the transformation of a single radium atom. Observations extending
over limited periods may therefore give quite a wrong impression of the rate
of radioactive decay of a given substance, but as the period of observation is
extended so that the number of atoms observed to decay is increased, the value
of the average number of atoms decaying per second becomes known with
more and more reliability, although even extended measurements will be
subject to uncertainty arising from the fluctuating process of radioactive
decay.

187

APPENDIX III

Appendix 111

0 JP le whole process is described mathematically by supposing that radio-
ctive decay follows the laws of chance. There is a certain definite chance
any given atom of radium, now in existence, will decay within the next
second. ; each atom behaves in a manner which is uninfluenced by what
o er atoms are doing. This chance of decay of an atom in 1 second is A,
e transformation constant of the radioactive substance. In the case of
fSL™- ^ im!' 373 X P®* sec * so tliat in a sample of radium containing
t j 10 a * oras > 011 the average 1 atom decays every second. This
r»fu, ry ^ oes ^ ot . a ttempt to explain why a radioactive atom decays, for it is
ob^iv^ 1 ^^ 41 ^ <lescrl P^ on ’ 35 suc h it is in complete accord with what is

In no problem of nuclear physics is it possible to predict the behaviour of
* uc 3 eus - But *>y discussing the matter in terms of probabilities it is
P si e to form a precise picture of what will happen, on the average, if the
e^penment is repeated a sufficient number of times. This idea is implicit in
y numerical values given throughout this book ; neutron collision and
neutron capture cross sections, fission cross sections and the number of neu-
f d ** fission > re Production factors of a pile or of a bomb and the
a neut ^ on operation, all are statistical averages, and on occasion
xxr+u ^re are most marked departures from these

niwW?’ Without the use of this idea, no interpretation of the results of
nuclear physics experiments can make :

ENERGY UNITS

1 MeV per

0.001 Mass

1 eV = 1.6 x 10- 19 joules or 1.6 x 10“ 18 ergs.
1 mass unit = 1.49 x 10“ 10 joules or 1.49 x 10~ 3 ergs,
molecule of 1 g. molecule = 9.55 x 10 10 joules

= 2.7 x 10* kWh
= 2.3 x 10 10 g. cal.

unit per molecule of 1 g. molecule = 9.0 x 10 10 joules

= 2.5 x 10‘ kWh
- 2.1 x 10 10 g. cal.

188

Number of NeutTOTis.

THE HEAVY RADIOACTIVE SUBSTANCES

THE HEAVY RADIOACTIVE SUBSTANCES

Substances in the uranium-radium series are enclosed in squares, those in
the thorium series in circles and those in the actinium series in octagons.
Radioactive substances discovered since 1939 are not shown as belonging to
aiiy of these series, although some of them are part of the uranium and acti-
nium series. Others of the substances listed do not belong to any of the old
radioactive series. It is likely that this diagram omits some heavy radio-
active substances which have been investigated during the recent war.

It is to be noted that the emission of a p particle transforms a substance
to an element having one less neutron and one more proton than the parent ;
the emission of an a particle removes two protons and two neutrons. The
relative positions of parent and product are seen by considering, as an
example, the case of U 289 which becomes Np 289 after one $ ray emission ;
a second p ray emission transforms Np 239 to Pu 289 and then an a ray emission
converts Pu 289 to U 285 .

190

A TABLE OF ELEMENTS*

The mass numbers of radioactive isotopes are written in italics.

Atomic

Element Known Isotopes Symbol No

Hydrogen

1

2

3

H

1

Helium

3

4

6

He

2

Lithium

6

7

8

Li

3

Beryllium

7

9

10

Be

4

Boron

10

11

12

B

5

Carbon

10

11

12

13

14

C

6

Nitrogen

13

14

15

16

N

7

Oxygen

15

16

17

18

19

O

8

Fluorine

17

18

19

20

F

9

Neon

19

20

21

22

23

Ne

10

Sodium

22

23

24

Na

11

Magnesium

23

24

25

26

27

Mg

12

Aluminium

26

27

28

29

A1

13

Silicon

27

28

29

30

31

Si

14

Phosphorus

29

30

31

32

P

15

Sulphur

31

32

33

34

35

36

S

16

Chlorine

33

34

35

36

37

38

Cl

17

Argon

35

36

37

38

40

41

A

18

Potassium

38

39

40

41

42

K

19

Calcium

40

42

43

44

45

46

48

49

Ca

20

Scandium

41

43

44

45

46

48

49

Sc

21

Titanium

45

46

47

48

49

50

51

Ti

22

Vanadium

48

50

51

52

V

23

Chromium

49

50

51

52

53

54

Cr

24

Manganese

51

52

54

55

56

Mn

25

Iron

53

54

55

56

57

58

59

Fe

26

Cobalt

55

56

57

58

59

60

Co

27

Nickel

57

58

60

61

62

63

64

Ni

28

Copper

62

63

64

65

66

Cu

29

Zinc

63

64

65

66

67

68

69

70

Zn

30

Gallium

65

66

67

68

69

70

71

72

Ga

31

Germanium

70

71

72

73

74

75

76

77

Ge

32

Arsenic

74

75

76

78

As

33

Selenium

74

75

16

77

78

80

82

83

Se

34

Bromine

78

79

80

81

82

83

84

85

Br

35

Krypton

78

80

82

83

84

85

86

88 89

Kr

36

Rubidium

85

86

87

88

89

Rb

37

Strontium

84

85

86

87

88

89

Sr

38

Yttrium

87

88

89

90

Y

39

* The existence of all the types of nuclei listed here is believed to be certain. There
are others of doubtful existence and probably still further types which have yet to
be discovered.

191

A TABLE OF ELEMENTS

Element

Known Isotopes

Atomic
Symbol No.

Zirconium

89 90

91

92-

94

96

Zr

40

Niobium

92 93

94

Nb

41

Molybdenum

92 94

95

96

97

98

100

Mo

42

Masurium

?

Ma

43

Ruthenium

96 98

99

100

101

102

103

104

Ru

44

Rhodium

103 104

105

Rh

45

Palladium

102 104

105

106

108

110

111

112

Pd

46

Silver

106 107

108

109

110

111

112

Ag

47

Cadmium

106 108

110

111

112

113

114

115

116

117

Cd

48

Indium

113 114

115

116

117

In

49

Tin

112 113

114

115

116

117

118

119

120

122

124

Sn

50

Antimony

120 121

122

123

124

127

129

Sb

51

Tellurium

120 121

122

123

124

125

126

127

128

129

130 131

135 Te

52

Iodine

124 126

127

128

130

131

133

135

I

53

Xenon 124 126 128 129 130 131 132 134 135 136 139 140 141 Xe 54

Caesium 133 134 136 139 141 Cs 55

Barium

130 132 133 134 135 136 137 138 139 140 141

Ba

56

T anthanum

139 140 141

La

57

Cerium

136 138 140 141 142

Ce

58

Praseodymium/40 141 142

Pr

59

Neodymium

141 142 143 144 145 146 148 150

Nd

60

Tllininm

?

11

61

Samarium

144 147 148 149 150 152 154

Sm

62

Europium

151 153

Eu

63

Gadolinium

152 154 155 156 157 158 160

Gd

64

Terbium

159 160

Tb

65

Dysprosium

158 160 161 162 163 164 165

Dy

66

Holmium

165

Ho

67

Erbium

162 164 166 167 168 170

Er

68

Thulium

169

Tm

69

Ytterbium

168 170 171 172 173 174 176

Yb

70

Lutecium

175 176

Lu

71

Hafnium

174 176 177 178 179 180 181

Hf

72

Tantalum

180 181 182

Ta

73

Tungsten

180 182 183 184 186

W

74

Rhenium

185 187

Re

75

Osmium

184 186 187 188 189 190 192

Os

76

Iridium

191 193

Ir

77

Platinum

192 194 195 196 198 199

Pt

78

Gold

197 198 199

Au

79

Mercury

196 197 198 199 200 201 202 204 205

Hg

80

Thallium

203 205 207 208 209 210

T1

81

Lead

204 206 207 208 209 210 211 212 213 214

Pb

82

Bismuth

207 209 210 211 212 213 214

Bi

83

Polonium

210 211 212 213 214 215 216 217 218

Po

84

—

211

85

Radon

219 220 221 222

Rn

86

—

223

87

Radium

223 224 225 226 228

Ra

88

192

A TABLE OF ELEMENTS

Atomic

Element

Known Isotopes

Symbol No,

Actinium

221 228

Ac

89

Thorium

227 228 229 230 231 232 233 234

Th

90

Protoactinium

231 233 234

Pa

91

Uranium

233 234 235 237 238 239

U

92

Neptunium

237 238 239

Np

93

Plutonium

238 239

Pu

94

THE PERIODIC TABLE

The numbers below the chemical symbols are atomic numbers.

Period

I

11

III

IV

V

VI

VII

0

VIII

I

H

He

1

2

II

Li

Be

B

mm

O

F

Ne

3

4

5

m

m

8

9

10

III

, Na

Mg

A1

Si

p

S

Cl

A

11

12

13

14

15

16

17

18

K

Ca

Sc

Ti

V

Cr

Mn

Fe Co

Ni

19

20

21

22

23

24

25

26

27

28

IV

•

Cu

Zn

Ga

Ge

As

Se

Br

Kr

29

30

31

32

33

34

35

36

Rb

Sr

Y

Zr

Nb

Mo

Ma

Ru Rh

Pd

37

38

39

40

41

42

43

44

45

46

V

Ag

Cd

In

Sn

Sb

Te

1

Xe

47

48

49

50

51

52

*53

54

Cs

Ba

R.E.

Hf

Ta

W

Re

Os

lr

Pt

55

56

57-71

72

73

74

75

76

77

78

VI

•

Au

Hg

T1

Pb

Bi

Po

—

-

Rn

79

80

81

82

83

84

85

86

vir

_

Ra

Ac

Th

Pa

U

87

88

89

90

91

92

Rare

La

Ce

Pr

Nd

II

Sm

Eu

Gd

Tb

Dy

Ho

nn

rm

Yb

Lu

Earths:

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

If a new group of rare earths begins at uranium, the space in the periodic table
occupied by uranium should also contain and ^

193

N

PARTICLES AND RAYS

Mass

Particle

Symbol

General Description Charge

when
at rest

Proton

p or H[

Fundamental positively charged heavy
particle : nucleus of the hydrogen atom.

+ 1

1.00758*

Neutron

n or nj

Fundamental heavy particle of zero
charge. Believed to transform into a
proton and an electron.

0

1.00893

Electron

|3 or e-

Fundamental negative unit of charge.
Emitted by many natural and artificial
radioactive substances : then called a £
particle.

—1

0.00055

Positron

e+

Positive electron. Emitted by certain
artificial radioactive substances. Formed
when 7 rays pass through heavy metals.

+ 1

0.00055

Deuteron

H; or D-

Heavy hydrogen nucleus : may be con-
verted by 7 rays into a proton and a
neutron.

+ 1

2.01418*

a particle

a or He*

Nucleus of the helium atom. Close com-
bination of two protons and two
neutrons. Emitted spontaneously by
some natural radioactive substances.

4-2

4.0028*

7 rays

7 or hv

Electromagnetic radiation emitted by
atomic nuclei. Moves with the velocity
of light.

0

—

1 Mass unit = 1.66 x 10- 24 g.

Unit charge = 1,6 x 10- 19 coulombs

*The mass listed is a nuclear mass. Atomic masses are obtained from those
given by adding 1 electronic mass in the case of hydrogen and 2 in the case of helium

194

INDEX

of atomic

A. See mass number.

Accleration of charged particles
Actino-uranium. See also U 335
Administrative details ' .
a particle emission
and mass energy equation
theories of .
a particle energies .
a particles

disintegrations caused by
from ThC .
from ThC' .
from uranium I
long range from ThC' .
nature of
properties of

transformations caused by
a rays (a particles) .

Aluminium cans
American monopoly
bomb ....
Argonne laboratory .

Artificial radioactivity
and atomic energy
Atom splitting

Atomic bomb. See also bomb.

American monopoly
Atomic bombs in war
Atomic energy. See also nuclear
energy

and artificial radioactivity
controlled release of
for electrical generators
for motor cars
for ships

for small plants .

Atomic fuels. Safety precautions
Atomic masses
and whole number rule .
from mass energy equation
measurement of
Atomic number
Atomic structure and electrons

180
95
109

29

54, 56, 57
42

. 44,45
. 55, 58
55

. 54,57
54, 57, 58
20, 194
31
42
20
129

171
.124
59, 62
177
45

171

170

. 177

110, 111

174

173

174
172
172

48
62
48
17
16

Atomic transformations in radio-
activity . . . . 20, 21

Atomic weight and mass number 18
Atomic weights, chemical . . 48

B

Barium from neutron bombard-

ment of uranium . . 82, 83

Beryllium as moderator . . 115

(3 particle emission ... 91

P particles ....
nature of 194, 21

properties of . . . 31

Pray energies of fission frag-
ments . . . . 97, 98

P rays. See p particles.

Binding energy, neutron

See also En . . . 91

Blackett, nitrogen disintegration 46, 47

Bohr 90

Bohr and Wheeler ... 90

Bomb

and fission material . 140

and neutron reflector 144, 145

as chain reactor . . .138

critical size of 141

deposition of fission products . 145

detonation . . 146, 148

explosion, commencement of . 147

explosion, growth of . 143

explosion, New Mexico . 148-151

explosion, time of 142-144

y rays from . 144, 146

life time of neutron generation 142

minimum requirements . . 143

pressure attained . . .145

radiation from . . 144, 146

requirements of . . 110,139

temperature . . . .150

Bombardment of uranium by

neutrons . . . 81

Boron

capture of neutrons . . 78

N*

195

INDEX

Boron

for pile control . .119

neutron capture cross section . 76

C

Cadmium for pile control .

Cadmium, radiative neutron
capture .

Canning ....

Cans, al uminium
Capture cross section
for neutrons
resonance .
variation inversely with
neutron velocity
Carbon as moderator
loss of neutron energy in
collisions with .

Carbon, neutron collisions with
Cascade process
Cascade, stripping .

Chadwick and nuclear charge
Chain reaction
and fast neutrons .
first ....
nature of
neutron balance in
realization of
requirements for .
size of reacting mass for.
with natural uranium
with protoactinium
with thorium
with uranium I
Chain reactor, bomb as
Charged particles, acceleration of
Charge to mass, ratio of
electron
hydrogen

Chemical atomic weights .

Chemistry, early
Clinton pile .

Clinton pile, plutonium yield
Cloud chamber
Cockcroft and Walton
Coincidence counter
Collisions, neutron .

Collisions of a particle and
hydrogen atoms.

Conservation
of mass

Conservation

of energy

Control of pile.

. 11-12

118

Cooling a pile .

. 128

Conversion of mass to energy

. 28, 29

Counters

38

Critical size

120

of bomb

141

of bomb, estimate of

142

Cross section for resonance

neutron capture

74

Cyclotron

details of

. 184

operation of

. 184

output

. 185

principle of .

182

sketch of

. 183

D

D on D reaction

64

Delayed neutrons

104, 105

and pile control .

. 119

Deutenum

49

neutron collisions with .

68

Diffusion

cascade, details of

155, 156

porous barrier

. 152

Diffusion plant

at Oak Ridge

161, 162

details

. 160

ideal ...

157-159

material hold up .

. 161

stage sizes .

156

start up period

161

Discovery of

neutrons

59

plutonium

. 125

positrons

59

radioactivity

20

Disintegration of lithium by

protons .

. 59-61

Disintegrations caused by a

particles .

44, 45

E

E ...

93

values of (Table I)

94

E. ... .

95

values of (Table I)

94

niectnc generators, atomic

energy for

174

. 119

77

. 129

. 129

72
74

76

115, 116

. 118
68

. 155

. 156

18

. 101
. 120
99, 100
. 107

. 113

. 114

. 115

102, 113, 114
101
100
101
138
180

14
14
48
11
122
134
. 32-37
. 59, 60, 62

40

66-68
43

11-12

INDEX

Electromagnetic separation

method . . • J62

advantages of • • .166

arrangement . • 163, 164

beam current and beam focus
in ’ . . • • 165, 166

current and yield . . .163

disadvantages of . . • 167

divergent ion beams in . 165, 166

enrichment factor in . 166

number of stages . • ■ 166

voltages and magnetic fields for 1 65
uranium ion paths in 164

Electron . . • .194

as unit of charge . . . . 13

charge to mass, ratio . . 14

mass of ... • 14-

motion in electric field . . 13

motion in magnetic field . 13

pair 60

volt . ... • . 14, 15

Electrons and atomic structure . 16

Element, definition of . . 1 1

Elements, table of . . 191-193

Energy

and mass . .... • 2o

balance in nitrogen disinte-
gration .... 47

of fission fragments . . 87-90

of neutrons, measurement of
kinetic . ... 79

release from heavy nuclei 97

release in fission ... 97

to initiate fission. See also E . 93

units . . . . .188

Enrichment factor . .153

in electromagnetic method 166

in uranium diffusion . . 154

Equations, nuclear reaction 62

Excited nucleus ... 74

disposition of energy . 95, 96

Excitation energy of nucleus 74

Expansion chamber . . 32-37

Explosion

time of bomb . 142-144

growth of bomb . .143

Explosions . . . .138

Explosive, requirements of 1 38, 1 39

F

Fast neutrons and chain reaction 101

Fission. Chapter 9 .

81

chain reaction, nature of

99-100

cross section in U 236

141

cross section in Pu a3# .

142

description of

83

diagram of .

94

energy of

. 83, 88

energy release in .

97

fragments, see below
from neutron capture .

. 96, 97

liquid drop analogy

93

mechanism of

93

neutrons, see below
of heavy elements

95

of plutonium

112, 113

process, theory of

90

products from bomb

145

spontaneous

132

Fission fragments

. 84, 85

8 ray energies of .

. 97, 98

energy released in radio-active

changes .

89

kinetic energy of

. 87-90

masses of .

89

nature of

. 86, 87

radioactivity of

86

velocity of .

. 104

Fission neutrons

102, 103

energy range of .

. 103

in reacting mass .

. 106

origin of

103, 104

time of emission .

. 104

Fissionable material

. 105

for bomb

140

Forces, nuclear

. 56, 90

G

y ray frequencies

24

yrays

from bomb .

144-146

nature of

24

origin of

. 53, 54

Geiger counter

38

Geiger-Mullcr tube .

. 38, 39

Graphite supply

. 116

H

Hahn and Strassmann

83

Half life of radioactive substance 23

Hanford ....

. 128

Heat energy from radium .

23

197

INDEX

Heat produced by plutonium pile 127

Heavy hydrogen. See deuterium
Heavy water .... 49

as moderator . 115, 1 16, 123

from Norway . .115

preparation of . .123

Hiroshima Bomb ... 168

Hydrogen

capture of neutrons by . . 76

charge to mass ratio . . 14

collision cross section for
neutrons .... 72

heavy, see deuterium
neutron capture in . . 73

neutron collisions with . . 67

Hydrogens, knock-on . . 70

I

Identity of atoms of given mass
and atomic number .
Increase of mass
with increase of kinetic energy
with increase of temperature .
Indium, radiative neutron capture
Ion, definition of
Ionization, definition of .
Ionizing particles, properties of .
Isotope

definition

separation

Isotopes

radioactive .
separation of

52

26-28

28

77

16

16

31

19

175

21

152

K

k (reproduction factor) 99

*». . . - , • • .117

determination of . . . H8

Kinetic energy of fission frag-
ments .... 87-90
Kinetic energy in electron volts ! 15

L

Lanthanum from neutron bom-
bardment of uranium . 82

Lattice, uranium . . .114

Leak detection . . .160

Life time of neutron generation
in bomb .... 142

Linear accelerator . . 181

Linear amplifier 38

Liquid drop analogy with nucleus 91, 92
Lithium

atom, mass of . . 61

capture of neutrons . 78

disintegration by protons . 59-61
neutron capture cross section . 72,76
Long range a particles from

TbCf . . .54, 57, 58

M

Manhattan District Engineers . 110

Mass

and energy .... 26

conservation of . . . 11, 12

defect . . . . 49, 50

energy equation, see below
number .... 18

of lithium atom ... 61

Mass energy equation and

absorption of light . . 29,30

and a particle emission 29

and atomic masses . . 62

and masses of fission fragments 89

Matter

passage of neutrons . . 64-65

passage of protons . . 66

tenuous nature of . . 65

Metabolism . . . .178

Moderator .... 105

advantages of 106

beryllium as . . 115

carbon as . . . 115,116

choice of . . .115

heavy water as . . 115,116

Moseley and atomic number . 17

Motor cars and atomic energy . 173

N

Natural uranium chain reaction . 102

Neptunium . . . 112, 189

Neutron. See also under neutrons 1 94

balance in chain reaction . 107

binding energy. See also E n . 91

capture, see below
collisions, see below
content of pile, growth of . 119

discovery of ... 59

emission . . . . 91, 92

energy losses from collisions . 66, 67
fission cross section . 141,142

198

INDEX

Neutron

free path length and scattering
cross section ... 70

path of fast in U m . . 141

reactions .... 76

scattering . . . . 68, 69

scattering cross section and
free path length . . 70

velocity and capture cross
section . . . . 73, 74

velocity, capture cross section
proportional to . 76

Neutron capture ... 72

by boron .... 78

by hydrogen .73, 76

by lithium .... 78

by nitrogen . . 77, 78

by uranium isotopes 101, 102

cross section and neutron
velocity . . . . 73, 74

cross sections of lithium and
boron .... 76

processes .... 77

radiative .... 76

resonance .... 74

resonance cross section . 74

resulting in fission . . 96

Neutron collisions

head on .... 66

with carbon .... 68

with deuterium ... 68

with heavy atoms ... 68

with hydrogens ... 67

Neutrons

bombardment of uranium by . 81

cross section for scattering of . 69

delayed . . . 104-105

detection by knock-on protons 72

detection of .
energy losses in carbon
moderator

energy range of fission .
in pile, number of
in nucleus .
in reacting mass .
measurement of energy .
origin of fission .
slow, detection of .
stray ....
thermal

time of emission of fission

Nitrogen disintegration
energy balance of .

Nitrogen, neutron capture by
Nuclear
atom .

attractive forces
binding forces
charge

energy from sun
excitation energy . •

experiments, fast particles for
physics, fundamental data
reaction equations
reactions in a pile . •
theory : potential barrier
Nuclei, stability of .

Nucleus
constituents of
excited. . . • •

excited, disposition of energy
forces in

liquid drop analogy
particles in
short range forces in
size of •

structure of

O

Oak Ridge pile
operation of
power output of .

4246
47
77, 78

17

56

90

17

108

74

180

177

62

121

57,58

49

17

60

74

95,96

90
91,92

53

91
53

52, 53

122

122

122

70

118

103
132

60
106
79
102, 103
78
132
67,72

104

50

49-51

194

180

53

193

178

76

Packing fractions
and atomic stability
Particles and rays . ;

Particles for nuclear experiments
Particles in nucleus .

Periodic table .

Phosphorus metabolism .
Photo-disintegration • .

Photographic plate for recording
heavy particles .
pile .

cadmium and boron for control
O* 197

Clinton • • *

control and delayed neutrons . 11^

control of . . • . 118.119

control of and depletion of ^

U«* . . •

38

117

199

INDEX

Pile

cooling

. 128

elements formed in

132, 133

growth of neutron content of

. 119

nuclear- reactions within

121

number of neutrons in .

. 132

operation of

132

reaction, initiation of .

. 132

sources of radiation from

. 133

uranium-heavy water .

. 124

West Stands

120

yield of plutonium and heat
Piles

Hanford

. 127

128, 136

radiations from

129-131

Planck’s constant

24

Plutonium . . Ill, 125. 189

chemical methods

. 135

discovery of

. 125

extraction of

. 133

fission of

112, 113

formation of

. 112

problems of large scale pro-

duction

126, 127

production of

125, 126

yield from Clinton pile .

. 134

Porous barrier diffusion .
Positive

. 152

charge in atoms

16

electron

59

Positron ... 59, 60, 194

Potential barrier theory of

nucleus . . . . 57, 58

Power output of Oak Ridge Pile . 122

Pressure reached in bomb . . 145

Probability and radioactivity 187, 188
Protoactinium, fission by

neutrons .... 95

Production of neutrons . . 64

Protons 194

and disintegration of lithium . 59-61
knock-on .... 70-71
knock-on, for detection of
neutrons .... 72

passage through matter . 66

Prout’s hypothesis . . .18, 19

R

r unit : definition of . . 130

Radiation

from bomb . . . 145, 146

Radiation

from pile . . . 129-131

Radiative neutron capture . 77

Radioactive

changes, properties of . 22

isotopes 21

substances, the heavy . 189-190

transformation constant. 22

transformations ... 22

Radioactivity

and atomic transformations

20, 21, 190

and probability . . 187,188

artificial, see below

discovery of 20

of fission fragments . . 86

of fission fragments, energy
released in 89

Radioactivity, artificial . . 59, 62

and atomic energy . - 177

Radio-phosphorus . . 63, 178

and tracer chemistry . . 186

Radon 20

Radium

and heat emission . . 23

calorific value 23

separation from uranium . 186

Rays and particles . . 194

Reacting mass . . .105

best shape for . . .107

for chain reaction, size of 115

Reaction equations, nuclear . 62

Reflector around reacting mass . 107

Relativity, theory of 26

Reproduction factor . . 99

and U* sa depletion . 135, 136

Reproduction time . . 110

Resonance neutron capture 74

cross section. ... 74

Rhodium radiative capture . 77

S

Scattering cross section . 69

Scattering of neutrons . . 68, 69

Scientific research :

organization of . . .169

future large scale . . . 170

Scintillations from a particles . 32

Shape of reacting mass . . 107

Ships, atomic energy for . . 174

Silver, radiative neutron capture 77

200

INDEX

Slow neutrons, detection of

78

Slugs, uranium

Smyth, Atomic Energy for

. 122

Military purposes

10

Stability of atoms and packing

fraction .

51

Standard air

20

Stray neutrons

. 132

Stripping cascade

156

Structure of nucleus .

53

Sun, nuclear energy from .

. 108

T

Table l ....

94

Table of elements .

191-193

Table, periodic

. 193

Temperature reached in bomb

. 150

Thermal neutrons .

. 67, 72

Thorium, fission by neutrons

95, 100

Thorium C, a particles from
Thorium C'‘

. 55, 58

a particles from .

55

long range a particles .

54, 57, 58

Tracer chemistry
Transformation constant,

. 186

radioactive

22

Trans-uranic elements

82

Tube Alloys .

. 109

u

Uranium

bombardment by neutrons
chain reaction with natural
heavy water pile .
hexafluoride
isotopes and neutron
capture .
lattice

requirements

slugs ....

81

113, 114
. 124

. 154

101 , 102
. 114

. 176

. 122

supplies . 116,117,175,176

Uranium I

a particles from . . .54, 57

fission by neutrons . . 95

Uranium II, fission by neutrons . 95

U a38 , formation (Footnote) . 112

U 235 , depletion in pile . 135, 136

effect on reproduction
factor . . 135, 136

U 235 , fission by neutrons . . 95

U 239 , formation . . 102

W

West Stands pile . 120

Z

Z. See atomic number or nuclear
charge

201