(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Biodiversity Heritage Library | Children's Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "The Birth And Death Of The Sun"

TIGHT BINDING BOOK 



> 

g< ou 

=5 CQ 



160108>[n 



Osmania University Librarij 

Call No. 5T2-3> -7 Accession No. (9i ' -^ ' -^ 



Auth r 



This book should J)e returned on or before the daw last 
marked below. 



THE 

Birth and Death of the 

SUN 

STELLAR EVOLUTION AND SUBATOMIC ENERGY 



GEORGE GAMOW 

PROFESSOR OF THEORETICAL PHYSICS, GEORGE WASHINGTON UNIVERSITY 

ILLUSTRATED BY THE AUTHOR 

THE VIKING PRESS NEW YORK 
1940 



COPYRIGHT 1940 BY GEORGE GAMOW 

PRINTED IN U.S.A. BY HADDON CRAFTSMEN, INC. 

FIRST PUBLISHED IN JUNE 1940 

PUBLISHED ON THE SAME DAY IN THE DOMINION OF CANADA BY 
THE MACMILLAN COMPANY OF CANADA LIMITED 



Dedicated to 
PROFESSOR H. N. RUSSELL 



rreiace 



HOW did our Sun come into being, what keeps it hot 
and luminous, and what will be its ultimate fate? 
These are questions that should be of interest to all the 
inhabitants of our globe, whose life and prosperity are 
entirely dependent upon the radiant energy coming from 
the Sun. 

Since the beginning of scientific thought, the problem 
of solar energy sources has been one of the most exciting, 
but also one of the most difficult puzzles of nature. But 
only during the last decade has it become possible to tackle 
the problem of solar energy generation with any hope of a 
correct scientific solution, and thereby to answer questions 
concerning the past, present, and future of our Sun. It has 
finally been demonstrated that the tremendous amounts of 
energy radiated by the Sun are generated by the transforma- 
tion of chemical elements taking place in its interior, pre- 
cisely those "transmutations of elements/' in fact, that had 
been so unsuccessfully pursued by medieval alchemists. 

As our Sun represents only one member of the numerous 
family of stars scattered through the vast spaces of the 
universe, the answer to this solar problem necessarily in- 
volves also the question of the evolutionary history of stars, 
and this brings us back to the fundamental puzzle concern- 
ing the creation of the stellar universe. 

In this book, the author, who has been closely connected 

vii 



viii Preface 

with the progress of research on these problems, attempts 
to give, in the simplest terms of which he is capable, an 
outline of the fundamental discoveries and theories that 
now permit us a general view of the evolution of our 
world. Many of the views touched on in this work have 
been so recently arrived at that they have never before been 
discussed in popular literature. 

Though the author cannot conclude this preface with 
the customary statement that "all the characters appearing 
herein are purely imaginary and have no connexion with 
any living person," it is perhaps best that he warn the 
reader against giving too great credence to such minutiae 
in the following pages as the untidiness of Democritus's 
beard, the rainy weather in Princeton at the time of the 
construction of the Russell diagram, and the relationship 
between Dr. Hans Bethe's famous appetite and his rapid 
solution of the problem of solar reaction. 

The author considers it his pleasant duty to express his 
gratitude to his friend Dr. Desmond H. Kuper for reading 
the manuscript and for giving much valuable advice on 
the translation of ergs into calories and on other similar 
questions. 

GEORGE GAMOW 
George Washington University 
January i, 1940 



Contents 



PAGE 

PREFACE vii 

NOTE ON UNITS OF MEASUREMENT xv 



I THE SUN AND ITS ENERGY 1 
The Sun and Life on Earth; The Unit of Energy; The Radiation Energy 
of the Sun; The Temperature of the Sun; The Density of the Sun; Sur- 
face Phenomena on the Sun; The Age of the Sun; Does the Sun Really 
"Burn'?; The Contraction Hypothesis; Subatomic Energy 

II THE ANATOMY OF ATOMS 17 
The Atom as Philosophic Idea; Alchemy and the Medieval Gold-Fever; 
Elementary Chemistry; The Kinetic Theory of Heat; The Energy of 
Molecular Motion; Measuring the Molecular Velocities; Statistics and 
the Maxwell Distribution; Are Atoms Really Elementary Particles?; An- 
dent Persian Electrogilding; The Elementary Electric Charge of Atoms; 
The Atomicity of Electric Charge on Small Bodies; The Electron as an 
Elementary Electric Particle; The Mass of an Electron; the Atomic 
Model; Atomic Number and the Sequence of Elements; Isotopes; The 
Shell Structure of an Atom; Chemical Binding; The Classical Theory 
Fails in the Atom!; Quantum Laws; The New Mechanics; The Problem of 
the Atomic Nucleus 

III THE TRANSMUTATION OF ELEMENTS 57 
The Discovery of Radioactivity; The Decay of Very Heavy Atoms; Lib- 
erated Energy and Decay Periods; The "Leaking Out" Theory of Radio- 
active a-Decay; The Process of &-Decay as an Electric Adjustment of 
the Nucleus; Back to Alchemy; Photographing Nuclear Bombardment; 
Cracking the Nitrogen Atom; Bombardment by Protons; The Electro- 
static "Atom-Smasher"; The Cyclotron; New "Penetrating* Projectiles; 
The Results of Neutron Bombardment; Bursting a Nucleus 

IV CAN SUBATOMIC ENERGY BE HARNESSED? 85 
Energy versus Gold; The Low Rate of Subatomic Energy Liberation; 



x Contents 

The Probability of a Charged Projectile's Hitting a Nucleus; Penetrating 
the Nuclear Fortress; Resonance Disintegration; Bombardment by Neu- 
trons; Multiplicative Nuclear Reactions; The Price of Uranium Energy; 
Recapitulation: The Structure of the Atom 

V THE ALCHEMY OF THE SUN 101 
Subatomic Energy and Solar Heat; Thermonuclear Reactions; The Tem- 
peratures Necessary for Thermonuclear Reactions; How to Make a "Sub- 
atomic Motor"; The Solar Furnace; The Solar Reaction; The Evolution 
of the Sun; What Then? 

VI THE SUN AMONG THE STARS 122 
How Bright Are the Stars?; The Colour of Stars and Spectral Classes; 
The Russell Diagram; Stellar Masses; Nuclear Reactions in Stars; A Com- 
peting Reaction in the Lighter Stars; Stellar Evolution; Stellar Evolution 
and the Mass-Luminosity Relation; The 'Youth and Old Age of Stars 

VII RED GIANTS AND THE YOUTH OF THE SUN 141 

Some Typical Red Giants; Inside the Red Giants; The Reactions of Light 
Elements; The Absence of the Lightest Elements in the Sun; The Reac- 
tions of Light Elements in Red Giants; The Evolution of Red Giants; 
Pulsating Stars; The Theory of Stellar Pulsation; Three Groups of Pul- 
sating Stars; The Cause of Pulsation 

VIII WHITE DWARFS AND THE DYING SUN 159 

The End of Stellar Evolution; The Collapse of Matter; The Properties of 
the Crushed State of Matter; How Large Can the Largest Stone Be?; 
Jupiter as the Largest Stone; The Mass-Radius Relationship of Collapsed 
Bodies; White Dwarfs; When Our Sun Is Dying 

IX CAN OUR SUN EXPLODE? 175 
The Novas; Two Classes of Stellar Explosion; The Chances of our Own 
Suns Exploding; The Prenova Stage of Stars; The Process of Explosion; 
What Causes Stellar Explosions?; Supernovas and the "Nuclear State" of 
Matter 

X THE FORMATION OF STARS AND PLANETS 194 

Stars as "Gas Drops"; Does the Process of Star Formation Continue at 
Present?; The Origin of White Dwarfs; What about Planets? 



Contents xi 

XI ISLAND UNIVERSES 206 

The Milky Way; The Number of Stars in the Sky; The Dimensions of 
Our Stellar System; The Motion of Stars within the Galaxy; The Veloc- 
ities of Stars; The Rotation of the Galaxy; The Age of the Milky Way; 
Other "Galaxies"; Distances and Dimensions of Extragalactic Nebulse; 
Extragalactic "Nebulse" Are Not Nebulae; The Rotation of Extragalactic 
Nebulae and the Origin of Spiral Arms 

XII THE BIRTH OF THE UNIVERSE 221 
Nebulas Running Away; An Expanding Universe; Which Are Older: 
Stars or Galaxies?; The Early Stages of Expansion and the Creation of 
Radioactive Elements; The Infinity of Space 

CONCLUSION 230 

CHRONOLOGY 233 

INDEX 235 



Illustrations 



PLATES 

FACING PAGE 

I. SUNSPOTS AND SOLAR PROMINENCES 8 

II. BLACKETT'S DISINTEGRATION PHOTOGRAPH OF NITROGEN 9 

III. NUCLEAR DISINTEGRATIONS 74 

A. Bombarding lithium with protons 

B. Bombarding boron with protons 

IV. THE VAN DE GRAFF ELECTROSTATIC GENERATOR 75 

V. CROSS-SECTION OF THE ELECTROSTATIC ATOM-SMASHER IN 

WASHINGTON, D. C. 78 

VI. THE LAWRENCE CYCLOTRON 79 

VII. THE HARVARD SPECTRAL CLASSIFICATION OF STARS 126 

VIII. NOVA AND SUPERNOVA 127 

A. Stages in the expansion of Nova Aquilse 1918 

B. Stages of the supernova in I.C. 4182 

IX. "PLANETARY" OR "RING NEBULA" IN LYRA 184 

X. FILAMENTARY NEBULA IN CYGNUS 185 

XI. GREAT NEBULA IN ORION 188 

XII. THE MILKY WAY AND A DARK GASEOUS NEBULA 189 

XIII. SPIRAL NEBULA IN ANDROMEDA 214 

XTV. SPIRAL NEBULA IN COMA BERENICES, ON EDGE 215 

XV. SPIRAL NEBULA IN URSA MAJOR, FROM ABOVE 218 

XVI. SPIRAL NEBULA IN CANES VENATICI, WITH SATELLITE 219 



xii 



Illustrations 



FIGURES 

PAGE 

1. The Sun at first sight, and a cross-section 2 

2. Dissociation of hydrogen peroxide into water and free oxygen 20 

3. The trajectory of Brownian motion 24 

4. The thermal energy of molecules decreases with the tempera- 

ture 26 

5. Stern's apparatus for the measurement of molecular velocities 28 

6. Maxwell curve 31 

7. Ancient Persian electric battery 33 

8. Millikan*s apparatus for measuring the elementary electric 

charge 37 

9. Thomson's arrangement for measuring the charge/mass ratio 

of electrons 40 

10. Detection of contraband in cotton bales, and of nuclei in atoms 42 

11. Rutherford's model of the atom 44 

12. Periodic system of elements on a cylindrical band 46-47 

13. Shells in different atoms 49 

14. Wave-mechanical picture of atoms 55 

15. Spontaneous disintegration of unstable nuclei 60 

16. Decay in the uranium family 61 

17. Wilson's cloud-chamber 70 

18. Analysis of Blackett's photograph of nuclear transformation 72 

19. Collision between nitrogen and helium nuclei 73 

20. Collision between lithium and hydrogen nuclei 75 

21. Principle of the electrostatic atom-smasher 77 

22. Principle of the cyclotron 81 

23. Spontaneous splitting of free neutrons 92 

24. Multiplicative disintegration in the bombardment of matter by 

neutrons 93 

25. Thermal ionization of a gas 103 

26. The maximum number of disintegrations correlated with 

thermal energy and number of particles 106 

27. A dream of a subatomic motor 109 

xiii 



xiv Illustrations 

PAGE 

28. The subatomic generator of the Sun 110 

29. The cyclic nuclear reaction chain in the Sun 114 

30. A furnace that burns stronger with less coal 117 

31. The evolution of the Sun 119 

32. The constellation of the Great Dog 123 

33. The continuous emission-spectrum changes with the tempera- 

ture 125 

34. Russell diagram 129 

35. Double stars 130 

36. Changes in luminosity and spectral class of the Sun, Sirius, and 

Krueger 60 B 136 

37. Red giants on the Russell diagram 142 

38. The size of c Aurigae I compared with the solar system 143 

39. The relative abundance of the lightest elements 148 

40. Regions of different nuclear reactions in the Russell diagram 150 

41. Eclipsing and pulsating variables, with their luminosity curves 154 

42. The collapse of a brick wall and of atoms 161 

43. Gaseous, solid (or liquid), and crushed states of matter 163 

44. Equilibrium between gas pressure and the gravitational forces 

in a large sphere of gas 166 

45. Chandrasekhar's graph for the radius-mass relationship of col- 

lapsed stars 170 

46. Luminosity changes of a typical nova and supernova 184 

47. Increasing separation of the two fragments formed by Nova 

Hercules 187 

48. Formation of the "nuclear state" of matter 191 

49. Collapse of the central regions in a supernova 192 

50. Formation of separate stars from a continuous gas 195 

51. Kant-Laplace hypothesis of the formation of planets 201 

52. "Hit-and-run" hypothesis of the formation of planets 203 

53. Schematic view of the Milky Way 207 

54. Changes in the constellation of the Great Bear 211 

55. Changes in Scorpio 212 

56. Hubble's classification of extragalactic "nebulas" 215 

57. The Galaxy and its nearest neighbours 217 

58. Extragalactic nebulae running away 222 

59. The dots on an expanding rubber balloon 224 

60. Formation of island universes 225 



Note on Units of Measurement 



In this book the decimal metric system, universally 
accepted in scientific research, is used. For those readers 
who are more accustomed to feet, pounds, and the Fahren- 
heit temperature scale, we give the following table of 
equivalences: 

i centimetre = 0.39 inch 

i kilometre = 0.62 mile 

i gramme = 0.035 un ce 

i kilogram =2.20 pounds 

To convert into Fahrenheit the temperatures here given 

in Centigrade, multiply by - and add 32 (e.g., 20 C. is the 

o 

same as 20 X ~ + 3* 68 F.). 

\s 



CHAPTER I 



The Sun and Its Energy 



THE SUN AND LIFE ON EARTH 

" *ir THIGH is more useful, the Sun or the Moon?" 
V V asks Kuzma Prutkov, the renowned Russian 
philosopher,* and after some reflection he answers himself: 
"The Moon is the more useful, since it gives us its light 
during the night, when it is dark, whereas the Sun shines 
only in the daytime, when it is light anyway/' 

Of course, every schoolboy knows that moonshine con- 
sists only of the reflected rays of the Sun, but it is still far 
from universally understood that there is scarcely a phe- 
nomenon on earth the origin of which cannot be similarly 
traced back to the energy radiated by the Sun. 

In particular do all the energy sources exploited by 
civilization have a solar origin. As yet, it is true, the direct 
utilization of solar heat, as for instance when collected by 
large concave mirrors, is employed only in a few tricky 
devices to run the refrigerators of cold-drink stands in the 
Arizona desert, or to heat water for the public baths of 
the oriental city of Tashkent. But when we burn wood, 
coal, or oil in our heating-plants and factories we are also 
merely liberating the energy of solar radiation that has 
been deposited in the form of carbon compounds in the 
forests of today or of long-past geological epochs. 

* A fictitious character created hy the idle imaginings of the Russian 
poets Count Alexei Tolstoy and the brothers Gemchushnikov. Prutkov's 
philosophic views are, however, at least as good as those of many ancient 
and contemporary philosophers. 

1 



2 The Birth and Death of the Sun 

The rays of the Sun, falling on the green leaves of grow- 
ing plants in the presence of the carbon dioxide of the air, 
decompose the latter into carbon and gaseous oxygen. The 
oxygen is liberated back into the atmosphere (that is why 
plants in a room "refresh" the air), whereas the carbon 
is deposited in the body of the plant, ready to unite again 
with atmospheric oxygen in a wood fire or in a furnace. 




FIGURE 1 
The Sun at first sight. A cross-section of the Sun. 

When we burn the tree we can never get back more 
energy than its growing leaves had received and stored up 
from the solar rays. Thus, without sunlight there would 
be no forests, either now or in the past, and consequently 
no coal and oil deposits on the surface of the earth. 

It should hardly be necessary to explain that water 
power is also a converted form of solar heat, which evapo- 
rates the water from the surfaces of oceans and seas and 
deposits it on higher levels from which it runs back to its 
original reservoirs. The same applies to wind power, which 



The Sun and Its Energy 3 

is caused by the uneven heating of the different parts of 
the earth's surface, with a consequent movement of air, 
Everywhere we find the source of our energy to be the 
Sun, without whose rays the surface of our globe would 
be dead and motionless. 

But what are the sources of solar energy? For how long 
have they been welling up, and how long will they go on 
doing so? How did our Sun come into being, and what 
will happen to it after all its energy resources are finally 
exhausted? To answer these questions we must, first of 
all, know something of the energy radiated daily by our 
Sun, and also of the total amounts of energy stored in its 
interior. 

THE UNIT OF ENERGY 

In physics energy is usually measured in standard units 
known as ergs, although in special cases other units as 
calories (in heat measurements) or kilowatt-hours (in elec- 
trotechnics) are also often employed. One erg is twice 
the kinetic energy of a mass of one gramme moving with 
the velocity of one centimetre per second, and is compara- 
tively a very small unit as far as our ordinary experience is 
concerned. 

For example, a flying mosquito possesses kinetic energy 
of several ergs; to warm a cup of tea we need several 
hundred billion ergs; and an ordinary table lamp uses 
25 billion ergs each second. One gramme of good coal 
liberates in the process of complete combustion 300 billion 
ergs of energy, and, at present coal prices, one erg of 
energy delivered in bags at our coal pits costs about 
0.000,000,000,000,003 cent. The price of the energy that 
comes to our houses along electric wires is higher, owing 



4 The Birth and Death of the Sun 

to the additional cost of the machinery that transforms the 

heat liberated by burning coal into the energy of electric 

current. 

THE RADIATION ENERGY OF THE SUN 

The energy of solar radiation that falls each second on 
one square centimetre of the earth's surface perpendicular 
to the direction of the rays has been measured at 1,350,000 
ergs, this value having been corrected for the absorption 
of our atmosphere. Thus, if we evaluate this energy in 
current coal prices, we find that on sunny days an average- 
sized backyard receives several dollars' worth of energy. 
Expressed in technical units of work, the flow of solar 
energy falling on the surface of the earth is equivalent 
to 4,690,000 horsepower per square mile; and the total 
amount of energy given yearly to our planet by the Sun 
is several million times the annual world production of 
energy obtained by burning coal and other fuels. 

But the earth collects only a very small fraction of the 
total energy radiated by the Sun, the largest part of which 
escapes freely into interstellar space and amounts to 3.8 X 
io 33 ergs per second, or 1.2 X io 41 ergs per year.* Dividing 
this energy radiation of the Sun by its surface area (6. i X 
io 22 square centimetres) we find that each square centi- 
metre of the Sun's surface emits 6.2 X io 10 ergs per second. 

THE TEMPERATURE OF THE SUN 

How hot must the surface of the Sun be in order to give 
rise to such intense thermal radiation? A very hot radiator 

* In physics and astronomy it is customary to express very large and very 
small numbers by the powers of ten. Thus 3 X io 4 = 3 X 10,000 (i.e., four 
zeros), or 30,000; and 7 X io~ 3 = 7 X .001 (i.e., three decimal places), or 
0,007. A "billion/' as used in this work, is a thousand million, or 
1,000,000,000, or io 9 . 



The Sun and Its Energy 5 

of a water-heating system (at the boiling-point temperature) 
radiates about one million ergs per second per square centi- 
metre of surface. The corresponding radiation of a red-hot 
stove (at about 500 C.) amounts to 20 million ergs, and 
that of a white-hot filament of an ordinary electric bulb (at 
about 2000 C.) to 2 billion ergs. The radiation of hot 
bodies regularly increases with their temperature, being 
proportional to the fourth power of the temperature as 
counted from absolute zero.* 

If we compare the surface radiation of the Sun with the 
examples given above, it is easy to calculate that the tem- 
perature of the solar surface must be very close to 6000 
degrees. This temperature is considerably higher than those 
obtainable under laboratory conditions by the use of spe- 
cially constructed electric furnaces; indeed, there is a very 
simple reason why no furnace could stand so high a tem- 
perature: at 6000 degrees all the materials from which a 
furnace might be constructed, including even such refrac- 
tory substances as platinum or carbon, will be not only 
melted but completely evaporated.f No material can exist 
at these high temperatures in a state other than gaseous, 
and this is exactly what we find on the surface of the Sun, 
where all elements are present in vapour form. 

But if this is true for the surface of the Sun, it must be 
also a fortiori true for its interior, where the temperatures 
must be still higher in order that there be the temperature 

* Absolute zero on the Centigrade scale is 273 degrees below the freezing- 
point (see below, p. 27). Hereafter all temperatures given will be assumed 
to be in the Centigrade scale. 

f By the utilization of this very principle, temperatures higher than that 
of the Sun's surface have actually been attained. Very strong electric cur- 
rents are sent through thin metallic filaments, which at the moment of 
discharge are instantaneously evaporated, and, for a very short interval of 
time, temperatures as high as 20,000 degrees have been registered. 



6 The Birth and Death of the Sun 

difference necessary for the flow of heat from the central 
regions toward the surface. In fact, a study of intrasolar 
conditions indicates that the temperature in the centre of 
the Sun reaches the tremendous value of 20 million degrees. 
It is a little difficult to appreciate the significance of such 
high temperatures, so it may perhaps be of some help to 
point out that an average-sized stove (made of some non- 
existent refractory substance capable of withstanding such 
heat) if brought to this temperature would by its thermal 
radiation burn up everything within a radius of many hun- 
dred miles. 

THE DENSITY OF THE SUN 

These considerations of solar temperature have brought 
us to the very important conclusion that our Sun is a giant 
sphere of an extremely hot gas, but it would be erroneous 
to imagine this gas as necessarily being a very rarefied state 
of matter. Under normal terrestrial conditions the gases 
with which we usually deal are much less dense than the 
liquid or solid forms of matter, but we must not forget that 
the pressure in the central regions of the Sun reaches the 
tremendous value of 10 billion atmospheres. Under such 
conditions any gas will be so compressed that its density 
may even exceed those of normally liquid or solid bodies. 
For the difference between the gaseous state on the one 
hand and the liquid or solid states on the other lies not in 
their relative densities but in the tendency of the gas 
toward an unlimited expansion and in its high compres- 
sibility under the action of external pressure. While a piece 
of rock taken from the interior of the earth will hardly 
change its volume when brought to the surface, the material 



The Sun and Its Energy ^ 

from the central regions of the Sun will expand without 
limit if the outside pressure is sufficiently reduced. 

The high compressibility of the gaseous matter in the 
Sun brings about a rapid increase of density as we go from 
the surface toward the centre, and it has been calculated 
that the central density of the Sun must exceed its mean 
density by a factor of 50 (that is, the core of the Sun is 50 
times denser than is the Sun taken as a whole). Since the 
mean density of the Sun, calculated by dividing its known 
mass by its dimensions (mass 2 X 1()33 grammes; volume 
1.4 X io 33 cubic centimetres), amounts to 1.41 times the 
density of water, we conclude that the gas filling the solar 
interior is compressed to a density six times that of mercury. 
On the other hand the outer layers of the Sun are quite 
rarefied, and the pressure in the chromosphere, where the 
absorption lines of the solar spectrum are formed, is only 
one-thousandth the pressure of atmospheric air. 

Although all our direct observational evidence concern- 
ing the physics and chemistry of the Sun is limited to the 
phenomena taking place in this rarefied solar atmosphere, 
it is possible, if we start with these surface conditions and 
make use of our general knowledge concerning the prop- 
erties of matter, to learn about the conditions existing in 
the solar interior almost with the same certainty as if we 
could see it with our own eyes. Our mathematical analysis 
of the solar interior is mainly owing to the work of the 
British astronomer Sir Arthur Eddington; and Figure i 
gives us the schematic picture of the internal structure of 
the Sun as obtained from his calculations. In this picture 
the values of T, P, and p give the temperatures, pressures, 
and densities respectively at different depths under the 
surface of the Sun. 



8 The Birth and Death of the Sun 

SURFACE PHENOMENA ON THE SUN 

The features of solar activity most familiar to the general 
public are the so-called sunspots (Plate IA) and solar promi- 
nences, the eruptions of hot and luminous gases that some- 
times rise to a height of hundreds of thousands of kilo- 
metres above the Sun's surface (Plate IB). The spots, which 
look dark only because of their contrast with the more 
luminous surface around them, are actually great funnel- 
shaped vortices in the outer layers of the Sun, within which 
the gases ascend spirally upwards and outwards. The expan- 
sion of the gases as they rise through these vortices decreases 
their temperature and makes the spots seem darker than 
the rest of the unperturbed surface. 

When the spot is situated close to the edge of the disk, 
we can see these gaseous eruptions in profile as giant col- 
umns of fire. The current theory of the origin of sunspots 
is based on the fact that the Sun, not being a rigid body, 
rotates with different angular velocities in its different 
parts; the rotation is somewhat slower in the equatorial 
regions than in the regions closer to the poles. This differ- 
ence of velocities causes the formation of whirls on the sur- 
face of the Sun, in the very same manner that the different 
velocities of water currents cause whirls on the surface of 
rapid rivers and streams. 

We cannot leave the subject without calling attention to 
the remarkable periodicity of sunspots, a phenomenon 
which has not yet received any satisfactory explanation. 
In an average period of about eleven and a half years, there 
is a cyclic increase and decrease in the number of spots on 
the solar surface. This periodicity has some minute in- 
fluence on^Jhe physics of our globe, manifested in slight 
ch&fcges of the average yearly temperature (within one de- 




PLATE 1A. Great suiispot group (Mt. Wilson Observatory, 1917). The 
black disk represents the relative size of the earth. ( See p. 8. ) 




PLATE IB. Solar prominence, 225,000 kilometres high (Mt. Wilson 

Observatory, 1917). The white disk represents the relative size of the 

earth. ( See p. 8. ) 



PLATE II. One of the first photographs (Blackett's) of artificial nuclear 

disintegration. An a-particle hits a nitrogen nucleus in the atmosphere, 

and ejects a fast proton (compare Figure 18). The \ievv at the right is 

the one described in the text. (See p. 71.) 



The Sun and Its Energy 9 

gree), magnetic disturbances, and the aurora. There have 
also been some attempts to correlate this periodic activity 
of the Sun with changes in the time of the migration of 
swallows, with wheat yields, and even with social revolu- 
tions, but such correlations can hardly be considered as 
well established.* 

Spots and prominences are limited to a comparatively 
thin layer of the solar surface, and probably have no more 
connexion with the evolutionary life of the Sun than slight 
skin irritations have with the developmental life of human 
beings. Thus, the group of problems represented by these 
phenomena will not concern us in the present book. 

THE AGE OF THE SUN 

We come now to the important question of the age of 
the Sun, which is, on the one hand, closely connected with 
the problem of the age of our earth and, on the other, with 
that of the age of the entire stellar universe. We know that 
the Sun of today is the same as it was last year, the same 
as it was when Napoleon pointed it out to his soldiers as 
the "Sun of Austerlitz," the same as it was when the priests 
of ancient Egypt worshipped it as Amon-Ra, the God 
of Gods. 

Of course, the period of recorded human history is only 
a quick wink as compared with the geological and palaeon- 
tological time scale, and the evidence hidden under the 
surface of the earth suggests a considerably longer, period 

Registered maxima occurred in the years 1778, 1788, 1804, 1816, 1830, 
1837, 1848, 1860, 1871, 1883, 1894, 1905, 1917, 1928. And, as a matter of 
fact, the American Revolution, the French Revolution, the Paris Commune, 
both Russian Revolutions, and also some others fell fairly close to the 
years of maximum solar activity. There has also been a distinct increase in 
activity lasting persistently through 1937-1940, which, if the reader wishes, 
he may tentatively associate with the highly perturbed state of the world 
during these years. 



10 The Birth and Death of the Sun 

during which the Sun's activity has remained unchanged. 
The coal we burn in our stoves today gives us excellent 
proof that the same Sun shone above the strange-looking 
forests of lepidodendrons and giant horse-tails of long-past 
geological epochs; the fossils found in different geological 
layers exhibit an unbroken course of organic evolution 
since pre-Cambrian times. During the past several hun- 
dreds of millions of years, therefore, the Sun cannot have 
changed in its brightness by an appreciable amount, for 
any appreciable change would have made life on earth 
quite impossible and cut short the progress of organic 
' evolution.* Indeed, halving the amount of solar radiation 
would bring the earth's temperature well below the freez- 
ing-point, and multiplying it by four would cause the 
oceans and seas to boil. 

Life on earth must surely be younger than the earth 
itself, and still larger age-estimates can be derived from the 
purely inorganic evidence contained in the chemical con- 
stitution of the rocks that form the crust of our planet. 
Many of these rocks contain minute amounts of the so- 
called radioactive elements, uranium and thorium, which 
are known to be unstable and to decay very slowly a 
process which takes billions of years and leads to a final 
product analogous to ordinary lead. As long as the surface 
of the earth was in a molten, lava-like state, these disinte- 
gration products must have been constantly separated from 
their mother-elements by the mixing processes of diffusion 
and convection; but, as soon as the solid crust had been 

* The possibility is not excluded that the so-called glacial periods, indi- 
cated by geological evidence, may have been connected with some small 
variation of solar activity. It should be noted, however, that such small 
changes of climate could also be easily produced by purely terrestrial 
factors, as, for example, the variation of the carbon-dioxide content in our 
atmosphere. 



The Sun and Its Energy 11 

formed, they must have begun to accumulate near the 
radioactive elements. Therefore, by measuring the relative 
amounts of these radioactive elements and their disintegra- 
tion products in different rocks, we can form an exact idea 
about the time when the rock became solidified, in the 
same way as we might estimate the age of a village from 
the number of bones in its cemetery. 

The investigations carried out along these lines lead to 
the conclusion that the solid crust of the earth was formed 
not later than 1.6 billion years ago. Since the formation of 
the crust must have taken place rather soon after the sepa- 
ration of the earth from the Sun, we also have by this 
means a fairly exact estimate of the age of our planet as 
an individual body. The Sun cannot be younger than this, 
but it may be considerably older, and, in order to put an 
upper limit on its possible age, we must turn to the evi- 
dence concerning the whole stellar universe of which our 
Sun is only one of numerous members. 

The process of the formation of stars, and in particular 
of our Sun, from a uniform gas previously filling all space, 
will be discussed in later chapters (X-XII). Here we shall 
merely mention that the study of the motion of stars in our 
stellar system, and of the motion of different stellar sys- 
tems relative to one another, strongly suggests that the 
process of star formation took place not earlier than 2 bil- 
lion years ago. This gives us rather narrow limits for the 
probable age of the Sun; it also indicates that our earth 
and other planets must have been formed during an early 
phase of the Sun's life. 

Multiplying the annual radiation of the Sun as given 
above (1.2 X io 41 ergs) by its estimated age in years (ap- 
proximately 2 billion), we arrive at the conclusion that 



12 The Birth and Death of the Sun 

since its formation the Sun must have radiated about 2.4 X 
/o 50 ergs of energy, or 1.2 X J 17 ergs f or each gramme of 
its mass. Where did these tremendous amounts of energy 
come from? 

DOES THE SUN REALLY "BURN"? 

The first hypothesis concerning the origin of solar heat 
and light was most probably uttered by some caveman of 
the Early Stone Age who, looking at the shining Sun, 
applied to it the same word that he used to denote the 
burning fire of his hearth. Prometheus, when he stole a 
piece of the eternal fire of the Sun for early man, prob- 
ably considered it to be just as good for cooking purposes 
as the fire fed by wood or coal. And this naive belief that 
the Sun "burned" firmly held its place in the mind of 
humanity up to comparatively recent times. 

The moment, however, we ask what it actually is that 
burns in the Sun, it becomes evident that the process of 
ordinary combustion is quite inadequate to explain the 
long period of solar activity. We have already seen that a 
gramme of coal when completely burned develops only 
3 X lo11 er g s which is half a million times less than the 
energy production per gramme of the Sun during its past 
life. If the Sun were made of pure coal and had been set 
afire at the time of the first Pharaohs of Egypt, it would by 
now have completely burned to ashes. The same inade- 
quacy applies to any other kind of chemical transforma- 
tion that might be offered in explanation of solar heat 
development; none of them could account for even a 
hundred-thousandth part of the Sun's life. 

As a matter of fact, the very notion of "burning" is quite 
inconsistent with the conditions to be found in the Sun. 



The Sun and Its Energy 13 

Spectroscopic analysis does show the presence of both car- 
bon and oxygen in the solar atmosphere, but the Sun is 
just too hot to burn. Ordinarily we are accustomed to think 
of combustion, or of any other chemical reaction resulting 
in the formation of complex compounds, as facilitated by 
an increase in temperature. A piece of wood will begin to 
burn, that is, to unite with the oxygen of the air, when it 
is set afire by the flame of a match, and to light a match 
we have to heat the phosphorus of its head by rubbing it 
against a rough surface; but too high temperatures are, on 
the other hand, destructive to complex chemical substances 
and cause their dissociation into elements water vapour 
being decomposed into hydrogen and oxygen, carbon diox- 
ide into carbon and oxygen. 

The temperature of 6000 degrees to be found in the 
solar atmosphere breaks the chemical bonds of all complex 
compounds, and the gas forming the Sun must consist only 
of a mechanical mixture of pure elementary substances. In 
the outer layers of some other stars, however, with con- 
siderably lower surface temperatures (1000 to 2000 degrees) 
the formation of complex substances, including carbon 
dioxide, could be expected to take place. 

THE CONTRACTION HYPOTHESIS 

We have gone somewhat afield from our original ques- 
tion concerning the origin of solar energy, and in return- 
ing to our theme we are brought to the work of a famous 
German physicist of the last century, Hermann von Helm- 
holtz, who was concerned not only with the problem of 
the present state of the Sun, but also with that of its origin. 

According to Helmholtz, the Sun was, once upon a time, 
a giant sphere of cool gas with a diameter much larger 



14 The Birth and Death of the Sun 

than its present one. It is clear that such a gas-sphere could 
not be in a state of equilibrium, for the comparatively 
slight pressure of a cool and highly rarefied gas could not 
balance the mutual gravitational attraction among its dif- 
ferent parts. Thus, under the action of its own weight, 
this primitive Sun must have started a rapid contraction, 
compressing the gas in its interior regions. But it is well 
known from elementary physics that the compression of a 
gas, as by a moving piston in a cylinder, causes a rise of its 
temperature. Thus, the progressive contraction, or falling 
in, of the original giant gas-sphere must have caused the 
heating of its material, until the rising pressure of the gas 
in the interior became great enough to hold up the weight 
of the outer layers. 

At this stage the rapid falling-in process of the solar 
substance must have been stopped, and the Sun would have 
come to a perfect equilibrium if there were no loss of 
energy from its surface. But, owing to the continuous 
radiation from the surface into the surrounding cold space, 
our gas-sphere will be constantly losing some energy, and, 
to compensate these losses, a further progressive contrac- 
tion becomes necessary. According to the Helmholtz point 
of view, then, the Sun is actually in this state of progressive 
contraction, its radiation being due not to any chemical 
action but entirely to the gravitational energy liberated 
in this process. 

From Newton's laws of gravity, it is not difficult to cal- 
culate that, in order to maintain the observed intensity of 
solar radiation, the Sun's radius must decrease every cen- 
tury by 0.0003 percent, or by approximately two kilo- 
metres. Such a change would, of course, pass quite un- 
noticed, not only during the life of a given individual, but 



The Sun and Its Energy 15 

also during the entire period of human history. Neverthe- 
less, from the point of view of the geological time scale, it 
is much too rapid. 

The total gravitational energy that would have been 
liberated in the contraction of the Sun down to its present 
radius, even from almost infinite dimensions, can be cal- 
culated: it is only 2 X io 47 ergs, which still gives us 1000 
times less energy than has actually been expended. Thus, 
although it seems very likely that Helmholtz's contrac- 
tion hypothesis may quite correctly account for the early 
stages of solar evolution, we must conclude that in its 
present state our Sun possesses other energy sources much 
more powerful than those of chemical or gravitational 
origin. 

SUBATOMIC ENERGY 

The physical science of the last century was quite unable 
to explain the riddle of the energy supply of our Sun; but 
on the verge of the present century, the discovery of the 
phenomenon of the radioactive decay of matter, and with 
it the possibility of the artificial transmutation of elements, 
threw some light on this most fundamental question of 
astrophysics. It was found that in the very depths of matter, 
inside the infinitesimal nuclei of the atoms of which all 
material bodies are constituted, tremendous amounts of 
energy lay hidden. This so-called subatomic energy, which 
was first observed slowly leaking out from the atoms of 
radioactive bodies, may under certain circumstances flow 
out in a vigorous stream surpassing by a factor of millions 
the energy production of ordinary chemical reactions. 

The study of subatomic energy and of the physical con- 
ditions necessary for its liberation has permitted us in 



16 The Birth and Death of the Sun 

recent times to account not only for the radiation of our 
Sun but also for the radiation and other characteristic 
properties of the various types of stars known to the astron- 
omer. Furthermore, the questions concerning stellar evolu- 
tion, and in particular the question about the past and 
future of our own Sun, have been brought much nearer 
solution since the problem of energy sources was solved. 

But, before we may approach the discussion of these 
exciting problems, we must first make a long detour 
through the world of atoms, and learn certain important 
things about their properties and internal structure. The 
author regrets the pain that this excursion into the domain 
of pure physics may cause some readers who picked up this 
book for its astronomical title, but, except for poets, no 
one should speak about stars without knowing the proper- 
ties of matter of which they are constructed. Besides, if the 
reader pays close attention to the rather difficult subjects to 
be discussed in the next three chapters, he will be rewarded 
by a better understanding of astronomy, of which we prom- 
ise there will be plenty in the chapters that follow them. 
And, finally, it is possible merely to skim through these 
three chapters and to take their conclusions for granted 
without thereby sacrificing a clear picture of the evolu- 
tionary past, present, and future of our Sun. 



CHAPTER II 



The Anatomy of Atoms 



THE ATOM AS PHILOSOPHIC IDEA 

THE history of atomic theory begins in the ancient 
Greek city of Abdera, approximately in the year 375 
B.C. Its first proponent was an elderly man with an untidy 
grey beard who taught his doctrines outdoors, in the 
shadow of the temple. Democritus was his name, and he 
has been known as the Laughing Philosopher. 

"Any piece of matter, as for example this stone," we may 
imagine him lecturing, "is constructed of a great number 
of extremely small separate particles, in the very same way 
that this temple is constructed of its separate stones. These 
particles, constituting all material bodies, come together in 
different order and positions, like the letters of the alpha- 
bet, which, though they are few, form innumerable words. 
These basic particles represent the last thinkable step in 
the divisibility of matter. Thus, I call them atoms (that is, 
'indivisible'). They are so small that it must be logically 
impossible to divide them into still smaller parts." 

For the philosophic mind of Democritus, the existence 
of atoms was a logical necessity, the last step in the process 
of the successive division of matter, a process that he re- 
fused to recognize as being unlimited. The atomic hypoth- 
esis also appeared to him to reduce the infinite variety of 
observed phenomena to the combinations of a compara- 
tively few types of elementary particles, and thus to satisfy 

17 



18 The Birth and Death of the Sun 

his philosophic preconception concerning the fundamental 

simplicity of nature. 

In conformity with the ideas prevailing at this time in 
Greek philosophy, Democritus recognized four different 
types of basic particles: those of air, earth, water, and fire, 
which represented respectively the properties of lightness, 
heaviness, dampness, and dryness. He believed that all 
the known substances of nature could be obtained from 
different combinations of these four basic elements, as in 
the ordinary processes of making mud from a mixture of 
earth and water, or vapour from a "mixture of fire and 
water" in a saucepan. He even speculated about the prop- 
erties of these basic particles and, in particular, imagined 
the "atoms of fire" as slippery spherical bodies, thus ex- 
plaining the liveliness of flame. 

ALCHEMY AND THE MEDIEVAL GOLD-FEVER 

Many centuries passed after the time of the Greek 
thinker who had sought to penetrate into the riddles of 
matter by the sheer power of mind before the study of 
matter and its transformations took a more practical turn. 
Throughout the Middle Ages, in rooms dimly lit by dusty 
Gothic windows, the alchemists of Europe toiled vainly 
before great fireplaces, with innumerable odd-shaped re- 
torts, with jars of every conceivable substance. Ridden by 
the old philosophic doctrine of the unity of matter, and 
by the practical desire to enrich themselves, they powdered, 
mixed, melted, dissolved, boiled, precipitated, sublimated, 
and treated in every possible manner these various sub- 
stances of nature in a desperate search for a method of mak- 
ing artificial gold; and thereby they incidentally laid the 
foundations of modern chemistry. 



The Anatomy of Atoms 19 

At this time the four "elements" of ancient Greek philos- 
ophy had been replaced by four other supposedly ele- 
mentary substances: mercury, sulphur, salt, and fire. It was 
believed that their proper combination must finally lead 
to the formation of gold, silver, and all other known sub- 
stances. But as gold and silver stubbornly refused to be 
formed in spite of the centuries-long efforts of hundreds of 
alchemists, the conception began slowly to be advanced in 
many alchemical laboratories toward the end of the seven- 
teenth century that these precious metals, as well as many 
other substances, were themselves also elementary. It was 
thus that the mysterious art of making gold eventually 
developed into the science of chemistry, and the four ele- 
mentary substances of alchemy and philosophy gave place 
to a larger but still limited number of independent chem- 
ical elements. 

So persistent was the effect of the negative results of 
medieval alchemy, however, that in the chemistry of the 
eighteenth and nineteenth centuries the impossibility of 
transmuting one element into another was considered to 
be a basic principle of the science. The atoms of the differ- 
ent elements were thought of as absolutely indivisible par- 
ticles of matter, in complete agreement with the Greek 
meaning of their name, and "alchemist" became a word of 
reproach among scientists. But, as we shall see later, the 
pendulum of theory had swung much too far in the 
opposite direction. 

ELEMENTARY CHEMISTRY 

If there is only a limited number of different kinds of 
atoms (we know now that there are ninety-two elements), 
then all the vast number of other substances must be com- 



20 The Birth and Death of the Sun 

posed of different combinations of these atoms; and the 
complex constituent particles, or molecules, of the various 
chemical non-elementary substances must differ only in 
the kind and relative number of the atoms of which they 
are constructed. It is known at present to every schoolboy, 
for example, that the molecule of water consists of two 
hydrogen atoms and one oxygen atom, and that, on the 
other hand, the molecule of hydrogen peroxide familiar 
to all brunettes envious of platinum blondes consists of 
two hydrogen and two oxygen atoms. In the latter mole- 
cule, the second oxygen atom is bound comparatively 
loosely and can easily become free, thereby causing the 
oxidation and discoloration of different organic substances. 
The process by which a complex, unstable molecule of 
hydrogen peroxide is dissociated into a molecule of ordi- 
nary water and a free oxygen atom is shown schematically 
in Figure 2. 





FIGURE 2 
Dissociation of hydrogen peroxide into water and free oxygen. 



In order to save time, chemists prefer to express such 
processes in a somewhat simpler fashion, employing for- 
mulas in which each element is denoted by a symbol (an 
abbreviation of its Greek or Latin name), and in which 
the number of atoms of each kind in a given molecule is 
indicated by a small figure at the lower right-hand corner 
of the corresponding symbol. The chemical reaction de- 
scribed above can thus be written in the form: 



The Anatomy of Atoms 21 

H 2 O 2 >H 2 O + O 

In the same way we write CO 2 for the carbon dioxide of 
the air, C 2 H 5 OH for alcohol, CuSO 4 for the blue crystals 
of copper sulphate, and AgNO 3 for lunar caustic, or silver 
nitrate. 

The atomic-molecular hypothesis obviously requires that 
the relative amounts of different chemical elements neces- 
sary for the formation of any complex chemical substance 
should always be in the same proportions as the weights of 
the corresponding atoms, and the experimentally estab- 
lished fact that this is really so serves as one of the best 
proofs for the correctness of these views. This theory was 
first propounded by the English chemist John Dalton at 
the very beginning of the last century. 

' 'Suppose/' Dalton had argued, "that old Democritus 
were right, and that all elementary bodies do really consist 
of infinitely small atoms. If one were to go about construct- 
ing a particle of some chemical compound from these 
atoms, one should have to use one, two, three, or more of 
them. But one cannot use, say, three and a quarter atoms, 
just as one cannot build a gymnastic group out of three 
and a quarter acrobats/' After the publication in Man- 
chester, in 1808, of Dalton's book, New System of Chemical 
Philosophy, the existence of atoms and molecules became 
the established and unshakable basis of the science of mat- 
ter. The quantitative study of chemical reactions among 
various elements led to the exact evaluation of their rela- 
tive atomic weights, but the absolute weights and dimen- 
sions of individual atoms remained outside the scope of 
chemical science. The further progress of atomic theory 
now depended upon the development of the science of 
physics. 



22 The Birth and Death of the Sun 

THE KINETIC THEORY OF HEAT 

Does the hypothesis of the molecular structure of matter 
permit us to understand the differences between its three 
fundamental states the solid, the liquid, and the gaseous? 
We know that any substance in nature can be brought into 
each of these three states. Even iron evaporates at several 
thousand degrees, and even air freezes into a solid block at 
sufficiently low temperatures. Thus, the difference between 
the solid, liquid, and gaseous states of a given body depends 
upon its thermal condition. By adding heat to a solid body 
we transform it into a liquid. By adding still more heat we 
transform the liquid into a gas. But what is heat? 

In the early stage of the development of physics, it was 
thought that heat was a unique imponderable fluid that 
flowed from hot bodies into colder ones, warming them; a 
point of view that represented a survival of the ancient idea 
of fire as an independent element. But we can warm our 
hands simply by rubbing them against each other, and a 
piece of metal becomes hot if we strike it many times with 
a hammer. It seemed strange that this hypothetical "heat- 
fluid" should be produced by rubbing or striking. 

From the molecular theory of matter came a much more 
rational explanation, according to which a hot body does 
not contain any additional fluid of any kind, but differs 
from a cold body only in the state of motion of its particles. 
The molecules of every material body at normal tempera- 
ture are in a state of permanent motion; and the faster they 
move, the hotter the body seems. If we bring a hot body 
into contact with /a colder one (or, as we say, if there is a 
temperature gradient between two adjacent bodies), the 
fast-moving molecules of the first will collide, on their 
common boundary, with the slower-moving molecules of 



The Anatomy of Atoms 23 

the second and transfer to them a part of their kinetic 
energy. Thus, the fast molecules will gradually slow down, 
and the slow ones speed up, until a state of equilibrium 
will be reached in which the molecules in both bodies 
have equal average energies. We say then that both bodies 
possess the same temperature, and that the "flow of heat" 
from one into the other has ceased. 

From such a view of the nature of heat and temperature, 
it follows at once that there should exist a lowest possible 
temperature, or an absolute zero, at which the molecules 
of all material bodies are completely at rest. At this tem- 
perature the constituent particles of any substance will 
stick together, because of intermolecular cohesive forces, 
and demonstrate the properties of a solid. 

As the temperature rises, and the molecules begin to 
move, there comes, sooner or later, a stage when the cohe- 
sive forces are no longer able to keep the molecules rigidly 
in their places, though still strong enough to prevent them 
from flying apart. The body ceases to be rigid but still 
keeps its finite volume, and we then have matter in the 
liquid state. At still higher temperatures, the molecules 
move so fast that they tear apart from each other and fly 
off in all directions, thus forming a gas with a tendency 
toward unlimited expansion. The fact that some substances 
melt and evaporate at much lower temperatures than others 
is simply explained by differences in the strength of the 
cohesive forces of their respective molecules. 

THE ENERGY OF MOLECULAR MOTION 

Is there a direct empirical confirmation for these views; 
may one actually observe this, thus far hypothetical, ther- 
mal motion of molecules? The first step toward such a proof 



24 The Birth and Death of the Sun 

was actually made early in the nineteenth century, but the 
man who made it had not the slightest idea of the impor- 
tance of his discovery. 

Robert Brown, F.R.S., D.C.L., keeper of the botanical 
collections of the British Museum in London, was bent 
over his microscope, watching with great surprise the 
strange behaviour of certain tiny plant spores suspended 




FIGURE 3 
The trajectory of Brownian motion as seen through a microscope. 

in a little drop of water. The spores seemed to be animated 
by a continuous but irregular motion; they jumped to and 
fro and described complicated zigzag trajectories though 
they never went far from their original positions (Figure 3). 
It was as if all the inside of the drop were shaking, as things 
do on a fast train; yet the microscope on the old botanist's 



The Anatomy of Atoms 25 

table stood quite steady. This property of permanent 
restlessness is typical of any kind of very small particle 
suspended in a fluid; it was later found to hold for tiny 
metallic particles suspended in water (the so-called colloid 
suspension of metals) and even for miniature dust particles 
floating in the air. 

Brown announced his discovery in 1828, but could give 
no adequate explanation for it. Almost half a century later 
it was shown that the cause of this Brownian motion is 
the continual irregular bombardment of the suspended 
particles by molecules of the liquid or gas animated by 
thermal motion. The minute "Brownian particles" are just 
half-way in size between the invisibly small molecules and 
the objects we deal with in everyday life; they are small 
enough to be influenced by collisions with separate mole- 
cules, but still large enough to be seen through a good 
microscope. By examining the motion of these particles 
we can directly calculate the energy of thermal motion of 
the surrounding molecules. And the fundamental laws of 
mechanics tell us that, in a mixture of a great number of 
irregularly moving particles, they must all have, on the 
average, the same kinetic energy; the lighter particles must 
move faster and the heavier ones more slowly in such a way 
that the product of their individual masses by the square 
of their individual velocities (which product defines the 
kinetic energy) remains always the same. 

If this equipartition law of energy is not fulfilled in the 
beginning, the mutual collisions will very soon slow down 
the particles that move too fast and speed up those that 
move too slowly, until the total energy is equally divided 
among all of them. The Brownian particles, although they 
seem very small to us, are quite gigantic as compared with 



26 The Birth and Death of the Sun 

separate molecules, and must consequently have a consider- 
ably slower motion. Observing the velocity of motion of 
these particles, and also, by an ingenious device, measuring 
their mass, the French physicist Jean Perrin was able to 
show that at room temperature (20 C. or 68 F.) their 
average kinetic energy amounts to 0.000,000,000,000,063 
(i.e., 6.3 X io~ 14 ) erg. According to the equipartition law, 



ENER&Y 

14 

xtO ergs ^ 



-* 



'C 









FIGURE 4 

The thermal energy of molecules decreases with the temperature, and 
vanishes at -273* C. 

this must also be the kinetic energy of the molecules of any 
substance at this temperature. 

The study of Brownian motion permits us also to cor- 
relate the increase of molecular motion with the rise in 
temperature. If we heat the liquid in which the particles 
are suspended, their motion becomes more and more ani- 
mated, showing the increasing energy of the motion of 
separate molecules. In Figure 4 we illustrate the depend- 



The Anatomy of Atoms 27 

ence of the measured energy of Brownian particles (or, 
what is the same thing, of the separate molecules) upon the 
temperature of the liquid. For water the measurements 
can, of course, be made only between the freezing- and 
boiling-points (see the unbroken line between o and + 
100); but, since all the observed points between these 
limits are found to lie on a straight line, we can extrapolate 
this line for lower and higher temperatures, that is, con- 
tinue it in both directions, as in the dotted part of the line 
in Figure 4. 

Being extrapolated toward the lower temperatures, the 
observed line crosses the horizontal axis, representing zero 
energy, at the point 273 C. ( 459 F.). At this point 
the energy of molecular motion absolutely vanishes, and 
below this point it is therefore meaningless to speak of 
differences in temperature. It represents the lowest possible 
temperature, or absolute zero, and is the foundation of the 
so-called absolute, or Kelvin's, temperature scale. 

MEASURING THE MOLECULAR VELOCITIES 

Since the study of Brownian motion has led us to a 
direct estimate of the kinetic energy of the thermal motion 
of molecules, we need only find a method for directly meas- 
uring the velocities of molecules, and from these two meas- 
urements we shall readily estimate also their mass (since 
kinetic energy i/ mass X square of velocity). A very ex- 
cellent method for the direct estimation of molecular ve- 
locities was worked out by a skilful German physicist, Otto 
Stern. Stern knew that one could hardly hope to measure 
the velocities of molecules within a gas or a liquid, where, 
owing to the never-ending mutual collisions, the particles 
move too irregularly and their velocities are constantly 



28 The Birth and Death of the Sun 

changing direction. In the air, for example, under normal 
pressure and temperature, each molecule is subjected to 
many billions of collisions per second, and the free path 
between two collisions measures only 0.000,01 centimetre. 
The problem Stern set himself, therefore, was to give a 
few gas molecules unobstructed and measurable paths in 
free space; and in a few months he devised a new apparatus 
for this purpose (Figure 5). All the parts of this apparatus 




pump 



FIGURE 5 
Diagram of Stern's apparatus for the measurement of molecular velocities. 

were placed inside a long, cylindrical, completely evacuated 
vessel. At one end (left) of this large cylinder was a 
"molecular dungeon," a closed chamber into which was 
placed (through a special valve in the back) the substance 
to be investigated. A wire wound spirally around this 
chamber carried an electric current which developed 
enough heat to evaporate its contents. As the molecules 
of the vapour, animated by thermal motion, flew about in 
all directions inside the dungeon chamber, some of them 
were bound to escape, through the tiny hole provided in 
its wall, in a fine molecular spray. In front of the opening, 
however, two little diaphragms cut out from this spread- 



The Anatomy of Atoms 29 

ing molecular beam all except those particles which were 
moving along the axis of the cylinder. Thus was formed a 
parallel beam of molecules, all moving in the same direc- 
tion with their original thermal velocities. 

But the essence of the device was the means for actually 
measuring the velocity of the particles forming this beam. 
For this purpose Stern borrowed a method often used to 
regulate automobile traffic on long avenues of large cities, 
in which the traffic lights are so synchronized that only the 
cars driven at a certain speed can go all the way through 
without being stopped by red lights at intersections. In 
Stern's apparatus this same stop-and-go system was set up 
as follows: 

In the path of the parallel beam of molecules two cog- 
wheels, fastened on opposite ends of a rapidly rotating 
axis, were adjusted in such a way that the teeth of the first 
were exactly in front of the openings of the second, so that, 
when the axis was not rotating, no molecule could pass 
through. But if the wheels were rotated at such a speed 
that the time in which a tooth turned by one-half its width 
was exactly the time required for the molecule to cover the 
distance between the wheels, then all the molecules of the 
same velocity would pass both wheels and be registered on 
the screen at the right end of the large cylinder. Thus, by 
observing the speed of rotation necessary to let the molecu- 
lar beam through, Stern could easily calculate the velocity 
of the particles of the beam. The velocity of sodium atoms 
at a temperature of 500 degrees was found by him to be 
100,000 centimetres per second (2000 miles per hour!), 
which, when recalculated for hydrogen atoms at room tem- 
perature, gives the value of 2.8 X io 5 centimetres per 
second. 



30 The Birth and Death of the Sun 

If we now remember from Perrin's experiment (p. 26) 
that the kinetic energy of thermal motion for all particles 
at this temperature is 6.3 X io~ 14 erg, it is easy to calculate 
(from the formula: kinetic energy i/% mass X velocity 
squared) that the mass of a hydrogen atom amounts to 
1.6 X /o~ 24 gramme. The masses of other atoms and mole- 
cules can now also be calculated from their relative atomic 
and molecular weights as estimated by chemical methods. 
For instance, the water molecule is eighteen times heavier 
than the hydrogen atom, and since a cubic centimetre of 
water weighs one gramme, it must contain 3 X *o 22 water 
molecules, and the diameter of a water molecule must 
therefore roughly be 3 X io~ 8 centimetre.* To obtain 
some idea of the negligible weight and size given by the 
above quantities, one need only note that the number of 
molecules in a little drop of water is about the same as the 
number of drops of water in the great Lake Michigan. 

STATISTICS AND THE MAXWELL DISTRIBUTION 

We have mentioned above that, in any collection of a 
large number of irregularly moving particles, the mutual 
collisions must soon lead to a state in which the total 
energy of the system will be, on the average, equally dis- 
tributed among all the particles. By the phrase "on the 
average" we mean to indicate that this proposition can be 
only statistically true, for, as a matter of fact, owing to the 
irregularity of the collisions, any given molecule may, at 
any given instant, be travelling at an extraordinarily great 
velocity or may, on the other hand, be almost motionless. 
Thus, the kinetic energy of any given particle is constantly 

* The dimensions of a molecule can be given only with a rough average 
value, since, according to the present view of atomic structure, its exact 
limits are essentially undefined. (See Figure 14 below.) 



The Anatomy of Atoms 31 

increasing and decreasing quite irregularly, but the aver- 
age value will remain the same for all the particles in the 
collection. If at a given instant we could measure simul- 
taneously the velocities of all the molecules of a gas filling 
a vessel, we would find that, although the energies of most 
of the particles were very close to the average value, there 




FIGURE 6 

The Maxwell curve, showing the relative number of molecules with 
different energies at a given temperature. N = number of particles; 

E = energy. 

would always be a certain percentage of the particles with 
velocities considerably smaller or larger than the average. 
In Stern's apparatus, for instance, there were always 
found to be present in the molecular beam some particles 
that were moving faster or slower than the average. Experi- 
mentally this was shown by the fact that, when the speed 
of the rotating cogwheels was changed, the beam passing 
through did not immediately vanish, but its intensity 
decreased to zero rather gradually. This phenomenon pro- 



82 The Birth and Death of the Sun 

vides us with a method for finding out how many mole- 
cules of different energies are present in the beam. This 
energy distribution is described by a very simple formula 
developed, on the basis of purely statistical considerations, 
by the English physicist Clerk Maxwell and known as the 
Maxwell distribution law. 

The distribution, which is represented graphically in 
Figure 6, is quite general and applies to any large collec- 
tion of particles, from the molecules of a gas in a vessel to 
the stars forming our galactic system. We shall see later 
that this distribution of molecular velocities plays an 
important role in the questions concerning the liberation 
of subatomic energy from substances brought to very high 
temperatures. 

ARE ATOMS REALLY ELEMENTARY PARTICLES? 

Ever since the establishment of the atomic theory as 
fundamental to the science of matter, the atom has been 
the carrier of all the characteristic properties of the dif- 
ferent elements. Why is it that hydrogen will unite with 
oxygen and carbon, but will not form any chemical com- 
pounds with such elements as sodium or copper? Because 
such are the chemical properties of the atoms of these 
substances. Why does putting a sodium salt into a flame 
give rise to a brilliant yellow colour, while copper salts 
give off a green illumination? Because such are the dif- 
ferent optical properties of sodium and copper atoms. Why 
is iron hard and strong, tin so soft, and mercury, at normal 
temperature, liquid? Because of the differences of cohesive 
forces of the atoms of these metals. 

But is it possible to explain why different atoms possess 
such different properties? Yes, if we abandon the old idea 



The Anatomy of Atoms 33 

of the basic indivisibility of atoms, which was solemnly 
accepted in science up to comparatively recent times, and 
instead think of the atom as a complex structure built up 
of other, still smaller particles. Thus we may be able to 
relate the known properties of the atoms of different ele- 
ments to the differences in their internal structure. But if 
atoms are really complex systems, what then are the parti- 
cles of which they are constructed? Is it possible to make 
an "autopsy" of an atom, extract its various parts, and study 
them separately? To answer these questions we must first 
turn our attention to the study of electric phenomena, and 
particularly of the basic electric particles, or electrons. 

ANCIENT PERSIAN ELECTROGILDING 

The first practical use of electricity and electric current 
takes us back to the distant past. In recent excavations at 




FIGURE 7 
An ancient Persian electric battery. 



34 The Birth and Death of the Sun 

Khujut-Rabua, not far from the city of Baghdad, a very 
strange type of vessel has been found among the relics that 
probably belong to the first century B.C. It consists of a 
vase, made of clay, inside of which is fastened a cylinder of 
pure copper. Through a thick asphalt cover on its top is 
driven a solid iron rod, the lower part of which has been 
eaten away, probably by the action of some acid (Figure 7). 
This assembly could hardly have been used for any other 
purpose than that of generating a weak electric current, 
and was most probably used by Persian silversmiths, long 
before the reign of the fabulous Harun al Rashid, for 
electrogilding their wares. In the backs of little shops in 
colourful oriental bazaars, electric currents were depositing 
uniform layers of gold and silver on ear-rings and bracelets 
almost two thousand years before the phenomenon of 
electrolysis was rediscovered by the Italian Dottore Galvani 
and made widely known to humanity. 

THE ELEMENTARY ELECTRIC CHARGE OF ATOMS 

The very same process of transferring matter by electric 
current that had served to gild jewellery for oriental belles 
of long ago was the basis of some remarkable conclusions 
concerning the properties of matter and electricity by the 
celebrated English physicist of the last century, Michael 
Faraday. Investigating the relation between the amount of 
electricity that passed through an electrolytic solution and 
the amount of material deposited on the electrodes, Fara- 
day found that for the same amount of electricity the 
deposits of different elements were always proportional to 
their combining chemical weights. From the atomic- 
molecular point of view, this means that the electric charge 
carried by different atoms is always an integer multiple of 



The Anatomy of Atoms 35 

certain elementary amounts of electricity. For example, an 
ion (that is, a charged atom) of hydrogen carries one single 
positive charge, an ion of oxygen a double negative charge, 
and an ion of copper a double positive charge. 

Thus it became clear that there is some sort of atomicity 
of electric charge, paralleling the atomicity of matter. One 
can calculate the absolute amount of this elementary charge 
simply by dividing the total amount of electricity that has 
passed through an electrolyte by the number of hydrogen 
atoms deposited at the negative electrode. Expressed in 
customary units, this elementary portion of electricity is 
extremely small; for example, the current feeding an ordi- 
nary table lamp carries billions of billions of such portions 
every second. 

THE ATOMICITY OF ELECTRIC CHARGE ON SMALL 
BODIES 

We have previously seen that the atomicity of matter 
and the thermal motion of molecules are directly observ- 
able through their effects on the small, but still visible 
Brownian particles. Is it similarly possible to observe the 
discontinuity of electric charges by studying particles small 
enough to be influenced by very faint electric forces, yet 
still large enough to be seen through a microscope? Yes, 
this can and has been done. 

One foggy day in the autumn of 1911, Robert A. 
Millikan, then professor at the University of Chicago, was 
intently looking through a microscope attached to a rather 
complicated assembly of cylinders, pipes, and wires. In the 
brightly illuminated field of the microscope, a tiny droplet 
was floating in mid-air, near the intersection of two cob- 
webs that marked the centre of the visible field. It was one 



36 The Birth and Death of the Sun 

of many thousands of similar droplets under the micro- 
scope, produced by a special kind of atomizer and all 
together appearing to the naked eye as a little cloud of 
fog. Suddenly the droplet, which had been motionless for 
a while, started rapidly upwards, but, before it could 
escape completely from sight, Dr. Millikan rapidly shifted 
the handle of a rheostat, bringing the droplet to rest again. 
"Two fifty-eight," murmured his assistant, marking in his 
notebook the reading of the voltmeter. "One twenty-nine/' 
he said again, following the next motion of his chief's 
hand; "zero eighty-six, zero sixty-four and a half. . . ." 
Dr. Millikan, tired from watching the droplet so steadily 
and keeping it in its place, leaned back in his chair. 

"That was a nice run," he remarked, inspecting the 
record of the experiment; "just one electron at a time. 
I think we now have enough material to calculate the 
exact value of the elementary charge." 

What was it all about and why was it so necessary to 
keep the droplet motionless under the microscope? The 
point is that the droplet, which had made so many at- 
tempts to run away, was simply a very small charged 
material body, so small that it could be influenced by 
electric forces acting on one elementary charge. And the 
adjustment of the voltage to keep it at rest was merely a 
method of measuring its electric charge (Figure 8). 

The little cloud under Millikan's microscope was, inci- 
dentally, not the same kind of fog that was hanging that 
morning over the streets of Chicago. It was an "oil fog," 
consisting of tiny droplets of pure mineral oil, and was 
used instead of ordinary water fog because water droplets 
would gradually have evaporated and thus changed their 
mass during the experiment. Dr. Millikan's first problem, 



The Anatomy of Atoms 37 

after obtaining the fog, was that of picking one of the drop- 
lets up in the field of the microscope and charging it with 
electricity. But one cannot very well charge a body so 
small, almost invisible, by touching it with an ebonite stick 
that has been rubbed against one's woollen trousers. A 
good physicist, however, can always, or almost always, find 
a way out of such a difficulty, and Dr. Millikan did so by 



JxH"ic/t > s \ \ v.* I a. r 
*of ^ ^ x ^1 electee force 

l fog \* x ^ 
* \ K * x 

*] force of gravi 

V v -v s. 




FIGURE 8 

Diagram of Millikan's apparatus for the measurement of the elementary 

electric charge. 

using for his purpose the phenomenon of photoelectric 
effect. 

It is known that all bodies, when illuminated by ultra- 
violet rays (which are emitted, for example, in large 
amounts by an ordinary electric arc), lose their negative 
electricity and become positively charged. Illuminating 
his oil fog with the light of an electric arc, Millikan could 
induce in the droplets a positive electric charge which 



38 The Birth and Death of the Sun 

changed in value from time to time. If such an electrified 
fog is produced between two horizontal plates of a con- 
denser (the lower plate being charged positively and the 
upper one negatively), the electric force acting on the 
separate droplets will pull them upwards. By controlling 
the electric field between the plates, one can balance this 
upward force precisely against the weight of the droplet 
to make it float in the air like the coffin of Mohammed. 
Whenever the charge of the droplet changes under the 
action of ultraviolet illumination, the droplet begins to 
move and a new adjustment of voltage is made necessary. 
Knowing the applied voltage and the mass of the droplet, 
one can easily calculate the electric charge carried by the 
latter. 

By making a long series of experiments of this character 
Millikan came to the conclusion that the numerical values 
of the droplet charges are always integer multiples of a 
certain minimum charge, the smallest ever observed. Fur- 
thermore, this minimum amount of electric charge carried 
by the oil droplets turned out to be exactly the same as 
the minimum charge of a charged atom, or ion, as esti- 
mated from electrolytic phenomena. This definitely proved 
the universality of an elementary electric charge and its 
importance for larger material bodies just as much as for 
seoarate atoms. 

THE ELECTRON AS AN ELEMENTARY ELECTRIC 
PARTICLE 

Thus far we have spoken of definite portions of elec- 
tricity carried by atoms, by Millikan's oil droplets, or by 
still larger material bodies. But does the electric charge 
always stick to material bodies, and is it possible to sepa- 



The Anatomy of Atoms 39 

rate this charge from material carriers and study it sepa- 
rately in free space? 

We have already seen that all bodies illuminated by 
ultraviolet light become positively charged. Since the light 
does not carry any electric charge, and thus cannot supply 
with positive electricity the bodies on which it falls, we 
must conclude that the observed effect is actually due to 
the loss of negative electricity by the illuminated surfaces 
of material bodies, a phenomenon similar to that of the 
so-called thermionic emission, that is, the emission of 
negative charges by the surfaces of hot bodies. Moreover, 
since all bodies consist of separate atoms, it becomes evi- 
dent that the effect of illumination or heating is to extract 
and throw out elementary electric charges of separate 
atoms, and we come to the conclusion that these particles 
of negative electricity are comparatively loosely bound con- 
stituent parts of atoms. These free negative charges are 
usually called electrons^ and their discovery represents the 
first step toward the understanding of atomic structure. 

THE MASS OF AN ELECTRON 

Do these free electric charges possess any ponderable 
mass, and, if so, how large is it as compared with the mass 
of an atom? The mass of an electron, or, rather, the ratio 
of its electric charge to its mass, was first measured at the 
very end of the last century by the British physicist Sir 
Joseph John Thomson. If we let a beam of electrons, 
obtained by photoelectric or thermionic emission, pass 
between the two plates of a condenser (Figure 9), the elec- 
trons will be attracted to the positive electrode and repelled 
by the negative one, thus causing the beam to bend down- 
ward toward the former. This deflection can be easily 



40 The Birth and Death of the Sun 

observed by allowing the electronic beam to fall on a 
fluorescent screen placed behind the condenser. The elec- 
tric force acting on an electron is proportional to its charge, 
but the effect of the force in producing the deviation from 
the original direction of motion is inversely proportional 
to the mass of the moving particle. Thus it is only the ratio 








FIGURE 9 

J. J, Thomson's arrangement for the measurement of the charge/mass 
ratio of electrons. 

c ar e , or the so-called specific charge of the electron, that 
mass 

can be derived from that kind of experiment. 

But, in addition, the deflection also depends on the 
velocity of motion, and everyone knows that it is impos- 
sible to solve one equation with two unknown quantities. 
But it is not difficult to find another "equation" for our 
problem. If, instead of using an electric force, we use a 
magnetic one, produced by a magnet placed near the track 
of the electrons, the beam will also be deflected, but in a 
different way. Combining the results of these two experi- 
ments, we can calculate separately the values for the specific 
charge and for the velocity of electrons. From the values of 
the specific charge and of the known absolute charge, we 
get the mass of an electron, which turns out to be very 



The Anatomy of Atoms 41 

small indeed. The mass of an electron is 1840 times smaller 
than the mass of a hydrogen atom. 

This does not mean, of course, that a hydrogen atom con- 
sists of 1840 electrons, for, in addition to the negatively 
charged electrons, the atom also contains positively charged 
parts, which are responsible for the main portion of the 
atomic mass. 

THE ATOMIC MODEL 

The question of the distribution of negative and positive 
charges within the atom was studied by one of the greatest 
physicists of our time, Sir Ernest Rutherford (later Lord 
Rutherford of Nelson), the father of modern nuclear 
physics, who in the year 1911 made the first sounding of 
the depths of an atom. His chief problem was to find a 
"sound" that would be small enough to be plunged into the 
minute body of an atom, and to locate its "soft parts" and 
its "skeleton," if there happened to be any. 

To understand the method employed by Rutherford, 
imagine a hard-boiled customs officer of some little South 
American republic on the verge of revolution who must 
inspect a large shipment of cotton on the suspicion that 
inside the cotton bales there is hidden military contra- 
band, but who has not the time to open and examine each 
pack separately. After some reflection, he draws his re- 
volvers and opens fire on the pile of bales, sending bullet 
after bullet through the cotton. "If there is nothing but 
cotton inside these bales," he explains to the surprised 
bystanders, "my bullets will pass straight through or stick 
in the cotton. But if those damned revolutionists have 
hidden arms within that cotton, some of the bullets will 
ricochet and come out at unexpected angles." 



42 



The Birth and Death of the Sun 




FIGURE 10 

Detection of contraband in cotton bales, and of nuclei in atoms, by the 
ballistic method. 



The Anatomy of Atoms 43 

His solution is very simple and scientific and is essen- 
tially identical with the method applied by Rutherford 
(Figure 10), except that for tiny atoms the latter had to use 
correspondingly tiny projectiles. Rutherford bombarded 
his pile of atoms, that is, an ordinary piece of matter, with 
the so-called ^-particles* which ate the minute, positively 
charged projectiles emitted by some radioactive bodies. 
As it passes through the body of an atom, an a-particle will 
be influenced by the electric forces between its own charge 
and the charged parts of the atom, and must consequently 
deviate from its original direction of motion. Thus, by 
studying the scattering of a beam of a-particles that has 
passed through a thin foil of a given substance, one can 
form an idea of the distribution of electric charges within 
the atoms in question. If the positive and negative charges 
were distributed more or less uniformly through the body 
of the atom, no large scattering would be expected. If, on 
the contrary, there was a strong concentration of charge, 
let us say in the central parts of the atom, those a-particles 
which passed close to the centre would be strongly de- 
flected, much in the same way that the bullets of our in- 
genious customs official rebounded from metallic objects 
hidden inside the cotton bales. 

Rutherford's experiments actually showed very large 
scattering angles, indicating a strong concentration of 
charge in the very centre of each atom. Moreover, the char- 
acter of the scattering showed that the charge concentrated 
at the centre had the positive sign. This central region (in 
which the positive charge of the atom and also the largest 
part of atomic mass are concentrated) is at least 10,000 

* The rays involved in subatomic reactions are designated by the Greek 
letters alpha (a), beta (), and gamma (y). They will be described in the 
text below. 



44 The Birth and Death of the Sun 

times smaller (in linear dimensions) than the whole atom. 
It has received the name of atomic nucleus. The negative 
charge surrounding this "point-skeleton" of each atom and 
constituting, so to speak, the "atomic flesh" must evidently 
consist of a number of electrons revolving around the cen- 
tral nucleus under the forces of mutual electric attraction 
(Figure 11). Owing to the comparatively small mass of 




FIGURE 11 
Rutherford's model of the atom, 

electrons, this "negative atomic atmosphere" practically 
does not influence the motion of the heavy a-particles pass- 
ing through the body of the atom, any more than a swarm 
of mosquitoes could influence a frightened elephant rush- 
ing through the jungle. Only those a-particles that are 
aimed directly, or almost directly, at atomic nuclei will 
deviate sharply from their original track and, in some cases, 
even bounce directly backward. 

ATOMIC NUMBER AND THE SEQUENCE OF 
ELEMENTS 

Since the atom as a whole is electrically neutral, the 
number of negative electrons revolving around its nucleus 



The Anatomy of Atoms 45 

must be determined by the number of elementary positive 
charges carried by the nucleus itself, which, in its turn, 
can be directly calculated from the study of the scattering 
angles of a-particles that have been deflected by the nu- 
cleus. It was thus found that the atoms of the various ele- 
ments differ among themselves in the number of electrons 
revolving around their nuclei. The atom of hydrogen has 
one electron, that of helium two, and so on up to the 
heaviest known element, uranium, the atoms of which con- 
tain ninety-two electrons each. 

This numerical characteristic is generally known as the 
atomic number of the element in question, and it coin- 
cides with its positional number in the sequence in which 
the elements had already been arranged according to their 
chemical properties.* We see then that all the physical and 
chemical properties of any given element can be charac- 
terized simply by one number giving the positive charge 
of its atomic nucleus or, what is the same thing, the normal 
number of its atomic electrons. 

ISOTOPES 

But more recent research, due mostly to the British 
physicist F. W. Aston, has indicated that, although the 
charge of the atomic nucleus is well defined for any given 
chemical element, its mass may be different in different 
cases. It was shown, for example, that ordinary chlorine is 
actually a mixture of two kinds of atoms, each with the 
same number of electrons but with different nuclear masses. 
Three-quarters of the mixture consists of chlorine atoms 
with the mass 35 (relative to hydrogen), and one-quarter 
consists of those with the mass 37. The average atomic 

* Sec Figure 12 below, pp. 46-47. 



46 



The Birth and Death of the Sun 



FRONT VIEW 




FIGURE 12 

The periodic system of elements on a cylindrical band, showing the 

periods of 2, 8, and 18. The loop in the sixth period corresponds to the 

elements (rare earths) which fall out from regular periodicity owing to 

the reconstruction of atomic shells. 

weight of the mixture comes out to be (35 X ^4) + (37 X 
1/4) *= 35-5 which is in good agreement with the previous 
chemical estimates of the atomic weight of chlorine 

(3546). 

Atoms that are identical in their number of electrons 
and in all ordinary chemical and physical properties, but 
differ in their mass, have received the name of isotopes 
(i.e., "occupying the same place" in the natural sequence 
of elements). At the present time we have several good 



The Anatomy of Atoms 



47 



FIGURE 12 
BACK VIEW 




methods for separating isotopes from each other, so that 
we can now have, for instance, two chlorines, with exactly 
the same chemical properties but having different atomic 
weights. 

The researches of Aston and others have led to the con- 
clusion that most of the chemical elements as we know 
them represent a mixture of two or more isotopes. In 
atmospheric air, for example, consisting mostly of nitrogen 
with the mass 14 and oxygen with the mass 16, there is 
also a small admixture of the heavier isotopes of these ele- 
ments (0.3 percent of nitrogen 15, and 0.03 percent of 
oxygen 17). 

One of the most interesting findings of recent times is 
the discovery and isolation of the heavy isotope of hydro- 
gen (or deuterium) by the American chemist H. C. Urey. 



48 The Birth and Death of the Sun 

The water in the molecules of which ordinary hydrogen 
atoms are replaced by their heavier isotopes (heavy water) 
is about 5 percent heavier than ordinary water, and would 
represent a great advantage for poor swimmers. But heavy 
hydrogen presents other, much more valuable features; 
we shall see later that its use in the field of nuclear physics 
leads to very important information concerning the struc- 
ture of the atomic nucleus and the processes of the arti- 
ficial transmutation of elements. 

THE SHELL STRUCTURE OF AN ATOM 

It was first indicated by the Russian chemist Dmitri 
Mendelyeev that, in the series of elements arranged accord- 
ing to their increasing atomic weights, all physical and 
chemical properties repeat themselves with a rather regu- 
lar periodicity. This can easily be seen from Figure 12, 
where the elements are arranged in a cylinder in such a way 
that those with analogous properties are situated above 
each other.* 

The first period contains only two elements, hydrogen 
and helium; then we have two periods of eight elements 
each; and finally the properties repeat themselves after 
every eighteen elements. If we remember that each step 
horizontally along the sequence of elements corresponds 
to the addition of one more electron, we must inevitably 
conclude that the observed periodicity must be due to the 
recurrent formation of certain stable configurations of 
atomic electrons^ or "electronic shells." The first stable 
shell must consist of only two electrons, the next two shells 

* It is to be remembered that the diagram represents a cylinder, in 
which helium, for example, is midway between hydrogen and lithium. 
Helium, therefore, and the column of elements below it, might just as 
correctly have been placed at the extreme right of the "back view." 



The Anatomy of Atoms 49 

of eight electrons each, and all the following shells of 
eighteen electrons each.* 

In Figure 13 we give the schematic pictures of three 
different atoms, one with a completed and two with uncom- 
pleted shells. 



NEON 

saf orated shellsj 



. SODIUM 

( on extra electron.; 



\ *,** 



CHLORINE 

(orxe clccfron rmssmg) 



FIGURE 13 
Shells in different atoms. 

CHEMICAL BINDING 

We can now answer the question concerning the forces 
that give rise to the formation of complex molecules from 
the separate atoms of different elements. From Figure 13 
we see, for example, that the atom of chlorine is short only 
one e^ctron of having a completed outer shell. On the 
other hand, the atom of sodium has one electron left over 
after the formation of a completed shell. Thus, we should 
expect that, when atoms of these two elements meet, the 
extra electron of the sodium atom will go over to complete 
the shell of the atom of chlorine. As the result of such an 
exchange, the sodium atom will become positively charged 
(by losing a negative charge), while the atom of chlorine 
will become negatively charged. Under the action of the 
forces of electric attraction, the two atoms will therefore 

* Note that toward the end of the sequence the strict periodicity of 
properties is somewhat confused. This is due to the beginning of the 
internal reconstruction of some previously completed inside shells. 



50 The Birth and Death of the Sun 

cleave together, forming a molecule of sodium chloride, 

or ordinary table salt. 

In the same way an atom of oxygen, which lacks two 
electrons to complete its shell, will "rob" two hydrogen 
atoms of their single electrons, thus forming a molecule 
of water (H 2 O). On the other hand, there will be no ten- 
dency to combine as between the atoms of oxygen and 
those of chlorine (both "electron-lacking") or as between 
the atoms of hydrogen and those of sodium (both "glad to 
get rid of their extra electrons"). In the case of atoms with 
completed outer shells (helium, neon), there will be neither 
give nor take, and these elements therefore remain chemi- 
cally inert. 

From this picture of chemical reactions we may also con- 
clude that the energy liberated in the process of the forma- 
tion of a molecule must be given by the differences in the 
electronic bindings in the two or more atoms entering into 
the reaction. As the potential energy between the electron 
and the nucleus of an atom is of the order of magnitude of 
lo -i2 ergs, this must also be the order of magnitude of the 
energy liberated per atom in various chemical reactions. 

THE CLASSICAL THEORY FAILS IN THE ATOM! 

We come now to a critical point in the development of 
the atomic theory. The reader may already have noticed 
that Rutherford's model of an atom (Figure 1 1), consisting 
of a small and heavy central nucleus with a number of 
electrons revolving around it under the action of mutual 
electric attraction, is analogous to the system of planets 
revolving around the Sun under the action of the forces 
of gravity. The analogy seems still further emphasized by 
the fact that both electric and gravitational forces vary in 



The Anatomy of Atoms 51 

inverse proportion to the square of the distance and thus 
must both lead to the same type of elliptic orbit. 

But there is one important difference that should not 
be overlooked in this comparison. Electrons, revolving 
around the nucleus in an atom, carry a relatively large 
electric charge and thus are bound to emit electromagnetic 
waves, much as do the antennae of a radio-broadcasting sta- 
tion. But since these "atomic antennae" are so much 
smaller, the electromagnetic waves emitted by atoms are 
billions of times shorter than those of a standard broad- 
cast. Such short waves are perceived by the retina of our 
eye as the phenomenon of light, and their emission by the 
atoms of any given body make this body luminous. We 
are therefore obliged to conclude that the electrons revolv- 
ing around the nucleus in Rutherford's model must be 
emitting light waves and, as a consequence of this emis- 
sion, steadily losing their kinetic energy. It is easy to 
calculate that, if this were true, all atomic electrons would 
completely lose their kinetic energy in a negligibly small 
fraction of a second and fall down on the surface of the 
nucleus. 

And yet very good experimental evidence has shown 
that such a collapse does not take place, and that the 
atomic electrons are perpetually moving around the nu- 
cleus, remaining all the while at a comparatively large 
distance from it. Besides this contradiction as to the funda- 
mental nature of the atom itself, there appeared also a 
large number of other important discrepancies between 
theoretical predictions and experimental evidence. We 
have, for example, experiments showing that the light 
emitted by atoms consists of a number of well-defined wave 
lengths (line spectra), whereas the motion of electrons in 



52 The Birth and Death of the Sun 

Rutherford's model should lead to the emission of a con- 
tinuous spectrum containing waves of all possible lengths. 
Practically none of the predictions of the classical theory 
was verified in the interior of the atom! 

QUANTUM LAWS 

These contradictions were troubling the mind of the 
young physicist Niels Bohr when he came from the green- 
roofed city of Copenhagen to work with Rutherford on 
the problems of atomic structure. It was clear to him that 
the situation was too serious to be solved by some minute 
modifications of the theory; everything indicated that the 
internal structure of the atom was the rock upon which 
the glorious frigate of classical theory was doomed to be 
wrecked. 

For if the motions taking place in the interior of an 
atom cannot be described by means of classical mechanics, 
it is the fault of classical mechanics and not of the atom. 
After all, there were no a priori reasons, apart from those 
of tradition, why one should expect the system of classical 
mechanics, as created by Galileo and Newton for dealing 
with stars and massive bodies, to remain correct in its appli- 
cation to the "moving parts" of the tiny atomic mechanism. 
And so Bohr set out to deprive the classical system of 
mechanics of its rank as absolute and universal theory, 
which it had proudly claimed for centuries, and to look 
for a new, more general theory of motion, in respect to 
which the classical mechanics should be considered as only 
a special case. 

Following the German physicist Max Planck, who in 
the year 1900 had put forward the revolutionary hypothesis 
that the emission and absorption of light can take place 



The Anatomy of Atoms 53 

only in the form of certain discrete portions, or quanta, of 
energy, Bohr accepted also the principle that the mechan- 
ical energy of any moving system of particles must be 
"quantized," that is, it may take on only one of a certain 
set of discrete values. This concept of the discontinuity of 
energy (which is, of course, quite outside the scope of the 
classical theory) may be considered to be in a certain sense 
a statement of the atomicity of energy with the exception, 
of course, that in this case there is no universal elementary 
portion (such as, for example, the electron in the case of 
electricity), the size of the energy quantum being defined 
in each particular case by various additional conditions. 
Thus, in the case of radiation, the energy of each separate 
light quantum is inversely proportional to the wave length 
of the light, whereas in the case of a system of moving 
particles the quantum of mechanical energy increases with 
the decreasing dimensions of the system and also with the 
decreasing mass of the particles. 

We see now that in the case of radiation the energy por- 
tions, or quanta, though negligibly small and unimportant 
for the long waves of radio broadcasting, become of great 
significance for the much shorter light waves emitted by 
atoms. Similarly the quantum of mechanical energy comes 
into importance only for systems of such small size as that 
of electrons revolving around an atomic nucleus. And, 
whereas in ordinary life we can easily disregard the atomic- 
ity of energy, just as we disregard the atomicity of matter, 
in the microcosm of atoms the situation becomes entirely 
different. The electrons in Rutherford's model do not 
collapse on the nucleus simply because they possess the 
minimum amount of energy that such particles can possess 
under such conditions. Since they do possess this minimum 



54 The Birth and Death of the Sun 

of energy, which cannot on principle be decreased any 
further, their motion may be described as the "zero-point 
motion," which in classical physics would correspond to 
complete rest. 

If we seek to give some additional energy to the atom, 
the first quantum of it completely changes the atom's state 
of motion and brings its electrons into the so-called first 
excited quantum-state. In order to return to the normal 
state, our atom has to emit the previously obtained amount 
of energy in the form of a single light quantum, which 
accounts for the well-defined wave length of the emitted 
light. 

THE NEW MECHANICS 

In spite of the fact that Bohr's theory of the atom made 
for tremendous progress in our understanding of subatomic 
phenomena, it is clear that it did not yet represent a final 
form for a consistent theory of subatomic motion. Another 
startling development of the quantum theory followed in 
the year 1926, when the Austrian physicist Erwin Schro- 
dinger and the German physicist Werner Heisenberg, 
simultaneously and independently of each other, proposed 
what is now known as the new system of mechanics. 

Schrddinger based his theory on the ingenious idea of 
the brilliant Frenchman Louis de Broglie, according to 
whom any motion of a material body is accompanied and 
guided by some special material "pilot waves," which give 
to any such motion certain properties that are characteristic 
only of wave phenomena. Heisenberg's theory of the new 
mechanics was based upon a seemingly entirely different 
idea, according to which the position and velocity of any 
moving particle have to be described, not by ordinary num- 



The Anatomy of Atoms 55 

bers, but rather by certain noncommutable matrices, which 
have been known in pure mathematics for more than a 
century. In spite of these apparently profound differences, 
however, it was soon shown that the two theories were 
mathematically equivalent and represented only different 
approaches to the same physical reality. 



HYDROGEN 

The region of 
electronic motion 




LITHIUM 



V<^~-y - TVie region of the outer electron 
(JTT^S-The region of ifie two inner electrons 



FIGURE 14 
Wave-mechanical picture of atoms. 

This reality was revealed soon afterwards by the pene- 
trating criticisms of the classical ideas of measurement 
made by Heisenberg and especially by Bohr. It was shown 
that the existence of quantum phenomena makes neces- 
sary the introduction into the description of the physical 
world of a certain uncertainty principle, in contrast with 
the strict causality and dcterminacy of the classical theory. 
According to this principle of indeterminacy, the most 
fundamental notions of classical mechanics such as, for 
example, the notion of the trajectory must be 



56 The Birth and Death of the Sun 

rejected in this new mechanics, and the motion of an 
electron around the atomic nucleus is to be represented, 
not by a well-defined orbit, but rather by a continuous 
"spread-out" picture, as shown in Figure 14.* 

More detailed discussion of the principles of the new 
mechanics is, however, outside the scope of this book, and 
the reader who is interested in the problems of indeter- 
minacy in modern physics is advised to turn to the special 
books on that subject.*}" 

THE PROBLEM OF THE ATOMIC NUCLEUS 

We have seen in this chapter how the atom, introduced 
into science more than 2000 years ago as the smallest pos- 
sible and logically indivisible portion of matter, turned out 
to be, in the light of modern physics, a rather complicated 
mechanical system. If anything was left of the Democritean 
ideas of indivisibility and permanence, these attributes 
were now moved deeper into the atomic interior and 
ascribed to the nucleus, which, according to Rutherford's 
model, ought to be a dead, motionless centre of rotation 
for the atomic electrons. 

The phenomena of radioactivity, which are to be de- 
scribed in the next chapter, will show, however, that even 
this, at first sight dead and inactive, "atomic skeleton*' 
possesses a very definite internal structure, a structure that 
is probably even more complicated than that of the atom 
itself. 

* This is why it was impossible to determine precisely the geometrical 
dimensions of an atom or molecule (see p. 30 above). 

fA popular discussion of the new mechanics and of the principle of 
indeterminacy in physics may be found, for example, in the author's 
Mr. Tompkins in Wonderland (New York, Macmillan, 1940). It should be 
emphasized, however, that a knowledge of quantum mechanics is not 
necessary to an understanding of the rest of the book. 



CHAPTER III 



The Transmutation of Elements 



THE DISCOVERY OF RADIOACTIVITY 

FTH1HE discovery of radioactivity was due more or less to 
JL pure accident, though, if this accident had not hap- 
pened as it did to Professor Becquerel, the leakage of 
energy from the interior of slowly decaying atomic nuclei 
would surely have been noticed anyway in some other 
connexion. Henri Becquerel, professor of physics at the 
Sorbonne, was interested in the phenomena of fluorescence, 
which is the property certain substances have of accumulat- 
ing the energy of light falling upon them and of remaining 
luminous for a certain time after the source of light has 
been removed. Once during the year 1896 Becquerel ob- 
tained a preparation of uranium bisulphate for the pur- 
pose of studying the phosphorescence of this substance. 
But his interests were drawn in some other direction, and 
he threw the material into one of the drawers of his 
work-table. 

Now it happened that in this drawer was a box con- 
taining some unexposed photographic plates, and the 
ampoule of uranium bisulphate fell right on top of that 
box, remaining there undisturbed for several weeks. In- 
tending to take some photographs (whether a family por- 
trait or some complicated absorption spectrum we do not 
know), Becquerel finally opened the drawer, pushed aside 
the ampoule with the forgotten preparation, and took out 

57 



58 The Birth and Death of the Sun 

the box with the plates. But when he developed his photo- 
graphs he found that the plates were badly spoiled, as if 
they had been previously exposed to light. This was very 
strange, since the plates had been carefully wrapped in 
thick black paper and never yet opened. The only object 
in the drawer that might have been responsible for the 
damage was the preparation of uranium bisulphate, which 
had for so long rested so close to the plates. 

Is it possible, thought Becquerel, turning over in his 
hands the ampoule with the suspected material, that this 
substance, spontaneously and without any previous excita- 
tion, emits some invisible, highly penetrating radiation 
that can pass without difficulty through the cover of the 
box and the black paper and affect the photographic emul- 
sion? To answer this question, he repeated the experiment 
with some new plates. But this time he deliberately placed 
an iron key from one of the drawers between the photo- 
graphic plate and the hypothetical source of the mysteri- 
ous radiation. 

A few days later, Becquerel's hands were probably shak- 
ing with excitement as, under the red lamp of the photo- 
graphic darkroom, a diffuse silhouette of the key began to 
appear slowly against the darkening background of the 
negative. Yes, it definitely was a new kind of radiation 
coming from the atoms of uranium, a radiation that easily 
penetrated materials nontransparent to ordinary light but 
was still unable to pass through the thickness of an iron 
key! 

Subsequent investigations have shown that the only 
other element known at that time capable of the same type 
of spontaneous radiation was thorium, the heaviest element 
after uranium; but the laborious search undertaken by a 



The Transmutation of Elements 59 

scientific French couple, the Curies, soon led to the dis- 
covery of entirely new radioactive elements. After about 
two years of hard work Madame Curie finally succeeded in 
extracting from some uranium ores (pitchblende from Bo- 
hemia) two previously unknown elements with consider- 
ably higher radioactivity than either uranium or thorium; 
one of them was called radium and the other polonium, in 
honour of Madame Curie's native country. Still later, an- 
other radioactive element, called actinium, was discovered 
by one of the collaborators of the Curies; and it was also 
shown that the preparations of radium give rise to a 
strongly active gaseous substance, which received the name 
of emanation of radium or radon. 

The growing number of new radioactive elements rap- 
idly filled the hitherto blank spaces in the last line of the 
periodic system, and the fact that all these radioactive 
elements were grouped at the very end of the natural 
sequence of elements strongly suggested that their peculiar 
activity must in some way be connected with the increasing 
complexity of their atoms. 

THE DECAY OF VERY HEAVY ATOMS 

In the year 1903, the British physicist Ernest Rutherford, 
whose name we have already encountered in connexion 
with the nuclear model of the atom, advanced the hypoth- 
esis that the atoms of very heavy elements are inherently 
unstable, and decay slowly with the emission of their con- 
stituent parts. He showed, indeed, that the so-called a-rays 
emitted by radioactive substances are actually beams of 
very fast-moving, positively charged nuclei of the element 
helium. (It was with these a-particles, it will be remem- 
bered, that Rutherford bombarded his atoms.) After it has 



60 The Birth and Death of the Sun 

lost its original high energy by collisions with the atoms of 
the matter through which it has passed, the a-particle slows 
down and, by capturing two free electrons for its orbit, 
forms an ordinary atom of helium. Helium, as a matter of 
fact, can always be detected in old radium. Since a-par- 
ticles are evidently ejected from the interior of the atomic 
nuclei of radioactive elements, we say that such nuclei are 
unstable; after losing one or more a-particles (i.e., four units 
of mass and two charges per particle), the nucleus of a 
radioactive atom is transformed into the nucleus of a 
comparatively lighter element occupying a less advanced 
position in the periodic system. 





-f- ENERGY 



FIGURE 15 

Spontaneous disintegration of unstable nuclei: (1) radium into radon 
and helium; (2) polonium into lead and helium. 

For example, the a-emission of radium (Z 88, A * 
226)* transforms it into the emanation, or radon (Z 86, 
A 222); and an a-particle escaping from the polonium 
nucleus (Z 84, A = 210) leaves behind it an atom of 
lead (Z 82, A 206). These two disintegration reactions 
may be written formally in the manner shown in Figure 15. 
With lead, the sequence of successive a-transformations 
comes to a stop because lead already belongs to the region 

* Z = the numerical position occupied by an element in the periodic 
table (see Figure 12); A = the atomic weight of the element relative to 
hydrogen (= i). 



The Transmutation of Elements 61 

of elements with stable nuclei and no decay beyond this 
point is possible. 

The progressive disintegration of heavy unstable ele- 
ments is from time to time, however, interrupted by the 
emission of a negative electron coming apparently from 
inside the decaying nucleus. This electronic emission from 
the nucleus, known as fi-ray emission, without changing 




FIGURE 16 

Decay in the uranium family. The arrows indicate the successive 
changes of position in the periodic table due to a- and ^-transformations. 
The encircled letters are the chemical symbols of different radioactive 
elements, e.g., U, uranium; lo, ionium; Ra, radium; Rn, radon; Po, 

polonium. 

the actual mass of the atom (since the insignificant mass of 
the electron may be disregarded), increases its atomic num- 
ber, moving the corresponding element one step forward 
in the periodic table.* But this temporary advance is soon 
overcompensated by the following series of a-emissions, 
and the unstable element, moving sometimes two steps 
backward and sometimes one step forward, slowly retreats 
from the unstable region until it finally arrives at an im- 
pregnable position, having been transformed into lead. 

The loss of a negative electric charge is evidently equivalent to the 
increase of the total positive charge of the nucleus. See also p. 65 below. 



62 The Birth and Death of the Sun 

Such sequences of successive nuclear transformation are 
known as radioactive families; and we have the uranium 
family (Figure 16), containing radium as one of its mem- 
bers, the thorium family, and the family of actinium. 

Finally, the processes of a-particle and /?-ray ejection are 
often accompanied by a strong internal excitation of the 
decaying nucleus, leading to the emission of extremely 
short-wave electromagnetic radiation, analogous to ordi- 
nary X-rays and generally known under the name of y-rays. 
This highly penetrating radiation (unlike a- and /2-radia~ 
tion, it is not composed of material particles) is in many 
cases responsible for the photographic and other effects 
produced by radioactive substances. 

LIBERATED ENERGY AND DECAY PERIODS 

It has already been intimated as when we saw Ruther- 
ford use them for projectiles that the kinetic energies of 
a-particles emitted in the process of spontaneous nuclear 
disintegration reach extremely high values. The a-particles 
are emitted from radium, for example, with a velocity of 
1,500,000,000 centimetres (9000 miles) per second, surpass- 
ing the ordinary velocities of thermal motion at room tem- 
perature by a factor of thousands; and, in spite of their 
small mass, they possess an energy of 0.000,007 erg per par- 
ticle. Thus, the concentration of energy in a-particles (the 
energy calculated per unit mass) is actually a billion times 
greater than the corresponding concentration in the shells 
used in modern artillery. 

If all the atoms contained in a gramme of radium should 
emit their a-particles almost simultaneously, let us say 
within an hour, the tremendous energy of 2 X io 16 ergs 
would be liberated. Thus the subatomic energy contained 



The Transmutation of Elements 63 

in several pounds of radium would be sufficient to drive a 
big transatlantic liner to Europe and back, or to run an 
automobile motor continuously for several hundred years. 
However, the subatomic energy hidden in the interior of 
radium nuclei is not liberated in a single outburst but 
rather leaks out of them at a very slow rate. In fact, it takes 
1600 years for one-half of a given number of radium atoms 
to disintegrate and another 1600 years for the remaining 
half to be halved again. This slowness of radioactive decay 
makes the energy liberation per unit time comparatively 
low; and in order to warm up a cup of tea by the energy 
leaking from one gramme of radium (priced at $40,000) 
we should have to wait several weeks. 

In the case of uranium and thorium, with decay periods 
of 4.5 and 16 billions of years respectively, the rate of 
energy liberation is correspondingly still smaller. There 
are also short-lived elements, such as radon (with a life 
period of 3.8 days) or RaC' (disintegrating in 0.000,01 sec- 
ond); but, precisely because of their rapid disintegration, 
their presence in radioactive minerals is so minute that it 
cannot be even detected by the ordinary chemical methods. 

We shall see later (Chapter XII) that all the radioactive 
elements at present known have actually been formed in 
the very early stages of the development of the universe, 
and in this sense represent the "earliest documents of crea- 
tion." Only those of them, such as uranium and thorium, 
that possess lifetimes comparable with the present age of 
the universe (about two billions of years) can still be found 
at present, together with their various disintegration prod- 
ucts (the members of their corresponding families). If un- 
stable elements of even higher atomic number were created 
at this early epoch, when the formation of elements took 



64 The Birth and Death of the Sun 

place, they must have been completely disintegrated dur- 
ing the intervening billions of years and left no trace on 
our planet. 

THE "LEAKING OUT THEORY OF RADIOACTIVE 
a-DECAY 

If the nuclei of radioactive elements are unstable, and 
can decay by the emission of their constituent parts, what 
prevents them from doing so all at once? Why do the 
nuclei of uranium and thorium retain their a-particles for 
billions of years, whereas other nuclei eject their a-particles 
within a small fraction of a second? These questions, which 
were for a long time the heart of the great puzzle of the 
theory of radioactivity, insistently returned to the mind of 
the author of this book while he was visiting the University 
of Gottingen during the summer of 1928. Gottingen was a 
dull little town whose total of entertainment possibilities 
was represented by two poor movie theatres; and the au- 
thor, who had hoped for something more on his first trip 
abroad, had nothing better to do than to take up research. 

It was clear to him that the escape of a-particles through 
the "high potential walls" surrounding their nuclear dun- 
geon must be quite impossible from the point of view of 
classical physics; for, according to the experiments of 
Rutherford, which had just been published at that time, 
the "walls" surrounding radioactive nuclei were of an 
energy much higher than that of the a-particles. But, al- 
though in the frame of classical theory radioactive decay 
seemed to be made absolutely incredible, the new quan- 
tum mechanics offered a possible means for explaining the 
process. Thinking in this direction, the author was soon 
able to prove that the decay of the radioactive elements is 



The Transmutation of Elements 65 

really a purely quantum-mechanical process in which 
<x-particles "leak through" the nuclear potential walls, just 
as an old-fashioned ghost passes through the thick walls of 
an ancient castle. The quantum-mechanical formula ob- 
tained for the "transparency" of the nuclear walls proved 
to be in excellent agreement with the observed relation 
between the energy of emitted particles and the corre- 
sponding decay periods, leaving no doubt that the proposed 
explanation was correct. 

Practically at the same time that the author was develop- 
ing this theory of a-decay in the old German town, a very 
similar explanation of radioactive phenomena emerged 
from the discussion between two other physicists, R. W. 
Gurney and E. U. Condon, on the other side of the Atlantic. 

In the years that followed, the quantum theory of nuclear 
potential walls turned out to be very useful, not only for 
the understanding of the processes of spontaneous a-decay, 
but also in its various applications to the problems of the 
artificial transformations of elements caused by nuclear 
bombardment. It was useful also in describing the thermo- 
nuclear reactions which, as we shall see later, represent the 
main source of stellar energy. 

THE PROCESS OF p-DECAY AS AN ELECTRIC 
ADJUSTMENT OF THE NUCLEUS 

We have mentioned above (p. Go) that the sequence of 
successive a-emissions in any radioactive family is from 
time to time interrupted by the emission from the nuclei 
of free negative electric charges, or electrons. Thus it would 
be natural to suppose that electrons, along with a-particles, 
represent substantial constituent parts of atomic nuclei. 
Closer study of this question, into which we cannot enter 



66 The Birth and Death of the Sun 

here, has, however, led physicists to the conclusion that 
electrons, as such, do not actually exist inside the nuclei. 
For one thing, the size of electrons seems to be too large 
to admit of many of them being squeezed into the tiny 
volume of the nucleus. 

This conclusion, at first sight paradoxical, is resolved in 
the current point of view, according to which the electrons 
emitted by certain radioactive bodies are "created" just 
before their emission^ out of the "shapeless" electric charge 
carried by the nucleus. It is admittedly rather difficult to 
explain this point of view without going into much tech- 
nical detail; and we shall content ourselves with the prop- 
osition that electrons do not exist inside the nuclei before 
they are emitted^ just as soap-bubbles do not exist inside 
a pipe before they are blown out. 

Whenever a sequence of a-emissions disturbs the deli- 
cate balance between the electric charge and the mass of 
the decaying nucleus, an electric adjustment immediately 
takes place, and the superfluous charge is emitted in the 
form of a free electric particle. We may take as an example 
what happens when one of the members of the radioactive 
family of thorium, known as ThC, ejects a very energetic 
a-particle. The nucleus of ThC is thereby transformed 
into the nucleus of ThC", which possesses the atomic 
weight 208 and the positive charge of 81 elementary units. 
If, however, we look into the table of stable elements, we 
will find that the stable nucleus of mass 208 should possess 
an electric charge of 82 units, since it is an isotope of lead. 
It follows that, in order to become stable, the product of 
ThC disintegration must emit one free negative charge 
(a ^-particle), upon which it will become transformed into 
ordinary lead and will thus exist for ever after. 



The Transmutation of Elements 67 

We shall see later that the nuclei formed in the processes 
of so-called artificial nuclear transformation may sometimes 
have their electric balance restored in the opposite direc- 
tion, stabilizing themselves by emitting a free positive 
charge. For instance, the artificially produced nuclei of 
nitrogen, with atomic weight 13 (light isotope), transform 
themselves into stable carbon nuclei (the heavy isotope, 
also of atomic weight 13) by such an emission. The dis- 
covery of these hitherto unknown positive electrons, 
the existence of which was predicted theoretically by P. A. 
M. Dirac, opened up a new epoch in the progress of our 
knowledge of the properties of /?-decay, but the discussion 
of this falls outside the scope of the present book. 

BACK TO ALCHEMY 

The discovery of decaying radioactive elements showed 
that the medieval alchemists had not been so far wrong 
after all in dreaming of the artificial transmutation of one 
element into another. If the internally unstable elements 
situated near the upper end of the natural sequence could 
be spontaneously transformed into one another, there was 
every reason to believe that in the case of the lighter, 
normally stable elements, too, such transformations might 
be artificially caused under sufficiently strong external 
influences. 

The alchemists had failed ignominiously in the attempt, 
but the only influences they could bring to bear in their 
time were those of ordinary chemical and thermal reac- 
tions, whereas the binding energies within atomic nuclei 
exceed the ordinary chemical binding energies by a factor 
of millions. The alchemists 1 attack on the nucleus may be 
compared to an attempt to bombard the modern fortifica- 



68 The Birth and Death of the Sun 

tions of the Maginot or Siegfried Lines with medieval 

catapults. 

In order to crack the walls of the stronghold of the 
atomic nucleus, one must use projectiles with an energy 
comparable to that of the particles shot out by the nuclei 
themselves. Having at our disposal various radioactive ele- 
ments that emit high-energy a-particles, we can perhaps 
turn the fire of these nuclear batteries against the walls of 
lighter, ordinarily stable nuclei in the hope that some of 
the a-particles, making direct hits, will penetrate the walls 
and produce the desired damage in their interiors. 

It was with this thought in mind that that restless ex- 
plorer of the atomic interior, Ernest Rutherford, had in 
1919 directed a beam of fast a-particles, as they came from 
some radioactive body, against the atoms of nitrogen mov- 
ing quietly in a gas-filled chamber and had cracked them! 

PHOTOGRAPHING NUCLEAR BOMBARDMENT 

The process of nuclear bombardment and its demolish- 
ing results may actually be observed in the aerial photo- 
graphs of the nuclear battlefield taken soon after Ruther- 
ford's discovery by one of his students, Patrick Blackett. 
One would think that the nuclear projectiles are too small 
and move too fast to be directly photographed, but in a 
certain sense this is not so, and as a matter of fact it is 
much easier to photograph the trajectories of these minute 
but destructive particles than the trajectories of shells from 
army cannons. 

The apparatus used for such photographs is usually 
known as a cloud-chamber, or Wilson chamber, and its 
operation is based on the fact that fast-moving charged 
particles, such as a-particles, produce on their way through 



The Transmutation of Elements 69 

the air, or through any other gas, a certain distortion in 
the atoms situated along their route. With their strong 
electric fields, these projectiles tear off one or more elec- 
trons from the atoms of gas that happen to be in their way, 
leaving behind a large number of ionized atoms. This state 
of affairs does not last very long, for very soon after the 
passage of the projectile the ionized atoms will catch back 
their electrons, returning to the normal state. But if the 
gas in which such ionization takes place is saturated with 
water vapour, tiny droplets will be formed on each of the 
ions (it is the property of water vapour that it tends to 
accumulate on ions, dust particles, etc.), producing a thin 
band of fog along the track of the projectile. In other 
words, the track of any charged particle moving through a 
gas thus becomes visible in the same way as does the track 
of a smoke-writing airplane. 

From the technical point of view, the cloud-chamber is 
a very simple apparatus (see Figure 17), consisting essen- 
tially of a metallic cylinder (A) with a glass cover (B) con- 
taining a piston (C), which can be moved up and down by 
an arrangement not shown in the picture. The space be- 
tween the glass cover and the surface of the piston is filled 
with ordinary atmospheric air (or any other gas, if so 
desired) containing a considerable amount of water vapour. 
If the piston is abruptly pulled down, immediately after 
some atomic projectiles have entered the chamber through 
the window (),* the air above the piston will cool and 
the water vapour will begin to precipitate, in the form of 
thin bands of fog, along the tracks of the projectiles. These 
bands of fog, being illumined by a strong light through 

* This window is usually covered by a thin layer of mica, through which 
East atomic projectiles can pass with very little difficulty. 



70 The Birth and Death of the Sun 

another side window (D), will stand out clearly against the 
blackened surface of the piston and can be observed vis- 
ually or photographed by the camera (F), which is operated 
automatically by the action of the piston. This simple 
arrangement represents one of the most valuable apparatus 





FIGURE 17 
The scheme of Wilson's cloud-chamber. 



of modern physics, and permits us to obtain beautiful 
photographs of the results of nuclear bombardment. 

CRACKING THE NITROGEN ATOM 

For the study of the bombardment of nitrogen atoms, 
Blackett needed to fill his chamber with nothing more 
than atmospheric air, which already consists largely of 
nitrogen. Of course, it is impossible to aim an a-particle 
through the side window directly at the nucleus of a 
nitrogen atom; one must simply count on the chance that, 



The Transmutation of Elements 71 

with a sufficiently intense scattered fire of nuclear batteries, 
such a direct hit will occur once in a while. 

On the first photographs taken with this arrangement no 
direct smashing hits were registered; the tracks of the 
a-particles passed straight through the chamber. But after 
taking a sufficiently large number of photographs 23,000 
in fact Blackett finally succeeded in obtaining eight that 
showed the head-on collisions of incident a-particles with 
the nuclei of nitrogen atoms. The observed extremely small 
chance of a smashing hit clearly indicated that, at this stage 
at least, the processes of nuclear transformation hardly 
represented any practical possibility either for the mass- 
production of new elements or for a large-scale source of 
subatomic energy. 

One of the Blackett disintegration photographs is repro- 
duced in Plate II, and a schematic representation of what 
actually happened during the collision is shown in Figure 
18. This figure shows an a-particle approaching a nitrogen 
atom with great speed and making a head-on collision with 
its nucleus. We also see the results of this impact: a proton 
(i.e., a hydrogen nucleus) is ejected leftward from the 
nuclear interior, while the main body of the nucleus itself 
is shot at a rightward angle away from the site of the 
accident.* But the track of the a-particle itself has dis- 



* It must be explained here that the cloud -chamber photographs not 
only give us the trajectories of participating particles, but also permit us 
to determine their nature. The amount of ionization produced by a moving 
particle depends on its electric charge, and the higher the charge, the 
thicker will be the band of fog formed in the cloud-chamber. We see from 
the photograph and Figure 18 that the left branch of the fork created by 
the collision is somewhat thinner than the track of the incident a-particle; 
this means that the particle that made the former track has a smaller 
charge than an a-particle and must consequently be a proton. On the 
other hand, the right branch of the fork is very thick, indicating a heavily 
charged nucleus. 



72 The Birth and Death of the Sun 

appeared, from which we conclude that it must have stuck 

to the nucleus at the instant of collision. 

The nucleus we observe as the product of the collision is 
therefore no longer a nucleus of nitrogen, but something 






A *. 




*** * 

"* 

. v ^% 

5C-f ? 



FIGURE 18 

Analysis of Blackett's photograph of nuclear transformation given on 
Plate II (right). Separate points represent the drops of the fog. 

quite different that has been formed by the addition to a 
nitrogen nucleus of an a-particle (a nucleus of helium) and 
the subtraction of a proton (a nucleus of hydrogen). This 



The Transmutation of Elements 73 

operation causes an increase of nuclear charge by one unit 
(+ 2 i) and of nuclear mass by three units (+4 i); 
so that, instead of a nitrogen nucleus with atomic number 
7 and atomic weight 14, we now have the nucleus of an 
oxygen atom with atomic number 8 and atomic weight 17. 
Thus the ^bombardment of nitrogen atoms leads to their 
transformation into the atoms of oxygen, and the old 
alchemic dream of the transmutation of elements is at last 
realized. 

The processes of nuclear transformation can be formally 
represented (Figure 19) in a way very similar to the presen- 




FlGURE 19 

The collision between nitrogen and helium nuclei gives rise to the nuclei 
of oxygen and hydrogen. The superscripts represent atomic weights. 

tation of ordinary chemical reactions between atoms, with 
the essential difference that we deal here with the processes 
going on within atoms themselves and not only with their 
position in molecules. 

It should be noted also that the oxygen formed in the 
nuclear reaction described above possesses an atomic weight 
of 17 instead of 16, and therefore represents the heavy 
isotope of this element. We have already seen in Chapter II 
that atmospheric oxygen actually consists of two isotopes: 
the very abundant one O 16 and a very rare one O 17 , the 
latter present in a proportion of less than 0.03 percent. 

Further experiments of Rutherford and his school have 
shown that many other light elements, when bombarded 
by fast a-particles, are subject to the same kind of nuclear 



74 The Birth and Death of the Sun 

transformation as the one observed in the case of nitrogen. 
Thus, boron (Z 5) was transformed into carbon (Z 6), 
sodium (Z 1 1) into magnesium (Z 12), and aluminium 
(Z 13) into silicon (Z = 14). But the rate of these trans- 
formations, which is in any case very small, decreased 
rapidly with the increasing atomic weight of the bombarded 
element, so that no disintegration could be observed for 
any of the elements in the periodic system beyond argon. 

BOMBARDMENT BY PROTONS 

In all the classical experiments on the artificial trans- 
formation of elements, a-particles were always used for the 
bombardment, since these were the only heavy projectiles 
spontaneously emitted by the nuclei of radioactive ele- 
ments. The theory of nuclear transformation developed by 
the author of this book indicated, however, that a much 
higher efficiency could be expected if, instead of a-particles, 
fast protons could be used. Owing to the smaller electric 
charge of protons, they would suffer less repulsion in their 
approach to heavily charged nuclei, and would thus have 
a greater capacity for penetrating the nuclear interior. Be- 
sides, the use of new particles for nuclear bombardment 
could be expected to give rise to rather different types of 
nuclear reactions than those studied before. 

But, since protons are not spontaneously emitted by 
ordinary radioactive elements, it was first necessary to pro- 
duce artificially a high-energy beam of these particles by 
accelerating hydrogen atoms (or rather hydrogen ions) in 
very intense electric fields. The first successful experiments 
in this direction were carried out in Rutherford's labora- 
tory in Cambridge by his young and gifted pupil J. Cock- 
croft. Using a high-tension transformer for 500,000 volts, 




A. An artificially accelerated pioton, emerging from the end of the ion 

tube of an atom-smasher, transforms a lithium nucleus into two a-par- 

ticles. The cloud-tracks seen on the photograph coi respond to these 

two a-particles flying in opposite directions. (See p. 75.) 




B. An artificially accelerated proton splits a nucleus of boron into three 
a-particles flying in three different directions. (See p. 75.) 



PLATE III. NUCLEAR DISINTEGRATIONS 




PLATE IV. Sparks in the Van de Graff electrostatic generator. The man- 
sized door at the bottom gives some idea of the height of the structure. 

(See p. 77.) 



The Transmutation of Elements 75 

Cockcroft was able to produce a parallel beam of protons 
moving with the velocity of 10,000 kilometres per second. 
Although the kinetic energy of these artificially accelerated 
particles was still considerably smaller than the energy of 
the a-par tides used by Rutherford, they turned out to be 
a quite efficient instrument for nuclear bombardment. 
Directing his beam at a target covered with a layer of 
lithium, Cockcroft noticed that many of the lithium nuclei, 
when hit by the incident protons, cracked and split into 
two equal parts (see Plate I II A). 

The equation of the nuclear reaction that took place in 
this case is shown in Figure 20, which makes it clear that 




FIGURE 20 

The collision between lithium and hydrogen nuclei gives rise to two helium 
nuclei (or a-particles ) . 



the observed collision led to the complete transformation 
of the colliding hydrogen and lithium nuclei into pure 
helium. Among the other reactions that have been pro- 
duced by proton bombardment we shall note here the 
transformation of nitrogen into carbon*: 



and the extremely interesting case (Plate His) of boron, 

* The numeral at the lower left-hand corner of each chemical symbol 
in these formulas represents the atomic number (Z) of that element; the 
upper right-hand numeral represents its atomic weight (A). Note that the 
Z's and A's are both balanced on either side of each "equation." In the first 
case the light isotope of carbon has been obtained, ordinary carbon 
being eC 12 . 



76 The Birth and Death of the Sun 

which under the proton bombardment splits into three 

a-particles: 

6 Bii + lH i ^He* + 2 He< + 2 He< 

As to the probability of the disintegrations produced by 
protons, it should be said that, while in general rather 
higher than that in the case of a-particle bombardment (in 
agreement with the theoretical prediction), it follows the 
same general laws, rapidly decreasing with the increasing 
weight of the bombardment element and the decreasing 
energy of the incident protons. However, some traces of 
the nuclear transformation of light elements have been 
observed for energies of incident protons as low as io~ 8 erg. 
The pioneering work of Cockcroft in the production of 
artificial beams of fast protons opened a period of great 
progress in the application of the high-tension technique 
to nuclear problems. At the present time many physical 
laboratories throughout the world arfe in possession of 
giant apparatus known under such diverse and curious 
names as voltage-multipliers (of the Cockcroft type), electro- 
static generators, and cyclotrons. 

THE ELECTROSTATIC ''ATOM-SMASHER 99 

"Hey, Larry I" shouts Dr. Merle Tuve, sticking his head 
into a narrow opening of a giant steel sphere, sixty feet tall, 
erected on the grounds of the Carnegie Institution in Wash- 
ington. "There's a telephone call for you!" 

Suspended from the end of a rope high in the air, in the 
dim light of the cupola, Dr. L. Hafstad is carefully clean- 
ing the surface of the sphere with an ordinary household 
vacuum cleaner. The surface of the sphere must be kept 
spotlessly clean and smooth, because any irregularity might 
produce an unwanted electric discharge. It was this neces- 



The Transmutation of Elements 77 

sity that forced the usually kind-hearted Dr. Van de Graff, 
who was the first to build such a giant electrostatic gen- 
erator in an abandoned dirigible hangar near New Bedford 




FIGURE 21 

The principle of the electrostatic atom-smasher. A small spherical con- 
ductor charged with electricity gives its charge to a larger conductor if 
brought inside it through a hole. 

(Plate IV), to shoot down several pigeons that lived under 
the roof of the hangar and were not sufficiently careful 
about the cleanliness of the sphere's surface. 



78 The Birth and Death of the Sun 

While Dr. Hafstad is answering the phone call, let us 
inspect more carefully this giant atom-smasher. The reader 
will probably remember from his course in high school 
physics that an electric charge always tends to be distrib- 
uted only over the surface of a charged conductor. This 
property of electricity is usually demonstrated in class- 
rooms by introducing a small charged spherical conductor, 
mounted on a glass stick, into the hollow interior of a 
larger sphere and touching with it the inner surface of the 
latter (Figure 21). In this case, the electric charge from the 
small conductor goes over completely onto the outer sur- 
face of the larger sphere. By repeating this operation many 
times one can charge the larger sphere to arbitrarily deter- 
mined high electric potentials, so that it will give off long 
sparks directed toward the nearest conducting objects. 

In general, modern electrostatic generators differ from 
this simple arrangement only in size, but there are a great 
number of minute differences in elaborate detail. In par- 
ticular, the transfer of the charge to the inside of the con- 
ductor is achieved not by the repeated introduction of a 
smaller charged body, but by a sort of conveyor system 
which supplies the charge continuously. An insulated cir- 
cular belt runs between an electric transformer in the 
lower part of the structure, which provides the voltage, 
and a pulley fixed in the interior of the upper sphere; this 
belt steadily carries up electric charges and raises the poten- 
tial of the sphere to a very high degree. 

In the generator shown in Plate V, a potential of 5 mil- 
lion volts can be attained a few minutes after the belt 
starts carrying up its first electric charge. Although in prin- 
ciple there is no limit to the potential that can be obtained 
by this arrangement, in practice the limit is attained as 




PLATE V. The electrostatic atom-smasher at the Carnegie Institution in 
Washington, D. C., which produces static electric tension up to 5 million 
volts. The cross-section shows the spherical conductor, its insulating sup- 
ports, and the tube in which particles are accelerated. The charging belt 
is shown cut off near top and bottom. (See p. 78.) 



The Transmutation of Elements 79 

soon as the charged sphere begins to spark into the 
surrounding walls of the protective steel sphere built 
around it.* 

With this highly charged sphere, one can produce a 
beam of fast-moving particles of any kind protons, a-par- 
ticles, lithium nuclei, etc. by accelerating the correspond- 
ing ions in an evacuated glass tube, one end of which 
enters the charged sphere from below and the other end 
of which is grounded. As these ions arrive at the bottom of 
the glass tube, with tremendous kinetic energies, they pass 
through a thin mica window and enter the underground 
laboratory, where they can be directed at the substance 
under investigation. Here, under the opening in the ceiling 
that lets in the beam of high-energy protons, are crowded 
a large number of complicated and odd-looking apparatus 
so designed as to register the results of nuclear disintegra- 
tion. 

THE CYCLOTRON 

Whereas the principle of the electrostatic generator can 
be traced back almost to the beginning of our acquaintance 
with electricity, the cyclotron, first constructed in Cali- 
fornia by Dr. Ernest O. Lawrence, is based on an entirely 
new and original idea. Instead of accelerating the particles 
by letting them go through a potential gradient of several 
million volts, Lawrence decided to let the particles run 
around in a circle and to give them a slight push, by apply- 
ing some electric tension, each time they passed a definite 

* This outside steel sphere is necessary not only as protection against 
the rain or snow, but also to keep the air dry, thus making unwanted 
electric discharges more difficult. In the generator shown in Plate IV, the 
air inside the protective sphere is put under a pressure of several atmos- 
pheres, which also helps in the achievement of higher potentials by 
reducing the sparking distance. 



80 The Birth and Death of the Sun 

"sign post/' thus stepping up their energy at each revo- 
lution. 

To make a charged particle travel in a circular orbit it 
is necessary to place it in a uniform magnetic field, for it 
is known from elementary physics that a magnetic field 
directed perpendicularly to the direction of motion of a 
charged particle curves its trajectory and forces it to move 
in circles. As the particles gain energy from the successive 
"electric shocks" administered at each new revolution, the 
deflection produced by the magnetic field becomes smaller 
and smaller and consequently the radii of the circular 
orbits grow larger and larger. Fortunately for Lawrence, 
the increasing length of orbit is exactly compensated by 
the increasing velocity of motion, so that the particles 
return to the same sign post of this "electric race track" in 
equal intervals of time. This makes it possible to use for 
electric shocks the potential produced by an ordinary high- 
frequency generator (Figure 22). 

In the cyclotron constructed by Lawrence at the Uni- 
versity of California and shown in Plate VI, the particle 
(a proton) makes many successive revolutions before it gets 
out of the apparatus. After each revolution, lasting only a 
negligible part of a second, it receives an electric shock, 
so that toward the end of its journey through the system it 
accumulates a total potential of several million volts. These 
high-energy particles come out of the apparatus through a 
thin mica window, placed at the end of their spiral tra- 
jectory, and can be used now for any kind of nuclear 
bombardment. 

The experiments with artificial beams of particles, 
whereby the type of projectiles needed and their velocities 
could be conveniently selected at will, resulted in great 



The Transmutation of Elements 81 

progress in our knowledge of various nuclear reactions. 
In addition to those few mentioned above, dozens and 
dozens of other interesting nuclear transformations have 
been extensively studied by these means. 



fasf pqrficles 




t - voltage 
oscillotrons 
from a transformer 

FIGURE 22 

The principle of the cyclotron. Particles move in spirals of constantly 

increasing speed. 

NEW "PENETRATING" PROJECTILES 

The progress of nuclear physics during the last decade 
has also been considerably advanced by the discovery of 
an entirely new kind of nuclear projectile, which, while in 
many respects similar to ordinary protons, does not, how- 
ever, carry any electric charge. These chargeless protons, 
or neutrons, to use the more conventional term, represent 
the ideal projectiles for nuclear bombardment, because, 



82 The Birth and Death of the Sun 

having no electric charge, they will not suffer any repul- 

sion from heavily charged nuclei, and will penetrate with- 

out much difficulty into the very interior of the nuclear 

structure. 

Although a hypothesis concerning the possibility of 
such kinds of particles was expressed by Rutherford as 
early as 1925, the actual proof of their existence was given 
only in 1932, when Rutherford's collaborator, Dr. James 
Chadwick, succeeded in showing that the peculiar radia- 
tion emitted by beryllium under a-particle bombardment 
consists of neutral particles with a mass comparable to that 
of a proton. The resulting nucleus corresponds to that of 
ordinary carbon. 

At the present time neutrons are usually produced by 
bringing about the collisions of two deuterons, that is, the 
nuclei of heavy hydrogen atoms.* Accelerating the ions of 
heavy hydrogen in one of the modern high-tension gen- 
erators, one lets them fall on some substance, such as heavy 
water, that contains in its molecules the bound atoms of 
heavy hydrogen. In the resulting collisions a very large 
number of fast-moving neutrons are produced, according 
to the equation: 

!D 2 + iD 2 - ^He 3 + on 1 



As we see, another product of this reaction represents the 
light isotope of helium of mass 3, which is known to be 
mixed in very small quantities with the ordinary helium 
of mass 4. 

It should be noted here that, owing to the absence of 
electric charge, neutrons do not produce any ionization of 
the air along their track and consequently do not leave 

* Heavy hydrogen is usually called deuterium, and its symbol in nuclear 
notation is: iD 2 (charge i; mass 2). 



The Transmutation of Elements 83 

any visible trace on passing through a cloud-chamber. They 
are ordinarily observed only through the traces left by the 
products of their collisions with the particles of the air 
that happen to be directly in their way. 

THE RESULTS OF NEUTRON BOMBARDMENT 

As indicated above, neutrons can easily penetrate any, 
even the most heavily charged, nucleus and produce devas- 
tating effects in its interior. These effects have been inves- 
tigated mostly by the Italian physicist Enrico Fermi and 
his collaborators. In the case of lighter elements, the pene- 
tration of a neutron is often followed by the ejection either 
of an a-particle or of a proton as, for example, in the 
reactions: 



which represents the transformation of nitrogen into boron 
and helium; or 

on 1 



which represents the transformation of iron into man- 
ganese and hydrogen. 

In the heavier elements, the potential walls surrounding 
the atomic nucleus are too high, and, though they cannot 
prevent the neutron from entering, they make it impossible 
for any charged nuclear constituent particle to be thrown 
out. In this case neutrons entering the nucleus must get 
rid of their energy through electromagnetic radiation, and 
the nucleus emits hard y-rays, as, for example, in the 
reaction: 

79 Au 197 + on 1 - > 79 Au 198 + -y-rays 

in which a heavier isotope of gold is built. This process of 



84 The Birth and Death of the Sun 

building the heavier isotope of the bombarded element 

may often be followed by an adjustment of the electric 

charge through the emission of an electron (see p. 66 

above). 

BURSTING A NUCLEUS 

In all the nuclear reactions we have thus far discussed, 
the transformations consisted mainly of the ejection of 
some comparatively small nuclear structural parts (such as 
a-particles, protons, or neutrons); up to this point in the 
development of subatomic physics there had not yet been 
observed the bursting of the nucleus of a heavy element 
into two or more approximately equal parts. But quite 
recently (the winter of 1939) just such "smashing results" 
were observed by the two German physicists O. Hahn and 
Lise Meitner, who found that the atoms of uranium, which 
are already unstable in themselves, would split into two 
large fragments under the intense bombardment of a beam 
of neutrons. One of the splinters represents a nucleus of 
barium and the other presumably that of krypton. The 
process is accompanied by an energy liberation exceeding 
by a factor of hundreds the energy produced in any other 
known nuclear reaction. As we shall see in the next chapter, 
this entirely new type of nuclear transformation gives us, 
for the first time, some hope for the practical utilization of 
subatomic energy. 



CHAPTER IV 



Can Subatomic Energy Be Harnessed? 



ENERGY VERSUS GOLD 

WE HAVE seen in the last chapter that the progress 
of physics in the last few decades has revived the 
golden dream of the medieval alchemists, and has put on 
a solid scientific basis the fascinating possibility of arti- 
ficially transforming the elements into one another. But, 
whereas the alchemists were exclusively interested in the 
transmutation of base metals into precious gold, it is energy 
and not gold we are now after. Indeed, the immense stores 
of energy that might be liberated in nuclear reactions 
would make gold, or any other material product obtainable 
from such transformations, relatively worthless. 

For example, in the splitting of a lithium atom by the 
impact of a proton (see Figure 20) there is set free 2.8 X 
io~ 5 erg of energy. Thus, one gramme of lithium, if en- 
tirely transformed into helium by proton bombardment, 
would liberate a grand total of 2.5 X io 18 ergs, which is 
worth $7500 according to present energy prices. If any gold 
or silver were formed along with this liberation of energy, it 
would represent such a small fraction of the "total profit" 
one gramme of gold costs about one dollar that nobody 
would be interested in it. On the other hand, the prac- 
ticable utilization of the subatomic energy hidden in the 
depths of nuclei would produce a complete revolution in 
all modern technology and life! 

85 



86 The Birth and Death of the Sun 

THE LOW RATE OF SUBATOMIC ENERGY 
LIBERATION 

It is a little too early, however, to speculate on the pos- 
sible technical and economic consequences that would flow 
from the tapping of subatomic energy sources. There is, of 
course, no doubt that the energy is there, but, as we have 
seen in previous chapters, its liberation in the processes of 
both spontaneous and artificial transformation goes on at 
such an extremely slow rate that very sensitive physical 
apparatus are necessary in order even to detect it. In this 
respect the "nuclear reservoirs'* of subatomic energy may 
be compared to a vast elevated lake from which the water 
is leaking through a small channel at the rate of one drop 
per week. There is no sense in installing a large water 
turbine here until the way is found for opening the chan- 
nel much wider and letting the available water flow out in 
a powerful stream. 

In order to see whether such channel widening is at all 
possible in the case of subatomic energy sources, we have 
to discuss in more detail the various factors governing the 
rate of nuclear transformation. 

THE PROBABILITY OF A CHARGED PROJECTILE'S 
HITTING A NUCLEUS 

Suppose we send a nuclear projectile, such as a proton 
or an a-particle accelerated to very high energies, through 
some material, the nuclei of which we intend to bombard. 
What is the chance that our projectile will score a head-on 
collision with the nucleus of one of the atoms in our piece 
of material? We know that the diameter of an atomic 
nucleus is about 10,000 times smaller than the diameter of 
the atom itself, so that the target-area of the nucleus is 100 



Can Subatomic Energy Be Harnessed? 87 

million times (the square of the diameter ratio) smaller 
than the target-area of the whole atom. As we have no pos- 
sible method of aiming our projectiles, it follows that the 
incident particle must pierce on an average 100 million 
atoms before it will hit a nucleus. But as it passes through 
the bodies of so many atoms, our projectile will steadily 
slow down, losing its energy through electric interaction 
with orbital electrons,* and will, in most cases, come to a 
stop before it has had a chance to hit a nucleus. 

As a matter of fact, the a-particles used in the classical 
disintegration experiments and the protons produced in 
modern high-tension generators are stopped after they 
have passed through only 100,000 atomic bodies. The 
chance, therefore, of any given projectile's hitting a nucleus 
before it has lost all its energy is only one in a thousand 

/ 2 v consequently, of a thousand such projectiles 

v 1 00,000,000 / ~L / r j 

that enter the substance only one will probably score a hit. 
The bombardment of nuclei, wrapped as they are in their 
thick envelopes of atomic electrons, is rather like trying 
to crack walnuts hidden in sandbags by shooting at a pile 
of such bags with a machine gun. 

It is clear then that, although the projectile which scores 
a direct hit at the nucleus may crack it and liberate an 
amount of subatomic energy several times surpassing the 
energy of the impact, the total liberated nuclear energy 
will not be nearly enough to compensate for the useless 
expenditure of the thousand projectiles which missed their 
aim. It is true, of course, that by increasing the original 
energy of the particles used for the bombardment, we can 

*This interaction, leading to the ionization of atoms along the track, 
is responsible, as indicated above (p. 69), for the formation of the visible 
track in the cloud-chamber. 



88 The Birth and Death of the Sun 

increase the number of atoms pierced by each of them. 
But even at the tremendous energies of billions of volts 
that are observed for some particles of cosmic rays, the 
total energy balance of transformation will still be ex- 
tremely unfavourable. 

It should also be added here that any attempt to "strip 
the nuclei of their electronic shells" and to bombard a 
collection of "bare nuclei*' should be labelled as quite 
visionary. In fact, nuclei deprived of the electronic shells 
that neutralize their charges would repel each other with 
such strong force that, in order to keep together one cubic 
centimetre of such a de-electronized substance, the pressure 
of many billions of atmospheres would be necessary. This 
pressure is approximately equivalent to the weight that 
the moon would have if it were placed on the surface of 
the earth, and is clearly unattainable by any means at our 
disposal. 

PENETRATING THE NUCLEAR FORTRESS 

Let us consider now the case of the "lucky" projectile 
that happens to meet a nucleus before it has lost all its 
energy through the "intra-atomic friction" described above. 
Will it always be able to penetrate the nucleus and produce 
the necessary transformation? The answer is again no, for 
atomic nuclei are very strongly fortified against any intru- 
sion of other charged particles from outside. The repulsive 
forces between the electric charge of the nucleus and that 
of the projectile become stronger and stronger as the 
projectile approaches the nuclear boundaries, and are apt 
to throw the incident particle back, producing an ordinary 
scattering phenomenon. Thus, only a very small proportion 
of those particles which do score a direct hit manage to pass 



Can Subatomic Energy Be Harnessed? 89 

through this barrier of the repulsive electric forces and 
enter the nuclear interior. 

A detailed understanding of this process by which bom- 
barding particles penetrate the barriers surrounding atomic 
nuclei presented some very serious difficulties from the 
point of view of classical mechanics just as did the "leak- 
ing out" of a-par tides described in a previous chapter 
(p. 64) and their solution became possible only through 
the application of the modern quantum theory. The 
quantum-mechanical calculations carried out in 1928 by 
the author led to a rather simple formula permitting us 
to estimate the proportion of projectiles that would pene- 
trate the nuclear interior, expressed in terms of the charge 
of the bombarded nucleus and of the charge, mass, and 
energy of the projectiles used. 

This formula demonstrates in particular that the prob- 
ability of penetration decreases very rapidly with the in- 
creasing atomic number (nuclear charge) of the bombarded 
element. This explains why, under the bombardment of 
a-particles and protons, only the lightest elements could be 
disintegrated. On the other hand, the efficiency of bombard- 
ment increases very rapidly with the increasing energy of 
the projectiles; and at sufficiently high energies (25 million 
volts for lithium, 50 million volts for iron, and 100 million 
volts for lead) almost any direct hit will mean disin- 
tegration. 

RESONANCE DISINTEGRATION 

It must be mentioned here that such hundred-percent 
penetrations can sometimes also occur at considerably 
lower energies of the bombarding particles. This happens 
in cases where the barrier surrounding the nuclear fortress 



90 The Birth and Death of the Sun 

possesses certain "weak spots" which are usually known as 
resonance channels. It was shown by Gurney that, in the 
processes of nuclear bombardment, the penetration of the 
barrier by the incident particles can be considerably facili- 
tated if their energy is exactly the same as the energy 
corresponding to one of the harmonic vibrations within the 
bombarded nucleus itself. These harmonic vibrations of 
the struck nucleus are of the same kind as those of a bell 
or tuning-fork struck by a hammer, and this phenomenon 
is known as nuclear resonance because of its similarity to 
the resonance phenomena in ordinary mechanics, in which 
the amplitude of vibration rapidly increases if the vibrat- 
ing body is subjected to a sequence of shocks following 
each other within a certain definite period. 

The study of various nuclear reactions revealed that 
many nuclei actually possess such "resonance channels" 
and can be disintegrated much more easily if the bombard- 
ment is carried out with projectiles of just the proper 
energy. In many cases the use of "resonance bombardment'* 
can increase the probability of disintegration by a factor 
of many hundreds or even thousands; but it must not be 
forgotten that all these increases of disintegration efficiency 
that result from using either extremely high energies or 
especially selected "resonance values" pertain only to the 
probability of penetration after the head-on collision has 
taken place. There always remains the unfavourable ratio 
of one to a thousand as far as the probability of such a col- 
lision is concerned, which makes the total efficiency ex- 
tremely small in any case. 

All these considerations, taken together, mean that 
nuclear transformations produced by bombardment with 
fast-moving charged particles must necessarily have a very 



Can Subatomic Energy Be Harnessed? 91 

small efficiency; that is to say, although they are extremely 
interesting from a purely scientific point of view, they can 
hardly be considered to have any practical importance. 

BOMBARDMENT BY NEUTRONS 

In contrast to the charged nuclear projectiles, neutrons 
represent the ideal particles for nuclear bombardment. 
First, owing to their complete lack of electric charge, they 
will pierce the electronic shells of atoms without any loss 
of energy (as will be remembered, neutrons do not leave 
any visible track in a cloud-chamber); secondly, when they 
do finally collide with a nucleus, they will not be stopped 
by any repulsive electric forces. It follows that practically 
every neutron shot into a thick layer of matter will sooner 
or later find a nucleus in its path, and penetrate it. 

But precisely because of this penetrativity of neutrons, 
and the ease with which they are therefore captured,* free 
neutrons are very rare in nature, and there is no such 
element as "neuterium." It should also be noted that a 
free neutron cannot even exist as such for more than about 
half an hour because, being essentially unstable, it very 
soon emits a free negative charge (an ordinary electron), 
thus transforming itself into a proton (Figure 23). 

In order to produce a beam of neutrons for bombard- 
ment purposes we therefore first have to extract them from 
the interior of ordinary nuclei, where they are usually to 
be found, and this operation can be performed only by 
bombarding the latter with protons or a-particles. But in 
order to shoot one neutron out of the nucleus by proton 

* As we have seen in the last chapter (p. 83), a neutron, upon entering 
a nucleus, usually remains there, ejecting in its place either a proton or 
an a-particle or finally discharging its extra energy through a 7-ray 
emission. 



92 The Birth and Death of the Sun 

or a-particle bombardment, many thousands of incident 
charged particles are necessary, and we are back to our 
original difficulty. 



Ncufron before dismfegmhbn 



Half ar\ Hour later 



FIGURE 23 
Spontaneous splitting of a free neutron into a proton and an electron. 

MULTIPLICATIVE NUCLEAR REACTIONS 

The preceding discussion will have explained why our 
only hope of obtaining practical results from neutron 
bombardment is to discover some nuclear reaction in which 
the neutrons are, so to speak, self-multiplied. If every inci- 
dent neutron were only able to kick out from the bom- 
barded nucleus two or more "fresh" neutrons, and if these 
new particles could in their turn produce still more 
neutrons by colliding with other nuclei, so that the number 
of acting neutrons rapidly increased in geometric propor- 
tion (Figure 24), our problem would be solved. The situ- 
ation here is rather similar to the multiplication problem 
of human races; and just as the growth of the population 
is possible only if the average number of babies born per 
family is not less than two, so a nuclear multiplicative 
process requires that not less than two neutrons should 
be emitted by each nucleus that is "fertilized" by collision 
with one of the incident neutrons of the previous genera- 
tion. 

As recently as 1939 it was generally believed that such a 



Can Subatomic Energy Be Harnessed? 93 

multiplicative process did not usually take place in nature, 
and that nuclear reactions represented a strictly one-to- 
one relationship (i.e., one particle shot out for every one 
going in). As was suggested in the last chapter, however, 
recent experiments by Hahn and Meitner with the neutron 
bombardment of uranium and thorium have shown that 




>- Neutrons 
I- Nuclei 



FIGURE 24 

Multiplicative disintegration possible for certain cases of bombardment 
of matter by neutrons. 

the nuclei of these elements are considerably more fragile 
than those of any other. When struck by neutrons, these 
nuclei are apt to split into two large parts, and this major 
breakdown is also accompanied by the ejection of smaller 
nuclear splinters in the form of two, three, and sometimes 
even four other neutrons. Thus, we have here precisely the 
case in which the multiplicative process we have been 
seeking actually does take place; and the proper treat- 
ment of these nuclear reactions may lead us to the possi- 
bility of the large-scale liberation of subatomic energy. 



94 The Birth and Death of the Sun 

Two questions, however, immediately arise, and the first 
concerns the reasons why a piece of uranium, when bom- 
barded by neutrons in our laboratories, does not imme- 
diately explode, thereby wiping out the lives of the experi- 
menters as well as of any other living being within many 
hundreds of miles. For, theoretically, such a multiplica- 
tive reaction, once started, should take the form of a 
terrific explosion, all the tremendous amounts of energy 
stored in uranium atoms (io 18 ergs per gramme, which is 
equivalent to the explosion energy of a ton of dynamite!) 
being liberated in a small fraction of a second. 

The answer to this important question is, first, that the 
ordinary uranium we have in our laboratories is wet 
not wet, of course, in the ordinary sense of this word, but 
rather in the sense that its active part is mixed in with a 
large amount of inactive material (as a piece of wood may 
be saturated with water), which absorbs most of the newly 
created neutrons and takes them out of active service. It is 
known that ordinary uranium is composed of a mixture 
of two isotopes Ui and Un (see Figure 16) with atomic 
weights, respectively, of 238 and 235. The lighter isotope 
Un is present in the mixture in a small concentration of 
only 0.7 percent; and it is certain that this is the isotope 
responsible for the observed splitting and intense neutron 
emission. The heavier isotope Ui, making up 99.3 percent 
of the mixture, also catches the incident neutrons, but, 
instead of splitting into parts with high energy liberation, 
it retains the neutrons and emits the surplus of energy in 
the form of hard y-radiation. Thus, only very few of the 
produced neutrons can take part in the actual multiplica- 
tive process; and, in order to obtain a progressive multi- 
plicative process, we must separate the lighter active iso- 



Can Subatomic Energy Be Harnessed? 95 

tope from the heavier one, a task which, with the present 
means at the disposal of experimental physics, is, if not 
impossible, at any rate rather difficult. The modern tech- 
nique of isotope separation involves a large number of 
successive diffusions, during which the concentration of 
the lighter isotope, in the diffused fractions of material, 
gradually increases.* 

Work on the separation of uranium isotopes is now 
under way in many laboratories and will probably soon 
lead to extremely interesting results.f There is little 
ground for fear, however, that one fine day the laboratory 
which first produces a highly concentrated Un isotope will 
jump into the air together with the whole city in which 
it is situated. For the steadily increasing concentration of 
the lighter uranium isotope will most probably be accom- 
panied by a correspondingly slow increase of the liberation 
of subatomic energy; and, before the developed heat be- 
comes too intense for safety, the separation process will 
be stopped in time to avert any danger of explosion.;}; Let 
us at least hope it will happen this way! 

The second important point regarding the possibility 
of a self-sustaining neutron-multiplication process in 
uranium concerns the amount of uranium needed. With 

* The rate of diffusion through porous walls depends essentially on 
differential atomic weight, the lighter isotope going through more rapidly. 
However, owing to the small relative difference of the atomic weights of 
the two uranium isotopes (less than one percent), the separation in this 
case is bound to be extremely slow. 

fOn March 15, 1940, such a separation was finally announced by 
Drs. O. Nier, E. T. Booth, J. R. Dunning, and A. V. Grosse, but for ex- 
tremely small quantities (0.000,000,001 gramme). 

J This will happen spontaneously, because the temperature developed in 
the reaction will melt all the vessels in which the separation of isotopes is 
taking place. It should be noted that the nuclear explosion process would 
not need a special neutron source to start it off. In fact there are so many 
neutrons passing occasionally by (for example, in the cosmic rays) that the 
"spark" can be struck almost any moment. 



96 The Birth and Death of the Sun 

a small piece of uranium, most of the neutrons produced in 
its interior will escape through the surface before they 
have had a chance to hit a nucleus. The progress of the 
multiplication process will then be stopped for the same 
reason that a small tribe cannot grow if it continually 
loses its younger members in the surrounding forest. Since 
there are no walls to prevent the neutrons from escaping 
into surrounding space, it becomes necessary to use such 
large pieces of uranium that a neutron produced in its 
interior will be sure to meet a nucleus before it can have 
come to the surface. But this would require several hun- 
dred tons of pure uranium 255,, which is not a very easy 
thing to acquire, especially in the form of separate isotopes. 

THE PRICE OF URANIUM ENERGY 

Supposing that these two difficulties large-scale isotope 
separation and the retention of active neutrons standing 
in the way of the practical utilization of the subatomic 
energy of uranium (and of its sister element thorium) were 
to be overcome by technical genius, and a method were 
found for running our engines on "uranium fuel," how 
much would it cost? 

Uranium is not a very cheap material; according to 
present market prices, a pound of uranium oxide, contain- 
ing 95 percent pure uranium, costs about two dollars, 
which is equivalent to the price of one ton of coal at the 
mine. As only 0.7 percent of uranium is active in neutron 
multiplication, the total subatomic energy released in the 
process by the pound of uranium oxide will amount to 
3 X io 18 ergs. On the other hand, a ton of coal (900,000 
grammes), costing the same as a pound of uranium oxide, 
will liberate only 3 X io 17 ergs, so that the subatomic 



Can Subatomic Energy Be Harnessed? 97 

energy that might be obtained from uranium would be 
about 10 times cheaper than the energy of coal. 

It should be added, however, that if uranium were com- 
pletely to replace coal as a source of energy, at the present 
rate of consumption, the reserves of uranium ore on our 
planet would be entirely exhausted in less than a century. 

RECAPITULATION: THE STRUCTURE OF THE ATOM 

Let us now plunge once more and for the last time into 
the depths of matter, briefly reviewing the main conclu- 
sions we have reached in the last three chapters. First we 
found that matter, seemingly so homogeneous in the light 
of everyday experience, consists in point of fact of very, 
very small granules known to scientists as molecules. No 
microscope is strong enough to make visible these con- 
stituent particles of matter, and very elaborate and subtle 
methods of modern physics are necessary to prove their 
existence and to study their characteristic properties. 

There are, for example, about 600,000,000,000,000,000,- 
000,000 (23 zeros!) molecules of H 2 O in each cubic inch of 
water, and they are all animated by a vigorous and dis- 
orderly thermal motion that should make them resemble 
a mess of freshly caught fish in an angler's basket. This 
molecular motion gradually slows down as matter gets 
colder, but we would need temperatures as low as 45gF. 
below zero to bring these restless particles to a complete 
standstill. On the other hand, raising the temperature 
makes the molecules move more and more briskly and 
leads at last to their mutual separation. We say then that 
the molecules form a gas, or vapour, in which each particle 
moves more or less freely through space and collides fre- 
quently with every other particle that comes its way. 



98 The Birth and Death of the Sun 

There are as many different types of molecules as there 
are different chemical substances (i.e., hundreds of thou- 
sands of them); but if we look more closely into any given 
molecule we find that it is always composed of a limited 
number of somewhat smaller constituent particles called 
atoms. There are only ninety-two kinds of atoms, corre- 
sponding to the ninety-two pure chemical elements, and 
through the different combinations of these atoms arise the 
innumerable complex compounds familiar to our chemists. 
The various redistributions of the atoms in the complex 
molecules is observed by us as specific chemical reactions, 
or the transformations of one chemically complex substance 
into another. But, despite all the attempts of medieval 
alchemy, atoms themselves had stubbornly refused to be 
transformed into one another, and this led chemists to the 
erroneous conclusion that atoms were really elementary 
and indivisible particles, as was suggested by the Greek 
meaning of their name. 

The progress of physics, however, shook this point of 
view, which prevailed in science throughout the last cen- 
tury, and we know now that an atom is actually a rather 
complicated mechanical system consisting of a central 
nucleus with a swarm of electrons revolving around it 
under the action of electric forces. Now it was these 
atomic nuclei that represented the citadel of indivisibility, 
but even this last stronghold of the Democritean idea gave 
up under the attack of that restless investigator of matter, 
Lord Rutherford of Nelson. 

In the year 1919 the first nitrogen nucleus was broken 
up by him under a bombardment of tiny projectiles, 
known as a-particles; and the following two decades saw 
an immense development of what is known as nuclear 



Can Subatomic Energy Be Harnessed? 99 

physics. Many dozens of nuclear reactions have been pro- 
duced and investigated in great detail, with the result 
that we now know more about the atomic nucleus than 
had been known about atoms themselves a few decades ago. 

The two most important facts that distinguish nuclear 
reactions from ordinary chemical reactions between mole- 
cules are the tremendous amounts of subatomic energy 
liberated in the former transformations, and the tremen- 
dous difficulties encountered in the attempts to produce 
these reactions on a large scale. In fact, owing to the thick 
layer of electronic shells surrounding individual nuclei, 
only a very small proportion of the projectiles used for 
bombardment purposes can score direct hits on the atomic 
nucleus, and of thousands of projectiles that attain their 
goal probably not more than one will actually produce 
the desired transformation. It is true that during recent 
years the discovery of neutrons and of the multiplicative 
reactions connected with this new type of particle gave us 
some hope for the possible technical utilization of the huge 
stores of subatomic energy hidden in the interiors of atoms, 
but these have so far remained only hopes. 

For though the study of the peculiar splitting properties 
of uranium and thorium nuclei brought us very close to 
the possible solution of the problem, these two elements 
were found to be exceptional in showing this instability 
and they are, moreover, rare in the world. The basic prob- 
lem of how to liberate the nuclear energy of all the other, 
more common elements is still left open. 

We shall, however, see In the following chapters, in 
which the impatient reader may at last return to the Sun, 
that the large-scale transformation of common elements, 
which so stubbornly retain their hidden energy even under 



100 The Birth and Death of the Sun 

the most intensive bombardment by artificially accelerated 
projectiles, occurs spontaneously under certain conditions 
of very high temperature practically unattainable in our 
terrestrial laboratories. And we shall also see that these 
very transformations are entirely responsible for the light 
and heat of our Sun and for the energy radiation of all the 
other stars in the sky. 



CHAPTER V 



The Alchemy of the Sun 



SUBATOMIC ENERGY AND SOLAR HEAT 

THE discovery of the enormous stores of energy that 
can be set free in the processes of nuclear transforma- 
tion gives us a key to the possible solution of the ancient 
riddle concerning the sources of solar radiation. We have, 
indeed, already mentioned that the nuclear reactions lead- 
ing to the transformation of one element into another are 
usually accompanied by a liberation of energy that sur- 
passes by a factor of many millions the energy set free in 
ordinary chemical reactions between molecules. Thus, 
whereas a Sun made of coal would have burned up com- 
pletely in fifty or sixty centuries, a Sun that takes its energy 
from subatomic sources can keep going strong for billions 
of years. 

But we also know that the ordinary radioactive ele- 
ments, such as uranium or thorium, are not abundant 
enough to account for the tremendous energy production 
in the Sun*; and we are left with the only possible con- 
clusion that the observed liberation of energy must be 
due to the induced transformations of the ordinarily stable 
common elements. We must therefore imagine the interior 
of the Sun as some gigantic kind of natural alchemical 
laboratory where the transformation of various elements 

* These elements are, however, sufficiently abundant to be mainly re- 
sponsible, through the heat they develop, for the fact that the interior of 
our globe is still in a state of hot molten lava. 

101 



102 The Birth and Death of the Sun 

into one another takes place almost as easily as do the 
ordinary chemical reactions in our terrestrial laboratories. 
What, then, are the extraordinary facilities of this cosmic 
energy plant, which produces the phenomena of nuclear 
transformation on such a large scale and sets free so vast 
an amount of subatomic energy? If we remember what was 
said in the first chapter about the physical conditions 
obtaining in the interior of the Sun, we shall see at once 
that the most striking characteristic of these regions is their 
extremely high temperatures, which cannot even be ap- 
proached under our terrestrial conditions. May it not be 
these high temperatures that are responsible for the high 
rates of nuclear transformation going on in the solar in- 
terior? We know that all ordinary chemical reactions be- 
tween molecules are greatly accelerated by heating; and if 
a log of wood or a piece of coal will begin to burn when 
it is heated to several hundred degrees in an ordinary 
furnace, why cannot we expect that the matter heated to 
many millions of degrees in the solar interior will start to 
"burn" in the nuclear sense? 

THERMONUCLEAR REACTIONS 

The answer to this important question was first pro- 
posed by two young scientists, Robert Atkinson and Fritz 
Houtermans, in 1929. Their explanation was to the effect 
that, at the very high temperatures obtaining in the in- 
terior of the Sun, the kinetic energy of thermal motion 
becomes so great that the violent mutual collisions among 
the irregularly moving particles of matter are as destructive 
of nuclei as are the impacts of atomic projectiles in ordi- 
nary bombardment experiments. In fact, at a temperature 
of 20 million degrees the average kinetic energy of thermal 



The Alchemy of the Sun 103 

motion amounts to 5 X io~" 9 erg, which is not very far 
from the value of io~ 8 erg actually observed in our labora- 
tories to accompany the artificial transformation of ele- 
ments. But, whereas the ordinary bombardment method 
might be compared to a bayonet attack of a single line of 
soldiers upon a comparatively large group of people, the 
thermonuclear process is more nearly analogous to a vio- 
lent hand-to-hand fight going on simultaneously through- 
out all parts of a highly excited and quarrelsome crowd. 






Vtvy KiflK 1<npV<!ituv< 



FIGURE 25 
Tliermal ionization of a gas. 

It should be remarked, too, that, at these very high 
temperatures at which the thermonuclear reactions take 
place, matter no longer consists of atoms and molecules in 
the proper sense of these words. At much lower tempera- 
tures the electronic shells of individual atoms will already 
have been completely stripped off by the mutual thermal 
collisions; and matter will then consist of a mixture of 
irregularly moving bare nuclei (completely ionized atoms), 
with unattached electrons rushing in all directions among 
them (Figure 25). The "naked" nuclei, unprotected by 
electronic shells, will no longer be cushioned against 
thermal collisions, and the violent direct impacts will often 
lead to fatal results. 



104 The Birth and Death of the Sun 

The persistency of the thermal collisions makes the 
thermonuclear reactions infinitely more effective than the 
ordinary bombardment process, where the initial energy of 
the artificially accelerated projectiles is completely lost after 
their passage through the electronic flesh of only a hun- 
dred thousand atoms of the bombarded substance. If, for 
example, we heat a mixture of hydrogen and lithium to 
a sufficiently high temperature, the violent thermal colli- 
sions among the particles of these two elements will go on 
and on without stopping until all the available nuclei have 
been transformed into helium. The subatomic energy 
liberated in the process will keep our reacting substances 
sufficiently hot to insure its continuance, so that all we 
need here is to raise the temperature of our mixture suffi- 
ciently high to get the reaction started. 

THE TEMPERATURES NECESSARY FOR 
THERMONUCLEAR REACTIONS 

In order to consider the question of the importance for 
the life of our Sun of the thermonuclear reactions among 
the various elements and also if we wish to discuss the 
possibility of the practical utilization here on earth of 
these same processes we must know first of all the tem- 
peratures at which these transformations would take place 
at a reasonably high rate. 

As in the case of ordinary nuclear bombardment pre- 
viously discussed, the rate of the thermonuclear reactions 
will be essentially determined by the penetrability of the 
barriers surrounding the colliding nuclei. It has already 
been indicated that the theory of nuclear transformations 
developed by the author permits us to calculate the prob- 
ability of such penetrations in terms of the kinetic energy 



The Alchemy of the Sun 105 

and the electric charges of the colliding particles. We have 
also seen that this probability increases extremely rapidly 
with the increasing energy of the colliding particles (i.e., 
with the temperature of the mixture), but falls quickly 
with their increasing electric charges. Thus, we should 
expect, on heating a mixture containing different types of 
nuclei, to observe first the reactions between the lightest 
nuclei, which carry the smallest charges; the reaction be- 
tween hydrogen and lithium mentioned above will there- 
fore be one of the first to take place. As the temperature of 
the mixture rises still further, we should expect more 
effective penetration of the heavier nuclei by thermal 
protons and also the beginning of activity between 
a-particles and the lightest elements. Finally, at still much 
higher temperatures, collisions between the heavy nuclei 
themselves might become of importance. 

In order to calculate from this penetration formula 
the rate of thermonuclear reaction between any two given 
types of nuclei, it is not sufficient, however, to know only 
the average kinetic energy of the particles at a given tem- 
perature. As we have seen in Chapter II, the particles of 
a hot gas do not all move with exactly the same velocity, 
but show a rather broad velocity dispersion known as the 
Maxwell distribution. It is true, of course, that the number 
of particles possessing anomalously large energies is com- 
paratively small; but we must not forget that the effective- 
ness of collision rapidly increases with the increasing energy 
of impact. Thus, although few, these high-energy particles 
can be of great importance for the total disintegration 
balance. In Figure 26 the curve A represents the familiar 
Maxwellian energy-distribution of thermal motion (com- 
pare Figure 6), giving the relative number of the particles 



106 The Birth and Death of the Sun 

of gas possessing different values of energy (). The curve 
B, on the other hand, gives us the disintegration ability 
(penetrativity of nuclear barriers) of particles correspond- 
ing to these energies. Finally, A X B, the product of these 
two curves, represents the total disintegration effect (num- 




FlGURE 26 

The maximum number of disintegrations (A X B) takes place for ther- 
mal energy for which the particles' penetrativity of nuclear barriers 
(B) is already sufficiently high, whereas their number (A) is not yet 

too small. 



ber of particles times their relative effectiveness). We see 
at once that the maximum effect corresponds to a certain 
intermediate energy value for which the number of par- 
ticles is not yet too small and their penetrativity of barriers 
is already sufficiently high. 

Thus combining Maxwell's distribution law with the 
author's formula for penetrativity, Atkinson and Houter- 



The Alchemy of the Sun 107 

mans succeeded in obtaining an expression for the de- 
pendence of the disintegration rate on the temperature of 
the mixture and on the atomic numbers of the participat- 
ing elements* We shall not terrify the reader by writing 
down their formula in all its mathematical magnificence, 
but shall rather give here the numerical results of its 
application to one characteristic nuclear reaction.f 

We shall select for this purpose the reaction between 
hydrogen and lithium, which has already been mentioned 
a few times and is, besides, one of the most effective reac- 
tions, owing both to its high reaction rate and to the high 
values of energy liberated per nucleus. One gramme of a 
mixture consisting of seven parts of lithium and one part 
of hydrogen will, if completely transformed into helium, 
produce 2.2 X io 18 ergs of subatomic energy. But even at 
a temperature of several thousand degrees (the highest 
available in our laboratories), the thermonuclear reaction 
will go so slowly that it would require billions of billions 
of years to produce the complete transformation. At so 
slow a rate, the energy liberation of one ton of the mix- 
ture would amount to only a few ergs per century, not 
enough even to raise a dead fly from the floor to the table. 
At one million degrees, however, the energy flow from 
several pounds of the hydrogen-lithium mixture would be 
sufficient to run an automobile engine. And, finally, at the 
central solar temperature of 20 million degrees, hydrogen 
and lithium will be transformed into helium in a few sec- 

* The rate of energy production depends also on the density of the 
matter, being proportional to the product of densities of the reacting 
substances. 

fThe numerical results given here are actually calculated not on the 
basis of the original formula as given by Atkinson and Houtermans, but 
on the basis of a new revised expression, corrected according to the latest 
development of nuclear physics. 



108 The Birth and Death of the Sun 

onds, and the energy liberation must take the form of a 

terrific explosion. 

If, however, we apply the same formula to the collisions 
of protons with the nuclei of heavier elements, we find that 
even at central solar temperatures the reaction between 
hydrogen and chlorine, for example, will take io 25 years 
to transform 50 percent of the mixture, and the penetra- 
tion of protons into the heavy nuclei of lead will require 
an unbelievably long time no less than io 250 (!) years. We 
find also that at this temperature the penetration of thermal 
a-particles is negligibly small even for collisions with the 
lightest nuclei, and that it becomes important only for a 
temperature above 50 million degrees. 

HOW TO MAKE A "SUBATOMIC MOTOR" 

"Excellent!" the reader may already have exclaimed. 
"Then all we have to do is to load the furnace of a steam 
engine with a lithium-hydrogen mixture and heat it up to 
several million degrees. Is that so difficult?" (Figure 27.) 
Well, it is not difficult, of course, to acquire an old 
steam engine for such an experiment; neither is it very 
hard to obtain the necessary nuclear fuel, since the solid 
lithium-hydrogen compound LiOH can be bought in 
almost any drug store. But what about the temperature of 
several million degrees? No chemical process, such as the 
combustion of coal, is capable of developing such high 
temperatures; and if we try to heat our furnace by the 
electric method, the wires even those made of the most 
refractory materials will have melted (and even evapo- 
rated) before we have attained several thousand degrees of 
temperature. The same fate will also befall the walls of the 
furnace itself, and there will be no means of keeping the 



The Alchemy of the Sun 109 

reacting gases within a given volume. The melting of 
the walls will permit the immediate expansion of the hot 
gases, and the temperature will inevitably fall. 

As all these undesirable events will have taken place 
long before the temperature has been given a chance to 




FIGURE 27 

A dream of a subatomic motor. No walls will, however, withstand 

such heat. 

rise to the necessary high values, it is very difficult to see 
how thermonuclear reactions can be forced to go on under 
laboratory conditions. This miracle, at least, would seeni 
to be beyond the powers of modern technique. 

THE SOLAR FURNACE 

The insurmountable difficulties in our way when we 
attempt to construct a thermonuclear furnace at home do 



110 The Birth and Death of the Sun 

not, however, exist in the case of the Sun, which is just 
such a giant furnace. This cosmic furnace actually pos- 
sesses "gaseous walls" the outer layers of its body which 
are kept together by the forces of mutual gravitational 
attraction (Figure 28). 




FIGURE 28 

The subatomic generator of the Sun. The gas walls are held together 

by gravity. 

The forces of gravity also provided the mechanism that 
was necessary to bring about the original rise of tempera- 
ture to the value at which the thermonuclear reactions 
could begin. We have seen in Chapter I that the Sun must 
have begun life as a comparatively cool giant mass of gas, 
which gradually became hotter and hotter because of pro- 
gressive gravitational contractions. As soon as the central 
temperature of this contracting Sun became sufficiently 



The Alchemy of the Sun 111 

high to keep the nuclear reactions going, the liberation of 
subatomic energy stopped further contractions and the Sun 
came into its present stable state. 

We should also note that the outside layers of our Sun 
provide an ideal regulative mechanism for the liberation 
of energy in its interior. If, for some reason, the rate of 
thermonuclear processes in the central regions of the Sun 
were to drop, there would follow an immediate contrac- 
tion of the whole solar body, and the resulting increase of 
temperature would rapidly bring the energy production 
back to its original value. If, on the other hand, the central 
energy production rose above the "red mark/' the Sun 
would expand and thereby bring down its central tem- 
perature. 

In this sense our Sun represents the most ingenious, 
and perhaps the only possible, type of "nuclear machine. 

THE SOLAR REACTION 

We have now learned that, at the temperatures obtain- 
ing in the solar interior, the thermonuclear reactions 
between protons and the nuclei of various light elements 
would proceed sufficiently rapidly to achieve the necessary 
energy production. From the theory of solar constitution 
as developed by Eddington we have also learned that the 
body of the Sun contains a considerable amount (about 
35 percent) of hydrogen, and it now remains to find the 
other participants of the reaction. To do this, one must 
calculate the rates of energy production for the multi- 
tude of possible nuclear reactions, and compare them with 
the actually observed radiation of the Sun. 

It is clear, for example, that the hydrogen-lithium re- 
action is too fast to be the main energy-producing reaction; 



112 The Birth and Death of the Sun 

for, as we have seen, at 20 million degrees the transforma- 
tion of lithium and hydrogen into helium would take only 
a few seconds, so that, if there were any appreciable amount 
of lithium in the central regions of the Sun, all its sub- 
atomic energy would be liberated in the form of a terrific 
explosion that would tear our Sun into a thousand pieces. 
We know, therefore, that our Sun cannot contain any 
appreciable amount of lithium in its interior, just as we 
know that a slowly burning barrel surely cannot contain 
any gunpowder.* 

On the other hand, the liberation of thermonuclear 
energy in the reaction between protons and the nuclei of 
oxygen, for example, is too slow to account for the Sun's 
radiation. 

"But it should not be so difficult after all to find the re- 
action which would just fit our old Sun/' thought Dr. Hans 
Bethe, returning home by train to Cornell from the Wash- 
ington Conference on Theoretical Physics of 1938, at which 
he first learned about the importance of nuclear reactions 
for the production of solar energy; "I must surely be able 
to figure it out before dinner!" And taking out a piece of 
paper, he began to cover it with rows of formulas and 
numerals, no doubt to the great surprise of his fellow- 
passengers. One nuclear reaction after another he dis- 
carded from the list of possible candidates for the solar life 
supply; and as the Sun, all unaware of the trouble it was 
causing, began to sink slowly under the horizon, the prob- 
lem was still unsolved. But Hans Bethe is not the man to 



* Spectroscopic evidence does, however, indicate the presence of a certain 
amount of lithium in the comparatively much cooler regions of the solar 
atmosphere. As this element cannot possibly be present in the hot interior 
regions, we must conclude that its abundance is limited to the outer layers 
(compare Chapter VII). 



The Alchemy of the Sun 113 

miss a good meal simply because of some difficulties with 
the Sun and, redoubling his efforts, he had the correct an- 
swer at the very moment when the passing dining-car 
steward announced the first call for dinner. Simultaneously 
with Bethe, the same thermonuclear process for the Sun was 
proposed in Germany by Dr. Carl von Weizsacker, who 
was also the first to recognize the importance of cyclic 
nuclear reactions for the problems of solar energy pro* 
duction. 

The thermonuclear process mainly responsible for the 
energy production of the Sun, it was discovered, is not 
limited to a single nuclear transformation, but consists of 
a whole sequence of linked transformations which together 
form, as we say, a reaction chain. One of the most interest- 
ing features of this sequence of reactions is that it is a closed 
circular chain, returning us to our starting-point after 
every six steps. From Figure 29, representing the scheme of 
this solar reaction chain, we see that the main participants 
of the sequence are the nuclei of carbon and of nitrogen, 
together with the thermal protons with which they collide. 

Starting, for instance, with ordinary carbon (C 12 ), we 
see that the result of a collision with a proton is the forma- 
tion of the lighter isotope of nitrogen (N 13 ), and the libera- 
tion of some subatomic energy in the form of a y-ray. This 
particular reaction is well known to nuclear physicists, and 
has also been obtained under laboratory conditions by the 
use of artificially accelerated high-energy protons. The 
nucleus of N 13 , being unstable, adjusts itself by emitting 
a positive electron, or positive ^-particle, and becoming 
the stable nucleus of the heavier carbon isotope (C 13 ), 
which is known to be present in small quantities in ordi- 
nary coal. Being struck by another thermal proton, this 



114 The Birth and Death of the Sun 

carbon isotope is transformed into ordinary nitrogen (N 14 ), 
with additional intense y-radiation. Now the nucleus of 
N 14 (from which we could just as easily have begun our 
description of the cycle) collides with still another (third) 




FIGURE 29 

The cyclic nuclear reaction chain responsible for the energy generation 

in the Sun. 

thermal proton and gives rise to an unstable oxygen isotope 
(O 15 ), which very rapidly goes over to the stable N 15 
through the emission of a positive electron. Finally, N 15 , 
receiving in its interior a fourth proton, splits into two 
unequal parts, one of which is the C 12 nucleus with which 



The Alchemy of the Sun 115 

we began and the other of which is a helium nucleus, or 
a-particle. 

Thus we see that the nuclei of carbon and nitrogen in 
our circular reaction chain are for ever being regenerated, 
and act only as catalysts, as chemists would say. The net 
result of the reaction chain is the formation of one helium 
nucleus from the four protons that have successively en- 
tered the cycle; and we may therefore describe the whole 
process as the transformation of hydrogen into helium as 
induced by high temperatures and aided by the catalytic 
action of carbon and nitrogen. 

It should be clear that, with a sufficient amount of 
hydrogen present, the rate of the cycle will depend essen- 
tially on the proportion of carbon (or nitrogen) in the 
matter of the Sun. Accepting the figure of one percent of 
carbon as given by astrophysical evidence, Bethe was able 
to show that the energy liberation of his reaction chain at 
the temperature of 20 million degrees exactly coincides 
with the actual amount of energy radiated by our Sun. 
Since all other possible reactions lead to results incon- 
sistent with the astrophysical evidence, it should be defi- 
nitely accepted that the carbon-nitrogen cycle represents 
the process mainly responsible for solar energy generation. 
It should also be noted here that, at the interior tempera- 
ture of the Sun, the complete cycle shown on Figure 29 
requires about 5 million years, so that at the end of this 
period each carbon (or nitrogen) nucleus that originally 
entered the reaction will emerge from it again as fresh and 
untouched as it was to start with. 

In view of the basic part played in this process by 
carbon, there is something to be said after all for the 
primitive view that the Sun's heat came from coal; only 



116 The Birth and Death of the Sun 

we know now that the "coal," instead of being a real fuel, 

plays rather the role of the legendary phoenix. 

THE EVOLUTION OF THE SUN 

What sort of changes may we expect in our Sun as a 
consequence of the slow consumption of its hydrogen 
"fuel"? At first sight this would seem to lead inevitably 
to a progressive decline of energy production, so that our 
Sun should be slowly dying, growing colder and dimmer 
every moment. The investigations of the author, however, 
have shown that this is not so, and that, as a matter of fact, 
our Sun must be steadily increasing in luminosity. 

For the rate of thermonuclear transformations depends 
not only on the amount of the reacting element (hydrogen 
in our case), but also on the temperature causing the re- 
action. If, let us suppose, the decrease of the total amount 
of "fuel" were somehow to cause an increase of the tem- 
perature, the last remaining pieces would burn much 
more brightly and give much more heat than when the 
"furnace" was loaded to the top. An arrangement of pre- 
cisely this sort is shown in Figure 30, where the opening 
of the air-blower of an ordinary coal furnace is so con- 
nected with the grate on which the coal rests that a decrease 
in the weight of coal makes a larger opening in the blow- 
pipe, creates more draught, and causes the fire to burn more 
strongly. 

An analogous mechanism exists in the solar furnace, with 
the difference that the regulating mechanism is provided 
by the opacity of the matter forming the body of the Sun. 
Helium, formed in the solar interior as a result of the 
hydrogen consumption, is less transparent than was the 



The Alchemy of the Sun 117 

original hydrogen,* and the energy liberated in the thermo- 
nuclear reaction undergoes more difficulties in its journey 
toward the surface. The more the hydrogen is transformed 



*95SfiE*^505^5%??^X/^^^ 




FIGURE 30 
A furnace that burns stronger when there is less coal. 

into helium, the more opaque becomes the blanket, and the 
resulting accumulation of energy in the central parts of 
the Sun leads to a corresponding rise in temperature and 
an increasing rate of energy production. 

* Under terrestrial conditions both helium and hydrogen gases are 
quite transparent; but, under the conditions of high density and high 
temperature obtaining in the solar interior, the thick layers of these gases 
effectively absorb radiation, helium being several times more opaque than 
hydrogen. 



118 The Birth and Death of the Sun 

The calculations carried out by the author on the basis 
of the accepted theory of the internal constitution of our 
Sun indicate that the solar radiation must be gradually 
increasing with time and will have increased a hundredfold 
by the time the amount of hydrogen is about to fall to zero. 
These calculations also indicate that, with its decreasing 
hydrogen content, the Sun's radius must first increase by 
several percent and then begin slowly to diminish. 

These results are represented graphically in Figure 31, 
where the luminosity and radius of the future states of our 
Sun are plotted on a logarithmic scale. We see from this 
that the new development of the problem of solar energy 
production leads us to conclusions quite opposite to those 
maintained by classical theory. Instead of being frozen to 
death by the decrease of solar activity, life on earth is rather 
doomed to burn out because of the intense heat which will 
be developed by our Sun toward the end of its normal 
evolution. The increase of solar radiation by a factor of a 
hundred will bring the temperature of the surface of our 
planet well above the boiling-point of water, and, although 
at this temperature the solid rocks forming the crust of the 
earth will probably not yet melt, the oceans and seas will 
boil. 

It is difficult to imagine any living being left on the 
surface of the earth under such conditions, though the 
progress of technique during the next few billions of years 
that separate us from these unpleasant circumstances may 
make it possible to dig safe, air-conditioned underground 
cellars for humanity or even to transport the whole popula- 
tion of the earth to some distant planet of our system where 
the heat will not be so intense. Moreover, we must re- 
member that the changes in solar radiation are going 



The Alchemy of the Sun 119 

forward extremely slowly. It can be calculated that the 
increasing solar activity raises the average surface tempera- 



looo- . 




FlGUBE 31 

The evolution of the Sun. After passing through a stage of extremely high 
luminosity, the Sun begins a rapid contraction accompanied by declining 

light emission. 

ture of our earth so slowly that during the whole geological 
period, while the Sun lost only about one percent of its hy- 
drogen content, the earth's temperature rose by barely a 



120 The Birth and Death of the Sun 

few degrees. Thus, it is not a sudden cosmic catastrophe we 
are expecting as a consequence of thermonuclear processes 
in the Sun (see Chapter IX), but a condition that can be 
foreseen in time and possibly avoided by the colonization 
of Neptune, for example. 

The slow rise in temperature will, however, most prob- 
ably be accompanied by such evolutionary changes in the 
biological world that terrestrial life will become more and 
more adapted to increasing heat. But since no highly devel- 
oped organism can live in boiling water, as conditions 
become more and more unfavourable for life the biological 
species will most probably begin to degenerate. It is, there- 
fore, quite probable that the higher species will have 
vanished long before the temperature becomes really in- 
tolerable; and the last radiation efforts of the aged Sun will 
be ' 'observed' ' only by the simplest and most stable of 
micro-organisms. 

WHAT THEN? 

As we have seen in a previous section, it is possible to 
construct a heating-machine that gives more heat the less 
fuel it has. But there is surely no mechanism that could 
give off heat without any fuel at all; and, as soon as the 
Sun completely consumes the last of its hydrogen, it will 
no longer have any subatomic energy sources left. Deprived 
of the resources that will have kept it going for ten billion 
years, our Sun will be forced to go back to an earlier energy- 
producing mechanism out of favour for all that long period 
of time. 

The Sun will begin to contract again. But, as we have 
seen, gravitational energy is practically as nothing com- 
pared to the wealth of energy supplied by nuclear reac- 



The Alchemy of the Sun 121 

tions, and the Sun's progressive collapse will have to pro- 
ceed at a pretty fast rate after the splendid life it has led 
on subatomic energy sources. From that point on our Sun 
will be shrinking rapidly in size; after a while its lumi- 
nosity will also begin to diminish. Rapidly retreating to its 
present luminosity and here rapidly means, of course, in 
a few million years!* the Sun's radiation will sink lower 
and lower as it approaches its ultimate stage of thermal 
death. These dying stages of solar evolution will be dis- 
cussed in more detail in one of the following chapters. 

* On the descending part of its evolutionary track the Sun will also 
have a much smaller radius than at its present stage, as can be readily seen 
from Figure 31. 



CHAPTER VI 



The Sun among the Stars 



HOW BRIGHT ARE THE STARS? 

IN THE long ago days of childhood many of us perhaps 
believed that the stars were only little silver lanterns 
attached to the blue firmament above our heads. This 
oldest and simplest of all hypotheses often came nostalgi- 
cally back to the author's mind when, during his researches 
on the sources of stellar radiation, he encountered so many 
seemingly unsurpassable difficulties. But unfortunately he 
could not doubt that this good old theory is incorrect, and 
that the stars are actually giant masses of extremely hot gas 
very similar to our Sun. The tremendously great distances 
separating us from these remote suns make them look 
small and faint, but astronomical observations permit us to 
estimate these interstellar distances and to compare the 
actual (or absolute) luminosities of different stars with the 
luminosity of our own Sun. 

Let us take, for example, the brilliant eye of the Great 
Dog. The Great Dog is, of course, a constellation to which 
this name was given by ancient astronomers in the course 
of their attempts to mark off different groups of bright 
stars by identifying them with animals or mythological 
persons. Though to the modern prosaic eye the combina- 
tion of stars forming this particular constellation (Figure 
325) hardly resembles any known breed of dog, or any animal 
whatsoever, one must have respect for the classics. The eye 

122 



The Sun among the Stars 123 

of this stellar dog is the brightest star seen in the sky and 
is well known under the name of Sirius. Astronomers tell 
us that it is about 500,000 times farther from us than is our 
Sun 52,000,000,000,000 miles away! and that, if it were 



/ 
/ 

X 

X 

s 



' CANIS MAJOR 



v ^-- 



FIGURE 32 
The constellation of the Great Dog. 

at the Sun's distance from us, Sirius would give us 40 times 
more light and heat than does the Sun. 

There are much more luminous stars, as for example 
Y Cygni,* which is 30,000 times brighter than our Sun, but 
not very conspicuous visually because of its exceedingly 
great distance. On the other hand, there is no lack of much 
fainter stars, as for example Krueger 60 Bf (not all stars 

* In the constellation of the Swan. 

f The B-component of the sixtieth star registered in Krueger's catalogue. 



124 The Birth and Death of the Sun 

have such elegant names as Sirius), with an absolute lumi- 
nosity (or total radiation) 1000 times smaller than the 
Sun's. If we compare our Sun's luminosity with that of all 
other known stars, we find that it occupies a more or less 
intermediate position among them and represents in this 
sense a typical average star. 

THE COLOUR OF STARS AND SPECTRAL CLASSES 

In the study of the physical properties of stars, it is very 
important to know, not only their absolute luminosities, 
but also the spectral composition of the emitted light, 
which permits us to determine the surface temperatures 
of these remote bodies. We have seen in Chapter I that 
the surface temperature of the Sun can easily be estimated 
from the amount of radiation emitted by each unit of its 
surface. In the case of most stars, however, we are unable 
to make direct measurements of their surface areas be- 
cause, owing to their very great distances, they look like 
dimensionless luminous points even through the most 
powerful telescopes.* 

Fortunately there are a number of other characteristic 
properties of the radiation emitted by hot bodies which 
enable us to estimate stellar temperatures even when we do 
not know their surface brightness. We know that all bodies 
when subjected to steadily increasing heat first emit a 
rather reddish radiation, which changes into a yellowish, 
then into a whitish, and finally into a bluish one as the 
temperature rises higher and higher. These colour changes 
of the emitted light are due to changes of relative intensity 
in the different parts of the emission spectrum in response 

* Only in a few cases of very near and large stars can such direct measure- 
ments of stellar diameters be carried out by means of an ingenious inter- 
ferometric method proposed by A. Michelson. 



The Sun among the Stars 



125 



TZSOO C C. 




FIGURE 33 
The continuous emission-spectrum changes with the temperature (T). 



126 The Birth and Death of the Sun 

to changes in the temperature. As may be seen from 
Figure 33, the maximum of light emission shifts gradu- 
ally from the red to the violet part of the spectrum as the 
temperature rises. Thus, by comparing the colour of the 
light emitted by different stars, we can form a very good 
idea of their relative surface temperatures and can say 
that reddish stars are comparatively cool, whereas bluish 
ones are very hot. 

A still more sensitive method for estimating stellar tem- 
peratures depends on the study of the relative intensities 
of the numerous dark thin lines (so-called Fraunhofer 
lines) that intersect the continuous emission spectra of 
different stars, including our Sun. These dark lines are 
due to the selective absorption of light by the stellar 
atmospheres. As the relative absorbing power of different 
atoms depends, to a very high degree, on the temperature, 
the appearance of this absorption -line pattern changes 
very markedly from star to star and permits us to estimate 
their respective surface temperatures simply by a glance 
at the character of the spectrum.* 

In astronomical practice, it is customary to divide the 
observed range of stellar temperatures into ten groups, 
which are known as the Harvard spectral classes and are 
reproduced in Plate VII. The ten classes of this system 
are called by different letters, which, evidently in order 
to mislead the layman, are not arranged in alphabetical 
sequence. There is, however, a simple mnemonic sentence, 
known to all English-speaking astronomers, which will 
help us not to get mixed up in this mess of absorption 

* The theory that gives the exact relation between the temperature of 
the absorbing gas and the character of the absorption spectrum was first 
worked out, on the basis of the quantum theory of atomic structure, by the 
Indian astrophysicist Meh-Nad-Saha. 




A. Expanding nebulous ring about Nova Aquilae 1918. Photographs 

taken on July 20, 1922, September 3, 1926, and August 14, 1931. (See 

p. 176.) (Mt. Wilson photograph.') 




B. Appearance and fading of the supernova in I.C. 4182. Photographs* 
taken on April 10, August 26, December 31, 1937, and June 8, 1938. 

( See p. 183. ) 
( Photographed by Dr. F. Zwicky . ) 



PLATE VIII. NOVA AND SUPERNOVA 



The Sun among the Stars 127 

lines. It reads: "Oh, Be A Fine Girl, Kiss Me Right 
Now . . ." As to whether S, the last letter, stands for 
"Sweetheart" or for "Smack/' there is a long-standing, still 
unconcluded dispute between the Harvard and the Yerkes , 
astronomers.* 

If the spectrum of a given star falls, according to its 
properties, somewhere in between two of the above classes, 
a decimal notation is used, e.g., As = two-tenths the dis- 
tance from A to F, or KS = five-tenths the distance from K 
to M (see Plate VII). In this Harvard classification our Sun 
belongs to the class G (6000 degrees), Sirius to the class 
A (i 1,200 degrees), and the faint star Krueger 60 B to the 
"cold" class M (3300 degrees). 

Knowing the star's surface temperature as given by its 
spectral class, we can now estimate also its geometrical 
dimensions by comparing the surface brightness that 
should correspond to this temperature with the star's 
absolute luminosity. We find in this way that the diameters 
of Sirius and Y Cygni are respectively 1.8 and 5.9 times 
larger than our Sun's, whereas the faint star Krueger 60 B 
has a diameter half as long. 

THE RUSSELL DIAGRAM 

When we compare these four stars (including the Sun) 
we may easily notice a very interesting regularity in the 
fact that stars of higher luminosity generally possess higher 
surface temperatures and larger radii. A more detailed 
study of this relationship has led to a remarkable classifica- 
tion of stars, which represents at the present time the most 
important basis for theories of stellar properties and 
evolution. 

* Plate VII does not show the spectra for classes O and S. 



128 The Birth and Death of the Sun 

The first weeks of March of the year 1913 turned out 
to be a very unfavourable period for astronomical observa- 
tion at Princeton. It was raining most of the time, and the 
overcast skies absolutely excluded any kind of observatory 
work. But this did not much disturb Professor H. N. 
Russell, director of the observatory, who was even glad 
that his enforced idleness was enabling him to bring some 
order out of his previous observations and to check certain 
ideas that had been preoccupying his mind for the last 
few months. 

On a large sheet of millimetre-paper, Russell began to 
construct a diagram to represent the relations between the 
absolute luminosities and the spectral classes of all the stars 
for which he had these data. It was rather tedious work, 
for many hundreds of stars had to be plotted on the dia- 
gram, but, as he approached the end of it, the pattern 
formed by the points began to take on a very interesting 
and peculiar shape (Figure 34). 

Clear across the diagram, from its lower right-hand to its 
upper left-hand corner, ran a narrow band that contained 
most of the plotted points and, in particular, the point 
representing our own Sun. All the stars belonging to this 
main sequence are evidently closely related and differ by 
only one factor, presumably their mass. These "normal 
stars" range continuously from the comparatively cool and 
faint "red dwarfs" up to the brilliantly blue and luminous 
"blue giants." 

But this marked regularity was broken by a number of 
striking exceptions, which, however, as the phrase goes, 
helped to prove the rule. There were two distinctly dif- 
ferent types of stars falling far from the main sequence. 
A number of points were scattered rather irregularly in the 



The Sun among the Stars 129 

upper right-hand corner of the diagram, and these corre- 
sponded to the stars possessing extremely high absolute 




FIGURE 34 

. the pattern formed by the points began to take on a very interesting 
and peculiar shape (the Russell diagram). 



luminosities in spite of their comparatively low surface 
temperatures. Since low surface temperature means a 
rather small intensity of light per surface unit, the high 



130 The Birth and Death of the Sun 

total luminosities can be understood only on the supposi- 
tion that they have extremely large geometrical dimen- 

eclipsing binary 



\ 




noneclipsing binary 

FIGURE 35 

Double stars. If the orbital plane of the two components is sufficiently 
inclined, the star system becomes an eclipsing variable. 

sions. These bodies have received the name of red giants, 
and include in their number such well-known stars as 
Capella and the cepheid variables (see p. 177). 



The Sun among the Stars 131 

The lower left-hand corner of the Russell diagram was 
occupied by the second class of abnormal stars, known as 
white dwarfs. The high surface temperatures together with 
the small total luminosities of these stellar bodies defi- 
nitely indicates their very small geometrical dimensions, 
which, as we shall see later, are only a few times larger 
than the dimensions of the earth. 

We shall leave the discussion of both these classes of 
"abnormal" stars to the following two chapters, and shall 
now concentrate our attention only on the normal stars of 
the main sequence. 

STELLAR MASSES 

Knowledge of the stellar masses represents one of the 
most important, but also one of the weakest points of 
observational astronomy. The only way to estimate the 
mass of a star is to observe the motion of some other body 
revolving around it; thus, for example, the period of the 
rotation of the earth around the Sun permits us to estimate 
the mass of the central body of our system. Although the 
possibility is not excluded that most of the other stars pos- 
sess planetary systems analogous to our own (see Chapter 
X), their great distances will not permit us to see them. 

Fortunately there are a considerable number of stars 
that "live in couples," forming the so-called binary, or 
double-star systems (Figure 35). In such cases the relative 
motions of the two components of the system may be 
directly observed, and their respective masses can then be 
estimated from the rotation periods.* But since an esti- 

* From the observational point of view the double-star systems could be 
divided into the visual binaries, seen separately through strong telescopes, 
and the spectroscopic binaries, the relative motions of which can be 
observed only through the Doppler effect on the lines in their spectra. 



132 The Birth and Death of the Sun 

mate of mass requires a complete knowledge of all the 
elements of motion, there are at present only several dozen 
stars for which the masses are known with sufficient cer- 
tainty. These few data are enough, however, to allow us 
to arrive at some very interesting conclusions concerning 
the relation between stellar masses and luminosities. 

It was indicated first by Sir Arthur Eddington that the 
luminosities of stars are a definite function of their mass, 
increasing very rapidly with the increase of mass. Taking, 
for example, the stars that have already been discussed, we 
find that the highly luminous Y Cygni (with a luminosity 
30,000 times that of the Sun) is 17 times heavier than the 
Sun; that Sirius (with 40 times the Sun's luminosity) is 
only 2.4 times heavier; and that the faint star Krueger 
60 B (with .001 times the Sun's luminosity) has but one- 
tenth the solar mass. 

As the total radiation of stars increases much more 
rapidly than their mass, the energy production per gramme 
of matter must be much greater in heavy stars than in 
light ones. From the above figures we see that the energy 
production per unit mass in Y Cygni, Sirius, and Krueger 
60 B is respectively 1800, 15, and 0.005, relative to that 
of the Sun. But if the energy generation in all stars comes 
from thermonuclear reactions, as it does in our Sun, the 
different rates of energy liberation must be due to dif- 
ferent physical conditions existing in their interiors, and 
chiefly to differences in their central temperatures. 

NUCLEAR REACTIONS IN STARS 

We have seen in Chapter I that Eddington's ingenious 
analysis of the equilibrium conditions of giant gas-spheres 
permits us to understand the different physical properties 



The Sun among the Stars 133 

of the Sun's matter at different depths from its surface, and 
to arrive at definite conclusions concerning the density and 
temperature in its internal energy-producing region. The 
same method, which proved so successful in the case of 
the Sun, can also be applied to the study of the internal 
conditions of other stars. In fact, knowing the mass, the 
radius (or the surface temperature), and the total radiation 
of a given star, we can, by way of rather complicated 
calculations, arrive at the values of its central temperature 
and density. The results of such analysis, as applied to the 
typical stars we have discussed above, are given in the fol- 
lowing table, which also includes their energy production 
per gramme of stellar material as estimated from the ob- 
served absolute luminosities and masses. 











ENERGY 


STAR 


MASS 
(relative to 
Sun) 


CENTRAL 
DENSITY 

(relative to 
water) 


CENTRAL 
TEMPERA- 
TURE 
(degrees C.) 


PRODUCTION 
PER UNIT 
MASS 
/ erg \ 


\gm. sec. ) 


Krucgcr 60 B 


O. I 


140 


14 X io 6 


O.OI 


Sun 


i .0 


75 


20 X io fi 


2 


Sirius 


2-4 


4i 


25 X io 6 


30 


Y Cygni 


17.0 


6-5 


32 X io 6 


3600 



The last two columns of this table make clear the tre- 
mendous effects of temperature on the observed energy 
production. An increase of the temperature in the stellar 
interior from 20 million to only 32 million degrees, is 
accompanied by an increase of the energy production per 



134 The Birth and Death of the Sun 

unit mass by a factor of 1800. But this is just what we 
should expect in the case of thermonuclear reactions, the 
rates of which, as we have already seen, usually increase 
proportionally to a very high power of the temperature. 
We have seen in the previous chapter that the energy 
production of our Sun is due entirely to the self- 
regenerative carbon-nitrogen reaction cycle, in which the 
hydrogen of the solar matter is steadily transformed into 
helium. It is natural to assume that the same reaction cycle 
is also responsible for the energy production in all other 
stars of the main sequence. The calculations do, in fact, 
show that the amounts of energy that would be set free by 
this thermonuclear reaction cycle, at the temperatures and 
densities obtaining inside the stars shown in the table, 
correspond very closely with their observed luminosities. 
Thus, the normal stars, like our own Sun, are living on the 
subatomic energy liberated in the process of the trans- 
formation of hydrogen into helium. 

A COMPETING REACTION IN THE LIGHTER STARS 
It should be pointed out, however, that, although the 
carbon-nitrogen cycle is of primary significance for most 
of the stars in the main sequence, it has a rather important 
competitor in the case of the comparatively light stellar 
bodies, such as Krueger 60 B. The central temperatures 
of these "cool" stars are relatively low, and the slow 
thermal protons experience difficulty in penetrating such 
heavy nuclei as those of carbon or nitrogen. Under these 
conditions it is necessary to take into account the possi- 
bility of a quite different nuclear reaction, one that takes 
place between protons themselves and does not need the 
catalysing action of any heavier element. This different 



The Sun among the Stars 135 

reaction, first studied by the young American physicist 
Charles Critchfield, consists of the formation of a heavy- 
hydrogen nucleus, or a denier on (see Chapters II and III), 
in the collision between two thermal protons. It can be 
written in the form: 

iH l -f iH 1 hD 2 + (positive electron) 

and is usually followed by the transformation of the new- 
born deuterium nuclei into the heavier nuclei of helium: 

l iy+ iH 1 > 2 He 3 + radiation, etc.* 

Exact calculations show that at temperatures as low as 
15 million degrees this reaction is just as important as the 
carbon-nitrogen cycle, and that, at still lower tempera- 
tures, it becomes of primary importance. Thus, for very 
light and faint stars of the main sequence, possessing 
central temperatures at or below 15 million degrees, the 
mechanism of energy production is slightly different than 
it is for their more brilliant relatives, such as our Sun 
or Sirius. 

STELLAR EVOLUTION 

It was mentioned in the previous chapter that the au- 
thor's study of the future evolution of our Sun leads to 
the surprising conclusion that its temperature and total 
radiation are bound to increase while its hydrogen content 
diminishes. In the frame of the Russell diagram this means 
that the point representing the Sun is slowly moving up- 
ward and leftward from its present position toward that 
of the hotter and more luminous stars. 

The results of such calculations are shown in Figure 36, 

* "Etc." is here an indication of the fact that this reaction is followed 
by a series of numerous and complicated reactions eventuating in normal 
helium 2He 4 . 



136 The Birth and Death of the Sun 



100 



10 



1 < 



JL 4 

10 




\\\ 




\\ 



\\v 

>^f\ K^l/6Q6f" 

present sfofe \ % \ ^Q 

y 
Q siafe toward . \ 

end of evoli/Koa ^ v % 



FIGURE 36 

Future changes in the luminosity and spectral class of three stars, accord- 
ing to the theory of stellar evolution. 



The Sun among the Stars 137 

which represents the evolutionary tracks of our Sun and 
two other stars (Sirius and Krueger 60 B) of the main 
sequence. We see that the track of stellar evolution runs 
more or less up along the main sequence of stars, and 
begins to bend toward the lower luminosities only after 
the original radiation has increased by a factor of 100. 
Thus, after 10 billions of years, our Sun will become as 
brilliant as Sirius is now, while Sirius itself will be ap- 
proaching a luminosity comparable to the present state 
of U Ophiuchi. 

This does not mean, however, that the stellar sky of, 
let us say, A.D. 10,000,001,940 will necessarily be more 
luminous than the sky of A.D. 1940. For, whereas some of 
the stars will gain considerably in luminosity, many others, 
which are already of age now, will have exhausted their 
remaining hydrogen resources and will be declining into 
obscurity. In this sense the migration of stars on the Russell 
diagram is rather analogous to the age changes taking place 
in a human society, where the places of the old and dying 
are constantly being taken by the growing younger genera- 
tions. But just as, in the case of human society, secular 
changes in the population can be produced by such factors 
as a falling birth rate, so stellar society can be strongly 
affected by factors governing the formation of new stars. 
If, as is very probable (see Chapter XII), the "stellar birth 
rate" is falling with the increasing age of the world, we 
must face the possibility that the general picture of the 
sky will change as the universe grows older. 

It needs to be said here that stars with different masses 
will run through their evolutionary lives at different speeds. 
Heavier, and therefore more luminous, stars will use up 
their hydrogen supply much faster than the lighter ones. 



138 The Birth and Death of the Sun 

Thus, if two stars of different mass have started life simul- 
taneously with equal proportions of hydrogen, the heavier 
one will be dying when the lighter one will still be in 
the ascending stage of its evolution. Sirius, for example, 
burning up its fuel 15 times faster than the Sun, will begin 
to end its life 15 times sooner; and the most brilliant stars 
of the main sequence (the blue giants) can hardly expect to 
live more than several millions of years. 

STELLAR EVOLUTION AND THE MASS-LUMINOSITY 
RELATION 

In this connexion a very important objection could be 
put forward by an attentive reader who has followed care- 
fully the exposition of the present chapter. 

"It was indicated above/' he might say, "that there is a 
definite empirical relation between the luminosities of 
different stars and their respective masses. But if, during 
the course of evolution, each star changes its luminosity 
by as much as a factor of 100, we should be able to find 
stars of equal mass but different luminosities, or stars 
greatly differing in mass but having the same luminosity. 
Does not the empirical mass-luminosity relation, as estab- 
lished by Eddington, contradict this view of stellar evo- 
lution?" 

In order to escape from this seeming dilemma we shall 
first have to pay more attention to the speed at which the 
evolving star passes through the different stages of its evo- 
lution; for if it should turn out that most stars are in the 
same evolutionary stage, our problem will be solved. We 
have already seen that the energy-producing plant in the 
stellar interior has the peculiar property of burning faster 
when less fuel is left. Thus, whereas in the lower part of 



The Sun among the Stars 139 

the evolutionary track the star uses its hydrogen fuel very 
sparingly, the consumption becomes much higher toward 
the later stages. The high luminosities characteristic of 
these later stages naturally require much higher rates of 
subatomic energy liberation and a correspondingly higher 
consumption of hydrogen. It follows that the star spends 
a considerably longer time in the lower stage of evolution, 
and runs through the later stages with comparative ra- 
pidity. 

The calculations show, for example, that our Sun will 
spend about 90 percent of its life in the first half of its 
evolutionary track (luminosity increase by a factor of 10) 
and only 10 percent in the remaining half (luminosity 
increase from 10 to 100). Consequently, there is a much 
greater chance of finding an arbitrarily chosen star in the 
beginning of its evolutionary track than at the end of it. 
In the same way, in an odd society where childhood took 
up 90 percent of the total life of every individual, we 
should expect to find an almost exclusively child popula- 
tion. Thus, only a few of the stars that were used for the 
construction of the mass-luminosity curve would show 
marked deviations from the smooth curve, and, as a matter 
of fact, several such deviations (in the direction of too large 
luminosities) are actually observed. 

The second reason we find most of the investigated 
stars in the same stage of their evolution lies in the fact 
that the stellar universe is still very young. It will take 
about 10 billion years more for our Sun completely to 
burn up its fuel and come to the end of its hydrogen evo- 
lution. On the other hand, there are definite indications 
(see Chapters XI and XII) that the whole stellar universe 
was formed not more than 2 billion years ago. It is clear 



140 The Birth and Death of the Sun 

that during this "short" period the stars comparable in 
their intensities to our Sun could not have evolved to any 
considerable degree. Only much brighter, and conse- 
quently much faster-living, stars from the upper part of 
the main sequence could have experienced such consider- 
able changes since the epoch of their formation, and it is 
precisely in this region that the striking deviations from 
the mass-luminosity relation are actually found. 

THE yOUTH AND OLD AGE OF STARS 

We have thus far considered only that part of stellar 
evolution which is determined by hydrogen consumption 
in the nuclear reactions produced by high temperatures. 
But what of the state of the star before its central tempera- 
ture reached the value of 20 million degrees necessary for 
the beginning of the carbon-nitrogen reaction cycle? And 
what happens to a star after all its original hydrogen 
content has been used up and no more subatomic energy 
is available? Can one find in the sky samples of stars that 
are still in their babyhood or, on the other hand, already 
in their very old age? 

These questions remind us of the existence of the two 
"abnormal" classes of stars which definitely did not fit into 
the normal scheme of hydrogen evolution the red giants 
and the white dwarfs. Let us, then, concentrate our atten- 
tion on these possible representatives of infancy and senility. 



CHAPTER VII 



Red Giants and the Youth of the Sun 



SOME TYPICAL RED GIANTS 

WE HAVE seen that the so-called red giants are stars 
of extremely large dimensions and very low surface 
temperatures. A typical representative of this peculiar class 
of stars can be found, for example, in Capella (or a Aurigae), 
a star that is probably familiar to those readers who are 
interested in the night sky. Telescopic observations reveal 
that Capella actually represents a double-star system, whose 
two components revolve rather closely around each other. 
The fainter component of the system (known as Capella 
B) is a normal star of the main sequence. But the brighter 
and larger star (Capella A) has rather unusual properties 
as compared with the multitude of other stars. The diam- 
eter of this giant is 10 times larger than the solar diameter, 
and its radiation surpasses that of our Sun by a factor of 
100. For a normal star of the main sequence that possessed 
such high luminosity we should also expect a very high 
surface temperature; but observations show that Capella A 
is in about the same spectral class as our Sun, that is, it is 
much redder than it should be. 

In Figure 37, representing the upper right-hand corner 
of the Russell diagram, we see that this star falls well away 
from the main sequence and may be considered a typical 
red giant.* The estimates of its mass (from the relative 

* In the case of Capella A the radiation is not yet quite red but rather 

141 



142 The Birth and Death of the Sun 

motion of the two stars forming the system) give a value 
of only 4 times the mass of the Sun, so that the average 
density of Capella A must be 250 times less than the density 
of solar matter, or 0.005 times that of water. These low 



-, * ^v 

ncsity ^ 

I 



4f Si " &t S* 



VsSSXSSS^ ' I 

^ ^ , e***y* 

>, ~< c -w- 

-\-yn>r?' ?* o. 



/ <- 

Hot \*~ S-nrCvs Coo ) 



FlGUEE 37 

TTie upper part of the Russell diagram, showing the position of the red 
giants and the region of pulsating stars. 

densities are characteristic of the reel giants and represent 
much more dilute states of matter than the normal stars 
of the main sequence. 

A still more typical example of the red giants is another 
star belonging to the same constellation as Capella itself, 
Aurigae K, which has a mass of about 15 Sun masses, but 
a diameter surpassing that of the Sun by a factor of 160, 
and therefore an average density only 0.000,005 that of 
water.* Although 56 times more luminous than Capella A, 

yellowish. It is, however, much redder than a normal star of such high 
luminosity would be. 

* In the central regions of this star, the density reaches the value 
0.000,14. 



Red Giants and the Youth of the Sun 143 

this star belongs to the cold spectral class M and looks 
quite red as compared with other stars. 

But the most striking cases of cold giant stars was re- 
vealed by recent observations at the Yerkes Observatory of 




FIGURE 38 
The relative sizes of Aurigae I and the solar system. 

e Aurigae (no, the red giants have no preference for the 
constellation Auriga; nor has the author any preference for 
this particular constellation in selecting his examples; it is 
only pure coincidence). These observations indicated 
that the star is actually a binary system, and that one of the 



144 The Birth and Death of the Sun 

components (E Aurigae I) is so large and so cool that the 
radiation it emits is mostly infrared (hence the I in its 
notation). There is no provision in the old Harvard spec- 
tral classification for stars of such exceedingly low tempera- 
tures (1700 degrees), and we might simply call it "Class I." 

Although the mass of this star is only 25 times larger 
than the solar mass, its diameter surpasses that of the Sun 
by a factor of 2000. This star is so large that almost our 
entire planetary system, including the orbits of Jupiter and 
Saturn, could be placed inside it, with only Neptune and 
Uranus sticking out (Figure 38). The mean density corre- 
sponding to such dimensions is only 0.000,000,003 relative 
to water 1 

But it should be noted that we speak only of mean 
densities. In any gaseous body, the density increases as we 
approach the central regions, and it has been shown, par- 
ticularly in the case of the red giants, that this density 
increase is especially large. 

INSIDE THE RED GIANTS 

In order to ascertain the physical conditions obtaining 
in the interior of the red giants, we can apply the same 
method we used in the case of the Sun and the other stars 
of the main sequence. Starting from directly observable 
conditions on the surface, we can proceed step by step into 
the deeper regions of the star, and finally arrive at values 
for temperature, density, and pressure near the stellar 
centre. 

This analysis will demonstrate that, although the central 
temperatures of red giants are much higher than their 
surface temperatures, they are still considerably lower than 



Red Giants and the youth of the Sun 145 

the central temperatures of our Sun and the other normal 
stars. In the case of Capella A, for example, we get a value 
of 5 million degrees (compared with the solar temperature 
of 20 millions), and for Aurigae K only 1.2 millions. The 
central temperature of the giant rarefied star e Aurigae I is 
probably considerably lower than one million degrees. 

Of course, from a terrestrial point of view, the interior 
of these stars is still very hot, but only very few thermonu- 
clear reactions could go on at such temperatures. In par- 
ticular, Bethe's carbon-nitrogen cycle, which supplies the 
energy for our Sun and other normal stars, would be 
practically stopped by such a "nuclear frost" and would 
lead to hardly any energy liberation at all. The same per- 
tains to Critchfield's deuteron-formation process. 

In order to find suitable subatomic energy sources for 
these comparatively cool stars, we must look for nuclear 
transformation processes which would go on at much lower 
temperatures than do the two above. The study of this 
problem was undertaken in 1939 by the author of this 
book and his colleague Dr. Edward Teller, with results 
that seem to give us a satisfactory explanation of the riddle 
of energy-production in red giants. 

THE REACTIONS OF LIGHT ELEMENTS 

As we have seen, the easiest reactions to start are those 
between protons and the nuclei of the lightest elements of 
the periodic system.* The following six reactions are a 
complete list of all the possible nuclear transformations 
that involve the elements lighter than carbon and nitrogen: 

* This does not include the proton-proton reaction leading to deuteron 
formation, which is comparatively slow owing to the small probability of 
electron emission. 



146 The Birth and Death of the Sun 



jD 2 + iH 1 -- 2 He s + radiation 
3 Li 6 + iH 1 -- 2 He 4 + 2 He 3 
s Li 7 + 




U + radiation 
He 4 + 2 He* + 2 He 4 

The available data of nuclear physics permit us to esti- 
mate the rate of subatomic energy liberation for each of 
the above reactions with the result that they fall into three 
distinctly separate types. 

The first type includes only the extremely rapid reac- 
tions between deuterons and protons (i). Owing to the 
small electric charges of both particles involved, this 
reaction leads to a very high energy liberation even at 
such low temperatures as a million degrees. 

The second type contains the slower reactions of both 
lithium isotopes (2, 3), the reaction of beryllium (4), and 
the reaction of the heavier isotope of boron (6). The 
temperatures necessary for these reactions lie in the range 
between 3 and 7 million degrees. 

Finally, the third type consists of the still slower reaction 
of the lighter isotope of boron (5), which requires a tem- 
perature only slightly lower than that to be found in the 
centres of the main-sequence stars. The reason for so com- 
paratively low a rate in this particular case is that the 
transformation involves the process of a y-ray emission, 
which causes a considerable decrease of its probability. In 
fact, it is well known that the emission of y-rays is as a rule 
many millions of times less probable than the ejection of a 
nuclear particle, so that in order to obtain an appreciable 
rate for that kind of reaction it is necessary to intensify 
the bombardment by raising the temperature of the gas.* 

* The reader may have noticed that the first reaction on our list (D-H) 



Red Giants and the Youth of the Sun 147 

THE ABSENCE OF THE LIGHTEST ELEMENTS IN THE 

SUN 

Since the liberation of energy through the three types 
of reactions discussed above begins at a comparatively low 
temperature, we should expect that, at the central solar 
temperature of 20 million degrees, the subatomic energy 
would flow out at quite fantastic rates. Indeed, if, with the 
present temperature, there were any appreciable amounts 
of the lightest elements in the solar interior, the liberated 
energy would cause a terrific explosion of the Sun. We 
must conclude, therefore, that these "dangerous" elements 
are absent from the solar interior, and that, if there were 
any in the earlier stages of evolution, the Sun must have 
exhausted them completely in that distant period of its his- 
tory when its central temperature was much lower than 
it is now. 

The analysis of the solar spectrum does seem to indicate, 
however, that a certain small amount of lithium, beryllium, 
and possibly boron is still present in the solar atmosphere. 
The presence of these elements in the earth also suggests 
that they must have been present, at least in the outer 
layers of the Sun, at the time when our globe was sepa- 
rated from the central body. But even on earth these 
lightest elements are relatively scarce (as may be seen from 
Figure 39), and this supports the conclusion that they dis- 
appeared early in the history of the world. 

Incidentally, these differences in chemical composition 
between the interior and the outer envelope of our Sun 

also involves *y-ray emission and yet is the fastest of them all. The point 
is, however, that in this case the high penetrability of the nuclear barrier, 
due to the small electric charges, overcompensates for the low probabilities 
of 7-ray emission. If the D-H reaction could go on without radiation, it 
would be millions of times more probable than it actually is. 



148 The Birth and Death of the Sun 

and other stars are of great importance for the problem of 
the origin of chemical elements and for questions concern- 
ing the early stages of the development of the universe. 



I 

1 

I0 1 
10* 

id 3 

I** 

16* 
io fc 

JO 7 

-i 

10 



\ 



* t 

\ I 

\ I 

\ I 

\ / 

\ 

\ I 

\ ' 

\ 



1 



Li s ' 



Q ^ 



S 



FIGURE 39 

The relative abundance of the lightest elements in the earth's crust, 

showing the extremely small amounts of lithium, beryllium, and boron. 

Approximately the same curve has been found to hold for the meteorites 

and for stellar atmospheres. 

THE REACTIONS OF LIGHT ELEMENTS IN RED 
GIANTS 

We shall now return to our original problem concerning 
the energy sources of red giants. From the discussion above 
we have seen that the thermonuclear reactions between 
hydrogen and the other lightest elements occur between 
temperatures of a million and 20 million degrees, which 
limits coincide with the estimated range of the central tern- 



Red Giants and the Youth of the Sun 149 

peratures of various red-giant stars. It is natural, therefore, 
to conclude that these stars are still "burning" their sup- 
plies of those light elements that were exhausted by our 
Sun a long time ago. The calculations show, in fact, that 
the presence of only a small percentage of these elements 
in the central regions of red giants would suffice to supply 
the energy of their observed radiation. 

Since, however, the central temperatures in different 
stars of this class exhibit a great range, we must choose 
different reactions to account for particular cases. For 
example, the coolest red giants, such as E Aurigae I and 
its extreme neighbours in the Russell diagram, must live 
exclusively on the deuterium-hydrogen reaction, and their 
lithium, beryllium, and boron supplies must be as yet 
untouched. Such stars as Capella A and Aurigae, on the 
other hand, have evidently already exhausted their deu- 
terium supply, and are using up the elements of the 
second reaction type mentioned above. Finally, the red 
giants that fall close to the main sequence in the frame of 
the Russell diagram must be using for their energy pro- 
duction the boron isotope sB 10 , and are getting ready to 
join the family of normal stars as soon as their light nuclear 
fuel comes to an end. 

Figure 40 gives a schematic presentation of the different 
parts of the Russell diagram in terms of the specific nuclear 
reactions that are of predominant importance in them. We 
see that, whereas the main sequence, with the exception of 
its lower part,* corresponds to one definite mode of energy 
production (the carbon-nitrogen cycle), the region of red 
giants includes a variety of stars that use different fuels in 
their furnaces. The parts corresponding to different light- 

* See p. 135 above. 



150 The Birth and Death of the Sun 

element reactions may often overlap, so that we may find 
stars in which two, or even three, elements are equally 
important for energy production. 



lA \ 



GRAVITATIONAL 

CONTRACTION 




Hot 



Cool 



-t- 



-f- 



-t- 



-*- 



-f" 



fc A F G- K M RfXS 

FIGURE 40 

The regions of different nuclear reactions in the Russell diagram and the 
evolutionary tracks of the Sun and Capella. 

THE EVOLUTION OF RED GIANTS 

The reactions of the light elements that supply energy 
for the red giants differ from the solar reaction in one very 
essential regard. They do not possess the self-regenerative 



Red Giants and the Youth of the Sun 151 

" phoenix-like" property of the carbon-nitrogen cycle, and 
the nuclei entering these reactions never return to their 
original form. Thus, whereas the carbon and nitrogen 
nuclei act only as catalysers for the transformation of 
hydrogen into helium, the nuclei of deuterium, lithium, 
beryllium, and boron disappear rapidly in the process of 
energy production. Consequently, the time spent by a star 
in each stage of its evolution as a red giant must be con- 
siderably shorter than the period it will spend in the main 
sequence,* and all the successive stages of this "stellar 
infancy" represent only a small fraction of the total evolu- 
tionary life of each star. 

We can now form a general picture of the early phases 
of stellar evolution, which will also describe, as one par- 
ticular case, the past development of our Sun. According 
to this picture, each star begins its life as a giant globe of 
rather rarefied and cold gas containing a mixture of all 
possible chemical elements. The gravitational attraction 
among the different parts of the sphere causes its progres- 
sive contraction and hence a gradual rise in the tempera- 
ture at its centre. As soon as the central temperature 
approaches the value of about one million degrees, the first 
nuclear reaction the reaction between deuterium and 
hydrogen begins in the stellar interior. The subatomic 
energy produced by this reaction stops any further con- 
traction of the body of the star, and it remains in a more 
or less stable state as long as there is enough deuterium to 
keep the reaction going. 

But as soon as the amount of deuterium becomes too 
small to provide sufficient energy for radiation, the con- 

* Because the main -sequence state lasts as long as there is any hydrogen 
left, and hydrogen constitutes a very large part (35 percent) of stellar 
material. 



152 The Birth and Death of the Sun 

traction process sets in again. After this, the star goes 
on contracting until the central temperature rises high 
enough to start the thermonuclear reaction between hy- 
drogen and lithium; this halts the contracting process a 
second time. 

Thus, shifting from one reaction to the next, and gradu- 
ally increasing its central temperature and total luminosity 
all the while, the red giant finally approaches the region of 
the main sequence, where the catalysing action of carbon 
and nitrogen nuclei sets in. As the original proportion of 
light elements in the stellar body is probably no more than 
a fraction of one percent, their complete ''burning*' during 
the red-giant stage will result in only a small decrease of 
the total hydrogen content. But, as soon as the star enters 
into the main sequence, and its central temperature be- 
comes sufficiently high to permit the carbon-nitrogen cycle 
to operate, the consumption of hydrogen will go on with- 
out interruption until it is used up to the last atom. And 
at this point begins the final contraction leading to the 
death of the star. 

The evolutionary tracks corresponding to these three 
main successive stages of stellar development have been 
calculated by the author for two stars and are shown in 
Figure 40. The upper track is that of Capella A, which at 
present is still in the red-giant state. We see that this star 
is bound to enter into the main sequence when its lumi- 
nosity has become several times higher than it is at present, 
and that it will later become one of the most luminous 
stars in the sky. The lower track belongs to our Sun, and 
shows that in its past history it must have been a giant red 
ball considerably less luminous than it is now. Stars still 
smaller than the Sun in their early stages possess such low 



Red Giants and the Youth of the Sun 153 

luminosities and surface temperatures that they are prac- 
tically invisible. 

PULSATING STARS 

Early observations discovered the existence of stars whose 
luminosity did not remain constant, but fluctuated over 
regular periods of time. In many cases this variability was 
explained by the fact that the stars concerned were actually 
binary systems with the two components moving approxi- 
mately in a plane parallel to our direction of vision. It is 
evident that in such cases one of the rotating components 
will from time to time come in front of the other, and that 
the repeated partial eclipse of the hind-star will cause a 
periodic decrease of light intensity. 

In the upper half of Figure 41 we give a schematic repre- 
sentation of such an eclipsing variable, and also a curve 
representing the changes of the observed intensity which 
result from the overlapping of the two disks. The time- 
luminosity curve has a very characteristic shape, and shows 
a constant illumination periodically interrupted by more 
or less sharp minima. 

But a careful survey of the skies has also shown the 
existence of other variable stars, which cannot possibly be 
explained by such a simple hypothesis. These stars, gen- 
erally known as cepheid variables (after 8 Cephei, the first 
star of this type discovered), exhibit very smooth and 
regular changes of luminosity, which can be very closely 
represented by an ordinary sinusoid curve (the lower half 
of Figure 41). The harmonic pendulum-like character of 
these observed luminosity oscillations suggests that they 
are due to regular pulsations of the whole stellar body 
between certain maximum and minimum values of the 



154 The Birth and Death of the Sun 

diameter. Observations of the Doppler effect* in the spec- 
tral lines of cepheid variables actually prove that these 





v5li, 



\J 



"U 



rn* 



i . 
Lunrunosrrv 







t, 



FIGURE 41 
Eclipsing and pulsating variables with their corresponding luminosity 

curves. 

* The so-called Doppler effect, previously referred to, consists of a change 
in the colour of the light emitted by a source moving relative to the 
observer. All the lines in the spectrum of a receding light source will be 
shifted toward the red end, whereas a source approaching the observer 
will show a shift toward violet. Thus, by comparing the spectrum of a 
stellar surface with the spectra of terrestrial light sources, we can detect 
periodic shifts of the spectral lines of the former if this surface is peri- 
odically moving to and fro. 



Red Giants and the Youth of the Sun 155 

stars are, so to speak, "breathing," that is, their surface 
layers are periodically rising and falling back again. 

It is very important to note that, whereas the compo- 
nents of the eclipsing-variable systems are most often nor- 
mal stars of the main sequence, the phenomenon of pulsa- 
tion has been observed exclusively among the red giants. 
The pulsating stars form a sharply defined group, being 
situated on the Russell diagram within a rather narrow 
band (see Figure 37) at the upper limit of the region gen- 
erally occupied by these dilute, cool stars. 

THE THEORY OF STELLAR PULSATION 

The mathematical theory of pulsating gas-spheres was 
first developed by Eddington, and it demonstrates a very 
interesting interdependence between the pulsation periods 
of the cepheid variables on the one hand and their geo- 
metrical dimensions and masses on the other. The laws 
governing stellar pulsations are quite analogous to those 
describing the harmonic vibrations of ordinary piano or 
violin strings. In the latter case the pitch (oscillation 
frequency) depends essentially upon the length and also 
upon the mass (thickness) of the vibrating string. A long 
string will give a lower note than a short one, and, with 
two strings of equal length, the lower note will come from 
the heavier (thicker) one. The pulsation period of gaseous 
stars increases with their dimensions and mass in exactly 
the same way. 

It follows from Eddington's theory that the period is 
exactly inversely proportional to the square root of the 
average density, so that more dilute stars must pulsate more 
slowly than dense ones. Since, in the family of red giants, 
we have observed that the average densities drop with the 



156 The Birth and Death of the Sun 

increasing masses and luminosities, we must conclude that 
the heavier and brighter stars must possess longer pulsa- 
tion periods. This relation, which was first established by 
the Harvard astronomer H. Shapley on the basis of observa- 
tional data, plays a very important role in stellar astronomy. 
In Figure 37 are shown the pulsation periods correspond- 
ing to various parts of the red giant region in the Russell 
diagram; they vary from values as short as several hours 
up to periods of several years. 

THREE GROUPS OF PULSATING STARS 

A detailed study of a large number of pulsating variables 
revealed that not all values for the periods are equally 
abundant, and that these stars can be subdivided by the 
length of their periods into three major groups. The first 
group contains the so-called short-period, or clustery vari- 
ables with periods lying between six hours and one day. 
Very few stars are known to possess periods of between 
one day and one week, but there are a good many that 
require from one to three weeks for one complete pulsa- 
tion. This second class includes the famous 8 Cephei itself, 
and the stars belonging to it are generally known as normal 
cepheids. Lastly, we find a large number of pulsating stars 
with periods crowded around the value of one year. These 
long-period variables are mira variables, so called after 
Mira Ceti (the "Wonderful" from the constellation of the 
Whale), which is the type representative of the class. 

In Figure 37 the position on the Russell diagram of 
these three groups of stars is indicated by heavier shading. 
The explanation of this grouping of pulsating stars into 
three separate regions of the diagram is based on the theory 



Red Giants and the Youth of the Sun 157 

of energy liberation in the red giants discussed earlier in 
this chapter. We saw then that there are three distinct 
types of nuclear reaction responsible for the energy supply 
of these stars, and it is only natural to suppose that the 
three groups of pulsating stars correspond to these three 
different modes of energy generation. 

If we compare the regions occupied by the three pulsa- 
tion groups, as shown in Figure 37, with Figure 40, which 
represents the position of stars living on different nuclear 
reactions, we see at once that this suggested relationship 
must be quite correct. We find, in fact, that the long- 
period variables are the stars that receive their energy from 
the deuteron-proton reaction; that the cepheid variables 
are "burning" lithium, beryllium, and heavy boron; and 
that the short-period variables live exclusively on the 
lighter isotope of boron. 

Thus, the observed pulsations of giant stellar bodies can 
be brought into a direct and simple connexion with the 
sequence of chemical elements in the periodic system. 

THE CAUSE OF PULSATION 

Why do stars pulsate, and, in particular, why is this 
property of pulsation found only in a certain narrow region 
of the Russell diagram? There are, of course, many causes 
which could bring the gaseous star out of a state of equi- 
librium. The close passage of two stars near each other, 
or a casual minute explosion in the interior, could easily 
do it. But in that case we should expect the pulsation to be 
an occasional phenomenon that would, moreover, not be 
strictly limited to one particular class of stars in the dia- 
gram. The narrowness of the region containing the pul- 



158 The Birth and Death of the Sun 

sating variables indicates that we are dealing here with 
certain peculiar conditions that could be attained only 
once during the whole evolutionary life of a star. 

The exact character of the conditions that could lead 
to the instability of these giant stellar bodies is not quite 
clear as yet, but the hypothesis recently advanced by the 
author strongly suggests that the pulsations come as the 
result of a conflict between the nuclear and the gravita- 
tional energy-producing forces in the stellar interior. It can, 
as a matter of fact, be shown that the region of the Russell 
diagram occupied by pulsating stars is characterized by the 
circumstance that the amount of energy liberated by 
thermonuclear reactions and the amount liberated by the 
gravitational contraction of the stellar body are of about 
the same order of magnitude. We might say that in these 
cases the stars "do not know which kind of energy pro- 
duction it is better to choose/' and are "oscillating be- 
tween the two possibilities/' But this attractive hypothesis 
needs additional confirmation, and cannot be considered 
as definitive before some rather long and tedious calcula- 
tions have been performed. 



CHAPTER VIM 



White Dwarfs and the Dying Sun 



THE END OF STELLAR EVOLUTION 

IN PREVIOUS chapters we have seen that, in the very 
distant future, when all the available sources of sub- 
atomic energy will finally have been exhausted, our Sun 
will begin its ultimate contraction. The gravitational en- 
ergy liberated in this process will still keep the Sun hot 
and luminous for a while, but, as the process of contraction 
approaches its final term, the intensity of solar radiation 
will gradually begin to decline. And, after another long 
period, our Sun will turn into a giant lump of lifeless 
matter covered with eternal ice and surrounded by a sys- 
tem of frozen but still faithful planets. 

When we speak of this "dead Sun" we are tempted, by 
analogy, to imagine it as a giant spherical stone, similar to 
our own planet but correspondingly larger in dimensions. 
We tend to imagine also that it will consist of various 
granites and basalts known to geology and that its interior 
will remain in a state of hot molten lava for a considerable 
time after the solid crust has been formed. But precisely 
because the Sun is so much larger than the earth, the anal- 
ogy turns out to be quite wrong; for our present knowledge 
of the properties of matter indicates that the interior 
of the dead Sun will be in a rather different physical state 
from the interior of our earth or of any other of the planets. 

159 



160 The Birth and Death of the Sun 

THE COLLAPSE OF MATTER 

In order to understand the physical causes that will pre- 
vent the formation of such a "granite Sun/' let us imagine 
a mad architect who builds a house without limiting him- 
self to a definite number of stories. As the house grows, 
he sends up more and more building materials, and every 
day more new floors are piled on top of the old ones. It will 
be clear, even to persons not familiar with the principles 
of civil engineering, that such a method will sooner or later 
lead to catastrophe. The lower walls of the house will give 
way under the increasing weight of the upper stories, and 
the whole house will collapse, turning into a formless heap 
of stones, considerably lower than the first stages of the 
construction. If our architect does not take into account 
the existence of a certain resistance limit of the building 
materials, the house will collapse as soon as the pressure at 
its base surpasses this limiting value. 

Very similar difficulties arise in the case of too massive 
stellar bodies built from solid matter. The weight of the 
external layers of such bodies creates tremendous pressures 
in their central regions, and we must consider the possi- 
bility that the resistance of matter can be broken down if 
this pressure surpasses certain values. This puts limits to 
the possible geometrical dimensions of cold stellar bodies, 
beyond which, in the case of very large masses, there would 
be a complete collapse similar to the one in the example 
on page 161 (Figure 42). 

"But the two cases are not quite analogous," the reader 
may say. "In the case of the house, the walls, which are 
subject to very strong pressure from above, will crack and 
spread sidewise. In the case of a giant spherical body, how- 
ever, the material in the central regions is subject to a 



White Dwarfs and the Dying Sun 



161 




FIGURE 42 

The collapse of a brick wall and of atoms, under the action of veiy 

large prevSsures. 



162 The Birth and Death of the Sun 

uniform pressure from all sides, and there is, seemingly, 

no direction in which it could give way." 

This is quite true, but, nevertheless, there is one direc- 
tion of possible collapse that has been overlooked by this 
reader. We must not forget that matter is built up of 
a large number of separate atoms, and that the solid state 
is the state in which those atoms are most closely packed 
together. But we also know that atoms are not at all the 
absolutely rigid spheres that Democritus imagined them to 
be, but are in fact systems of electronic shells surrounding 
central nuclei. Now, under normal pressures, the forces 
obtaining between the structural parts of the atom stub- 
bornly resist any attempt to squeeze it into a neighbouring 
atom; thus an increase of pressure will cause practically 
no change in the density of a solid body. But any resistance 
must have its limit, and, if the pressure surpasses a certain 
value, which is slightly different for different kinds of 
atoms, the electronic shells will be disrupted and the 
atoms will be crushed, like eggs packed in the bottom of a 
heavily laden basket. 

Electrons belonging to one atom will then penetrate 
into the interior of another, and there will no longer be 
any sense in speaking of the electronic systems of indi- 
vidual atoms. Instead of an orderly system of electronic 
shells surrounding separate nuclei, our "atom crush" will 
present a picturesque mixture of bare nuclei and freely 
moving, unattached electrons, all rushing in disorder 
through space (Figure 43). 

The rigidity of the solid state, caused by the mutual 
impenetrability of the electronic shells of separate atoms, 
will be gone, and an increase of outside pressure will lead 
to a corresponding increase of density. Thus, at sufficiently 



White Dwarfs and the Dying Sun 163 



I ' 

** // 
V. / ' N 

--- ' //> \\ 

' 1p\ I 

V A t/ 



\ 



v \\ ** ^ /'' % N I x ^ 

*Mv-^// ? K 

^/- v ^ j;- s 
^ %\\ ^ y x ^ 

^ ^ i -x- / ^ % 

^>^v> :\\^ 




?< 
'* ^ *t ^r* \^ ' " ; ^^ ' T i^" w ^H < ^^^ 

^vA^^tyVh^-;^ 




FlGTTHE 43 

Gaseous, solid (or liquid), and crushed states of matter. 



164 The Birth and Death of the Sun 

high pressures the solid (and liquid) state of matter, in the 
ordinary sense of these words, ceases to exist, and matter 
regains its compressibility. 

THE PROPERTIES OF THE CRUSHED STATE OF 
MATTER 

The state of matter that exhibits high compressibility 
under the action of outside pressure and a tendency toward 
unlimited expansion in the absence of it is usually desig- 
nated in physics as the gaseous state, and we are thus bound 
to consider the crushed matter described above as some 
kind of gas. Of course, this gas will not at all resemble the 
ordinary gases to which we are accustomed in classical 
physics, and apart from its high compressibility it must 
look rather like some molten heavy metal. From the point 
of view of internal constitution this peculiar new state of 
matter will differ still more from ordinary gases in that it 
represents not a collection of separate atoms or molecules, 
but an irregular mixture of rapidly moving atomic frag- 
ments. 

It should also be noted that, just as the rigidity of ordi- 
nary solid bodies is secured by the motion of atomic elec- 
trons along their quantum-orbits, so, too, the elastic prop- 
erties of crushed matter are essentially dependent upon 
the electronic, and not the nuclear, part of the mixture. 
When diverted from their stable trajectories inside the 
separate atoms (by lack of space to move in), these torn-off 
electrons retain their zero-point energy of motion (see 
p. 166), which is mainly responsible for the pressure of the 
new type of gas. Thus, the same zero-point motion that 
prevents the electron from falling on its atomic nucleus, 
thereby securing the very existence of the atom, will also 



White Dwarfs and the Dying Sun 165 

secure the high gas pressure of the crushed state of matter, 
even at the lowest possible temperature. 

The properties of this electronic gas were first investi- 
gated by the Italian physicist Enrico Fermi, and it is 
often referred to as Fermi gas. In particular, it was shown 
by Fermi that the pressure of an electronic gas> and conse- 
quently the pressure of crushed matter, increases rather 
rapidly with its density, being inversely proportional to the 
-| power of the volume occupied. 

HOW LARGE CAN THE LARGEST STONE BE? 

The discussion above will have made it clear why cold 
bodies massive enough to produce in their central regions 
pressures surpassing a certain critical atom-crushing value 
can no longer be considered to be giant stones; for the 
matter in their interiors completely loses the properties of 
a solid, and behaves in a way very similar to that of an 
ordinary gas. In order, then, for us to answer questions 
concerning the geometrical dimensions of such a collapsed 
stellar body, we must discuss in more detail the equilibrium 
conditions obtaining between the pressure of the Fermi 
gas of electrons, which fills its interior, and the forces of 
gravitational attraction among its various parts tending to 
compress it to still smaller radii. 

Consider a giant sphere of crushed matter with a given 
mass and radius in which the state of equilibrium between 
gas pressure and the forces of gravity has been already 
reached. What would happen if, without changing the 
radius of this sphere, we were to double its mass? The total 
gravitational force tending to compress the sphere is com- 
posed of the attractive forces acting between the different 
parts of the body, as, for example, between the two volume 



166 The Birth and Death of the Sun 

elements A and B, as indicated in Figure 44. By doubling 
the total mass of the sphere we double the mass contained 
in each of its volume elements. According to Newton's law, 
the forces of gravity are proportional to the product of the 
interacting masses. Thus, this doubling of mass will result 




FIGURE 44 

Equilibrium between gas pressure and the gravitational forces in a large 

sphere of gas. 

in a fourfold increase of the total force tending to compress 
the sphere. On the other hand, according to Fermi's law 
(see p. 165), the pressure of the electronic gas filling the 
interior of the sphere will increase only by a factor smaller 
than four (2* -=3.17). As a result, the balance will be 
destroyed in favour of the gravitational forces, and the 
sphere will begin to contract until equilibrium has been 
reached again for some smaller value of the radius. 



White Dwarfs and the Dying Sun 167 

We see from this that crushed matter is not a very suit- 
able material from which to construct geometrically large 
bodies, and that the more material we put in, the smaller 
will be the final dimensions. Thus, the finite resistance of 
atoms to high pressures puts a definite limit on the possible 
size of giant stones; bodies with a mass surpassing a definite 
upper limit cannot in principle be considered as solid 
bodies, and their geometrical dimensions will decrease with 
their increasing mass. 

JUPITER AS THE LARGEST STONE 

To find the largest mass at which a body can still be 
considered a solid, in the ordinary sense of the word, we 
must first of all estimate the numerical value of the pressure 
necessary to crush atoms. This can easily be done on the 
basis of the present theory of atomic structure; and, accord- 
ing to the calculations of the Indian astrophysicist D. S. 
Kothari, this critical atom-crushing pressure amounts to 
150 million atmospheres. 

If we compare this figure with the value of 22 million 
atmospheres, which represents the pressure in the central 
regions of the earth, we must conclude, with some pinprick 
to our earthly pride, that our whole globe is not heavy 
enough to crush atoms by its weight. Only for Jupiter, the 
largest planet of our system (317 times heavier than the 
earth), does the internal pressure approach the critical 
values necessary for the collapse of matter; and we may 
expect that the atoms in the central regions of this giant 
body, if not yet crushed, are at least on the very verge of 
giving way under the tremendous weight of the outside 
layers. 

All solid bodies more massive than Jupiter are inevitably 



168 The Birth and Death of the Sun 

destined to a complete internal collapse, and their ultimate 
radii must be expected to become smaller than that of 
Jupiter. Thus, Jupiter represents geometrically the largest 
piece of cooled matter that can in principle exist in the 
universe; and the "dead Sun," in spite of its larger mass (or f 
actually, precisely because of it), will have a diameter con- 
siderably smaller than that of Jupiter, one comparable with 
the diameter of the earth (see Figure 45). 

THE MASS-RADIUS RELATIONSHIP OF COLLAPSED 
BODIES 

To find the exact values for the radii of collapsed stars in 
their dependence upon their mass, rather complicated 
mathematical calculations are, of course, necessary. Such 
calculations must naturally take into account not only the 
mass, but also the chemical constitution of the body in 
question. For, as we have seen above, the gas pressure of 
the crushed state of matter is given essentially by the num- 
ber of free electrons resulting from the breaking down of 
the atoms; and, on the other hand, the weight of the out- 
side layers tending to compress the stellar body is deter- 
mined by the masses of bare atomic nuclei formed in the 
same process. Thus, the balance between these two oppos- 
ing forces will essentially depend on the mass to be carried 
by the pressure of each free electron, which will be differ- 
ent for different chemical elements. 

For example, in the case of pure hydrogen, there will be 
one proton mass for each electron freed by the crushing 
of the atoms, whereas, in the case of helium, two electrons 
will have to carry a nucleus of mass 4, so that the mass per 
electron will be twice as large for helium as in the case of 
hydrogen. It is clear, therefore, that a collapsed star formed 



White Dwarfs and the Dying Sun 169 

of pure helium would have to contract to a somewhat 
smaller radius than would a hydrogen star in order to 
attain a state of equilibrium. 

This large difference, of the factor of two, between 
crushed hydrogen and crushed helium is, however, about 
as large as can be found as we proceed farther along the 
periodic system of elements. For, in all the other elements 
of the periodic system, the ratio of atomic weight (mass) 
to atomic number (number of electrons) remains always 
the same as, or only slightly higher than, that of helium. 

(For example: for carbon = = 2; for oxygen ~ = = 

Z o Z o 

A ^6 

2; for iron = = 2.15.) From this we may conclude 
Z 26 

that collapsed stellar bodies formed of any of these ele- 
ments will have nearly the same radii as if they were 
formed of pure helium. 

Since, from the discussion in previous chapters, we have 
seen that the collapsed state of a star must represent the 
final stage of its evolution, it follows that the hydrogen 
content in its interior is vanishingly small,* which means, 

* In this particular question concerning the hydrogen content of col- 
lapsed stars, the opinion of most astronomers would be rather opposed to 
the views expressed above by the author. The point is that spectral analysis 
indicates the presence of considerable amounts of hydrogen in the atmos- 
pheres of the so-called white-dwarf stars, which, as we shall see later, 
actually are collapsed, or collapsing, stellar bodies. On this observational 
fact the opinion is usually based that these stars must also contain a great 
deal of hydrogen in their interiors. However, besides the almost unsurpass- 
able difficulties which one encounters when one asks oneself how a star 
containing enough hydrogen for the production of thermonuclear energy 
could start a contraction process, the hypothesis of a high hydrogen 
content in the present interiors of white dwarfs stands in direct contra- 
diction to our physical knowledge concerning nuclear transformations. It is 
not difficult to calculate that, if there were any appreciable hydrogen 
content in the central regions of white dwarfs, the process of deuteron- 
formation from two hydrogen atoms (as discussed in Chapter V) would 
lead to an energy liberation surpassing by millions of times the observed 



170 The Birth and Death of the Sun 

in turn, that we may ignore the question of the kind of 
atoms involved and that the radius of a collapsed star is 
completely defined as a function of its mass. 




FIGURE 45 

The relationship between the radii and the masses of cold stellar bodies, 
according to the calculations of the Indian astrophysicists Chandrasekhar 
and Kothari. The symbols C, , & , and C&, respectively represent the 
moon, the earth, Saturn, and Jupiter. Note that for masses greater than 
460,000 times the mass of the earth the radius becomes zero! The words 
for mass and radius are in Dr. Chandrasekhar's original Tamil. 

In Figure 45 we give a graphic representation of the 
results of such calculations (in stars with a hydrogen con- 
tent of zero) as carried out by another Indian astrophysicist 

radiation of these stars. Thus, we should conclude that the presence of 
hydrogen in the atmospheres of the observed collapsed stellar bodies is only 
an occasional surface effect, and that it is just as dangerous to make 
conclusions about stellar interiors on the basis of atmospheric analysis 
as it would be to conclude from looking at the map of our globe that the 
body of the earth consists two- thirds of water. 



White Dwarfs and the Dying Sun 171 

S. Chandrasekhar, to whom we owe the most complete 
study of the collapsed states of stellar bodies. We see that 
for bodies less massive than Jupiter, the volumes increase 
in direct proportion to the mass, which, of course, should 
be expected for the ordinary uncol lapsed state of solid 
bodies. But for larger masses the situation is essentially 
changed; and, owing to the collapse of matter in the in- 
terior, the volume of the body begins to decrease with the 
increasing mass. In particular we find from this curve that 
the radius of the "dead Sun" will be 10 times smaller than 
the radius of Jupiter, and comparable with the radius of 
the earth. The average density of the Sun in this ultimate 
stage of its evolution will exceed the density of water by a 
factor of 3 millions. 

Because of the high compressibility of the crushed state 
of matter, the density of this highly compact body will not 
be uniform (as it is, for example, in our globe) and will 
rapidly increase toward the centre. According to the calcu- 
lations of Chandrasekhar, the central density in this case 
must exceed the average density by a factor of 10, so that 
each cubic centimetre of the material in the central regions 
of the dead Sun will weight about 30 tons. Such will be 
the unusual conditions under the thick layer of eternal ice 
covering the surface of our Sun when it will finally have 
reached the end of its life. 

WHITE DWARFS 

"Well," the reader will probably now be saying, with a 
tone of scepticism, "this is, indeed, a very exciting picture, 
but who is to vouch for its correctness? Without Mr. H. G. 
Wells's time-machine it is not likely that anyone will actu- 
ally live several billion years into the future and check this 



172 The Birth and Death of the Sun 

prediction. But I should believe it better if I could see such 

a dead or dying Sun myself." 

We can, of course, hardly show the reader the actual 
dying stages of our own Sun, nor can we hope to see stars 
that are quite dead, since these emit no light; but we need 
only look around among the stars surrounding us in order 
to find such as have already exhausted all their hydrogen 
content and are slowly approaching their deathbeds. Thus 
we shall find plenty of observational evidence for the 
existence of collapsed stellar bodies that have not yet quite 
reached their final state and are still living on the gravi- 
tational energy liberated by their slow contraction. Such 
stars should be distinguishable from all other "still living*' 
stars by their comparatively low luminosities and abnor- 
mally small radii corresponding to very high densities. 

The first and most typical example of this moribund 
stage in stars is the "companion of Sirius." We have al- 
ready seen that Sirius is a normal star of the main sequence 
analogous in all its properties to our Sun. It is not Sirius, 
however, that interests us at present, but a star 13,000 times 
fainter, a mote in the dog's eye, revolving around Sirius 
and rather close to it. This faintness and proximity to Sirius 
prevented its discovery until comparatively recent times, by 
Clark in 1862. The first indication of its presence had been 
given in observations of the motion of Sirius, whose track 
among the fixed stars, instead of being a straight line, as 
one should expect of a single body freely moving in space, 
was found to be represented by a winding line, which sug- 
gested that some second body was disturbing its motion. 

To the great surprise of astronomers, the light emitted 
by this newly discovered stellar companion of Sirius, in- 
stead of being rather reddish in colour, as would be suit- 



White Dwarfs and the Dying Sun 173 

able for such small luminosity, turned out to be brilliantly 
white, indicating a very high surface temperature of about 
10,000 degrees. This character of the radiation, combined 
with its very low total luminosity, earned for the compan- 
ion of Sirius, and for other later-discovered stars of the 
same type, the rather poetical name of white dwarfs. 

It is easy to see that the observed properties of Sirius's 
companion fit very closely to the theoretical requirements 
we formulated above for dying stars. If a stellar body of 
such high surface temperature (and consequently of high 
energy-emission per unit surface) possesses an extremely 
small absolute luminosity, we must inevitably conclude 
that its geometrical dimensions are very small as compared 
with the dimensions of normal stars. From the total lumi- 
nosity and the surface temperature of Sirius's companion, 
it can easily be estimated that its surface area is 2500 times, 
and its radius 50 times, smaller than those of our Sun.* 

On the other hand its mass, estimated from its rotation 
period around Sirius, turns out to be almost equal to the 
mass of the Sun (95 percent), thus bringing the average 
density of this star to the tremendously high value of 
200,000 times the density of water. We see, therefore, that, 
as was first indicated by R. H. Fowler, the white dwarfs 
really represent the collapsed states of stars, the possibility 
of which we predicted above on the basis of purely theo- 
retical considerations. 



* The most exact values of the radii of white dwarfs are given not by 
the study of their surface temperatures, but by measuring the so-called 
red shift of spectral lines predicted by Einstein's theory of relativity for 
high gravitational potentials. Owing to the large masses and small radii of 
white dwarfs, the red shifts in their spectra are comparatively large and 
can easily be measured and will serve for exact estimates of their radii if 
the mass is known. The values given in this book are based exclusively 
on such measurements. 



174 The Birth and Death of the Sun 

If we plot the observed mass and radius of Sirius's com- 
panion on the theoretical curve for collapsed stellar bodies 
(Figure 45), we shall see that its present radius is still 2.5 
times larger than it should be in its final state. This fact 
suggests that this particular white dwarf has not yet quite 
reached the final stage of its contraction, or that the present 
estimate of its radius is wrong by at least a factor of two. 

WHEN OUR SUN IS DYING 

There is hardly any doubt that, after several billions of 
years, our Sun, in its decline, will look rather as Sirius's 
companion looks at present. At that distant future date 
the visible angular diameter of the Sun, as seen from the 
surface of the earth, will be about the same as the present 
visible diameter of the planet Jupiter, so that an ignorant 
observer would classify the Sun as an extremely bright 
distant star. 

In spite of this small angular diameter of the "Sun-star," 
its light will still be considerably more intense than that 
of any other star in the sky. The illumination of the surface 
of our planet in the middle of the day will be 1000 times 
brighter than that given by the full moon, but the moon 
itself will be so poorly illuminated by the dying Sun that 
it will be practically invisible. The temperature of the 
earth will drop down to 200 degrees below the freezing- 
point ( 328 F.), making any kind of life on the earth's 
surface quite impossible. But all these inconveniences of 
darkness and cold will probably be of no importance to 
humanity, which, as we have seen in Chapter V, will have 
been burned to death by the increasing solar activity long 
before the ultimate contraction and thermal death com- 
mences. 



CHAPTER IX 



Can Our Sun Explode? 



THE NOV& 

AJL the evolutionary changes in the history of stars 
discussed above are extremely slow from our human 
point of view and require at least several millions of years 
to become noticeable. Thus, even when applied to our 
own Sun its progressive heating up, and its ultimate con- 
traction to follow upon the state of maximum luminosity 
they represent for earth-dwellers matters of purely theo- 
retical interest only. But observation of the skies reveals 
the occurrence of much more catastrophic events, leading 
to a complete change in the status of a star within only a 
few days or even a few hours. 

Quite unexpectedly, and without any preliminary indi- 
cations, a star will blast into an intensity surpassing that 
of its normal state by a factor of several hundreds of thou- 
sands and, in some cases, even of several billions. The star, 
which before this explosion may have been very faint and 
inconspicuous, will suddenly become one of the brightest 
in the sky and attract the attention of astronomers and the 
superstitious. This state of maximum intensity will not, 
however, last long, and, after rapidly reaching its greatest 
brilliance, the exploded star will gradually begin to fade, 
returning to its original luminosity within a year or so. 

Early pretelescopic observations of such stellar explo- 
sions had previously failed to notice the original states of 

175 



176 The Birth and Death of the Sun 

the stars involved (because in most cases they could not be 
seen by the naked eye), and the exploding stars therefore 
received the somewhat misleading name of new stars or 
novce. Several recordings of the appearance of extremely 
bright novae of this kind may be found in ancient history, 
and, in particular, it is very possible that the "Star of 
Bethlehem* ' represented one of these cosmic catastrophes. 

In more recent times, a brilliant stellar explosion was 
observed in November 1572 by the famous Danish astron- 
omer Tycho Brahe; during the period of its maximum 
luminosity this star could be seen even in daylight. Another 
luminous nova appeared soon after that, in 1604, and is 
usually connected with the name of Johann Kepler, who 
gave us the laws of planetary motion. After these two bril- 
liant explosions, commemorating two brilliant names in 
the history of astronomy, the skies remained comparatively 
calm until the year 1918, when a star of very great lumi- 
nosity, surpassing even that of Sirius, appeared for a while 
in the constellation Aquila and presented the first con- 
venient case for study by modern observational methods 
(Plate VIIlA). 

It must be clear, however, that, apart from these very 
conspicuous novse, there must also be a large number of 
stellar explosions which, because of their vast distances 
from us, are too faint to be detected visually. Indeed, the 
modern systematic survey of the skies by means of photog- 
raphy indicates that at least twenty such explosions take 
place yearly among the stars forming our own stellar system. 

TWO CLASSES OF STELLAR EXPLOSION 

We have seen above that novae differ very widely in their 
observed brightness, some being so luminous that they can 



Can Our Sun Explode? 177 

easily be seen in the daylight, whereas others are accessible 
only to telescopic observation. To a great extent these dif- 
ferences are due to the unequal distances separating us 
from the exploding stars, and, when corrected for the dis- 
tance, most of these luminosities come much closer to each 
other and average about 200,000 times the normal lumi- 
nosity of the Sun. 

These do not include, however, such exceptional cases as 
the Bethlehem or Tycho stars, which must have been con- 
siderably more luminous. The study of all the available 
historical data on these exceptionally bright novae brought 
the astronomer W. Baade and the physicist F. Zwicky to 
the very interesting conclusion that we are here dealing 
with an essentially different class of stellar explosions, a 
class that has received the name of supernova. The maxi- 
mum luminosity of these supernovae is, on the average, 
10,000 times greater than that of ordinary novae and exceeds 
by a factor of several billions the luminosity of our Sun. 
Most of the historic novae probably fall into this class, and 
the Kepler star of 1604 was apparently the last explosion 
of this type within our stellar system.* 

From the historical data, Baade and Zwicky also esti- 
mated that the average frequency of appearance of super- 
novce in our stellar system is about one in every three cen- 
turies. During the 336 years separating us from this last 
"superexplosion," there has been no other similar catas- 
trophe in our stellar system, and we may permit ourselves 
the fairly good hope that modern astronomy will soon have 
the pleasure of observing another phenomenon like that 
of the Bethlehem, Tycho, and Kepler stars. 

* The Nova Aquilae 1918 was a normal nova, and its high visual 
luminosity was due only to its comparatively short distance from us. 



178 The Birth and Death of the Sun 

"What a bad joke on the astronomers," the reader will 
probably think, "that the supernovae represent such rare 
phenomena, and that one must wait centuries to see one. 
It must take at least a couple of thousand years before 
sufficient observational evidence of these explosions has 
been accumulated!** 

But the situation is not really so bad as all that. As we 
shall see in the following chapters, our stellar system, com- 
posed as it is of about 40 billions of individual stars, is not 
the only system of this kind in all the infinite universe. 
Very, very far away, at distances much greater than those 
separating us from the most remote stars of our own sys- 
tem, astronomical observations reveal the existence of other 
concentrations of stars floating freely in the vast spaces of 
the universe. These remote stellar systems can be seen 
from the earth only as very faint nebulosities of regular 
spherical or elliptical shape, and are known to astronomers 
as extragalactic nebula.* Popular literature christened 
them with a more appropriate name, "island universes." 
Many thousands of these remote systems, similar to our 
own stellar system of the Milky Way, have already been 
catalogued, and the most powerful telescopes reveal still 
larger numbers of these "stellar islands" in the remotest 
corners of the universe. 

Now, thought Dr. Zwicky, as he inspected the list of 
extragalactic nebulae, if these numerous stellar accumula- 
tions are really analogous to our own system, they must 

* The use of the term "nebula?" for these celestial objects dates back to 
the time when they were believed to be similar to the real nebulae, that is, 
the rarefied luminous gases in interstellar space of our own system (com- 
pare Plate XI). It is known now beyond any doubt that these extragalactic 
"nebula?" actually are concentrations of billions of individual stars. 



Can Our Sun Explode? 179 

also show the supernova phenomenon. And if each nebula 
experiences a supernova explosion at the average rate of 
one every 300 years, I have a fairly good chance of finding 
one supernova before it is time for summer vacations. 

Picking out from the catalogue several hundred conven- 
iently situated extragalactic nebulas, Dr. Zwicky began a 
systematic survey by photographing the selected regions of 
the celestial globe almost every night. For a couple of 
months no changes took place in any of the nebulae under 
observation, until finally, during the night of February 16, 
1937, there was a brilliant flash in one of them. It is not 
known though he surely would have been justified if 
Dr. Zwicky yodelled, after the fashion of his native coun- 
try, when he saw his first supernova. 

Yes, it was a supernova, a terrific explosion that took 
place in the nebula that is registered under the name 
N.G.C. 4157 and is separated from us by the tremendous 
distance of 40,000,000,000,000,000,000 kilometres. Strictly 
speaking, the actual explosion had taken place long before 
Zwicky began his investigation, and even before man ap- 
peared on the surface of the earth. To cover the distance 
between the nebula N.G.C. 4157 and the earth the light 
required 4 millions of years; and all this time since the 
explosion the light rays had been travelling through the 
vast empty spaces of the universe to enter Zwicky's tele- 
scope and make the photographic impression reproduced 
in his article in the Publications of the Astronomical So- 
ciety of the Pacific. 

Since this first success, about twenty fairly well-estab- 
lished cases of supernovae have been detected in various, 
more or less remote, extragalactic nebulae (see Plate VIIlB). 



180 The Birth and Death of the Sun 

THE CHANCES OF OUR OWN SUN'S EXPLODING 

Once we had observed a star, apparently quite peaceful 
and quite indistinguishable from billions of others, sud- 
denly within a few hours burst into a terrific explosion, 
the doubt inevitably crept into our minds: will our Sun 
not play the same trick on us, today, tomorrow, or next 
year? If, one fatal day, our Sun should choose to become a 
nova, the earth (and all the other planets as well) would 
instantly be turned into a thin gas; and it all would take 
place so fast that nobody would even have time to realize 
what had happened. Only the astronomers, if there are 
any, on some distant planetary system of another star would 
register the appearance of a new nova and would probably 
begin the study of its spectrum. But before this unpleasant 
experience overtakes us, if it ever does, it may be interest- 
ing to speculate about the chances of its happening, to see 
whether there is any possibility of predicting in advance 
the date of the catastrophe.* 

We must admit, to start with, that the a priori chances 
of our Sun's becoming an ordinary nova once during its 
total life period are fairly high. As a matter of fact, we have 
seen that at least twenty stars of our stellar system explode 
yearly. Since our universe is about 2 billion years old (see 
Chapter XII), it follows that some 40 billion stars have 
already exploded during this period (unless, which is rather 
improbable, there is a certain preference for such explo- 
sions in the present epoch). On the other hand, as we shall 
see from the following chapters, our stellar system con- 
tains only about 40 billion individual stars. Thus, we must 

* Such a prediction would, of course, be of no practical use whatever 
unless a method were found to detach our earth from the solar system and 
send it travelling away long before the explosion. 



Can Our Sun Explode? 181 

conclude that practically every star must explode at least 
once during its evolutionary history. But the a priori 
chance of a solar explosion within the next few years is 
still only about one in several billions, so that such an 
explosion is much less probable than many other unpleas- 
ant events that can happen to humanity. 

Also, probably each star can explode only once during 
its lifetime, and perhaps our Sun has already exploded in 
the very remote past? This question can hardly be answered 
before we know more clearly the nature of the physical 
processes leading to such catastrophes. 

There is a Russian proverb: "If you must die, die with 
pomp," and we may wonder whether the explosion of our 
Sun will make, not an ordinary nova, but rather a super- 
nova. This will not make any difference to us personally, 
but it will look so much nicer from the outside! It seems, 
however, that to ask for a superexplosion of our Sun is to 
ask too much. The supernova phenomena are very rare, 
and only certain selected stars have the privilege of showing 
such a splendid fireworks display. As we shall see later, 
these superexplosions probably take place only in the case 
of stars much larger and heavier than our Sun, so that we 
shall have to be satisfied to have our end announced 
through the universe only by a comparatively inconspicu- 
ous nova. 

THE PRENOVA STAGE OF STARS 

One of the most direct methods of discovering whether 
our Sun is at present in the pre-explosive state would be 
to compare its characteristics with those of stars that were 
later to become novae. Such comparisons might even re- 
veal certain specific features of stars preparing to burst, 



182 The Birth and Death of the Sun 

and the absence of such features in the case of our Sun 

would guarantee its stability for a fairly long period of 

time. 

Unfortunately, however, very little is known at present 
about these prenova stages of exploding stars. It is true that, 
in several instances of rather bright novae, the study of the 
old photographs of the corresponding regions of the sky, 
taken before the explosion, always revealed the presence 
of a faint star at exactly the same spot where the nova was 
seen later. The estimates of distance permit us to conclude 
also that in some cases this prenova stage went with an 
absolute luminosity comparable with that of our Sun, 
whereas in other cases the absolute luminosities were 
either higher or lower. But, since no one knew in advance 
that these particular stars were going to explode, their 
spectra and other properties had not been investigated in 
detail. 

Only in the case of Nova Hercules, which flashed on the 
northern sky in mid-December 1934, had the spectrum 
been photographed occasionally before the explosion. And 
the spectrogram reveals that before the explosion this star 
was not much different from any other star of the main 
sequence. In fact, its absolute luminosity and its spectral 
characteristics were very close to those of our Sun. Does 
this mean that our Sun is also destined to burst in a not 
very distant future? Not necessarily. First of all, a "not very 
distant future" might mean millions of years in the astro- 
nomical time scale, and, besides, there are millions of stars 
possessing the same characteristics which are not exploding. 

The preparations for these explosions apparently do not 
much change the observable surface properties of stars; if 
there are some minute alterations, they have escaped obser- 



Can Our Sun Explode? 183 

vation. The example of Nova Hercules 1934 tells us only 
that the star need not necessarily possess some clearly 
abnormal external properties in order to be able to ex- 
plode, and that an apparently perfectly normal star can 
burst into a terrific explosion if it chooses to do so. 

It should be noted that the pre-explosive states of super- 
novae are much more difficult to observe. In fact, except 
for a few historical outbursts, they all belong to very dis- 
tant stellar systems, so far from us that no individual stars 
can be distinguished. Only supernovae at their maximum 
can be clearly seen in these distant worlds, owing to the 
fact that the radiation emitted by such explosions is com- 
parable, and in some cases even surpasses, the total radia- 
tion of the billions of other stars forming those systems.* 

THE PROCESS OF EXPLOSION 

As was mentioned above, the main external feature of 
a nova outburst consists in the fact that the luminosity of 
the star increases tremendously within a short period of 
time, and then begins to drop back to its original value. 
In Figure 46 we give the luminosity curves for Nova 
Aquilae 1918 already cited, and for the supernova that 
appeared in 1937 in the extragalactic nebula known as 
I.C. 4182 (the photographs of the development of the 
latter are given in Plate VIIlB). We see that, apart from 
the amplitude, the two curves show a very similar charac- 
ter, with a very rapid rise in the beginning and a slow and 
somewhat irregular decrease of radiation after the maxi- 
mum. 

* In fact, since supernovae are billions of times more luminous than the 
average normal star, and since the average extragalactic nebula contains 
several billions of stars, the appearance of a supernova might double the 
total light emitted by such nebulas. 



184 The Birth and Death of the Sun 

Other important characteristics that change during the 
explosion are the surface temperature and the spectrum 
of the star. Whereas in the prenova stage all stars evidently 



io*t 

I0 1 
10*" 
I0 5 - 
io' 

ro* 

IG*" 



NOSITY 



SUPERNOVA ICH-I82 
(Au& 1937) 




NOVA AQUILAE 
(JUNE 1918) 



Sept Ocf-. Nov Dec. Jan. Feb. 
June July Au 9 . Sept Oct. Nov. 



FIGURE 46 

The luminosity changes of a typical nova and a typical supernova. 
Luminosities are given in terms of the luminosity of the Sun ( =1 ). 

possess a normal spectrum belonging to one of the Harvard 
classes, during the explosion the spectrum completely 
changes it character, indicating temperatures running into 
hundreds of thousands, if not millions, of degrees. But the 
study of these explosion spectra also reveals another ex- 
tremely interesting effect. The bright emission lines of 




PLATE IX. A "planetary" or "ring nebula" in the constellation Lyra. This 

is probably the result of a nova outburst of several centuries ago. 

( See p. 185. ) ( Mt. Wilson photograph. ) 




PLATE X. The filamentary nebula in the constellation Cygnus. This is 
probably the remainder of a gaseous shell ejected by a supernova about 
100,000 years ago. The bright star in the centre is not a part of the 
nebula, but appears there only by coincidence. ( See p. 186. ) ( Mt. Wil- 
son photograph.) 



Can Our Sun Explode? 185 

novae show a conspicuous shift toward the violet end of 
the spectrum, indicating a rapid expansion of the gaseous 
shell that is formed around the star during the process of 
explosion. 

In the best-studied case, Nova Aquilae 1918, the expan- 
sion velocity of this shell was estimated to be about 2000 
kilometres per second, and six months after the explosion 
it became directly observable through the telescope. The 
diameter of this faint greenish nebulosity enveloping the 
star is now gradually increasing at the rate of two angular 
seconds per year; and, if the velocity remains constant and 
the shell does not fade in the course of time, it will attain 
the visible diameter of the moon about a thousand years 
from now. 

Incidentally, astronomical observation has revealed the 
existence of a considerable number of bright hot stars that 
are surrounded by rather extensive gaseous envelopes. The 
question whether these so-called planetary nebula (again 
a quite unsuitable name!) actually represent the later 
stages of nova development is as yet unanswered (see 
Plate IX). 

We cannot pass on from here without mentioning also 
the case of the irregular gaseous nebula* in the constella- 
tion Taurus, known as the "Crab Nebula" because of its 
peculiar shape. This nebula is at present rapidly expand- 
ing at the rate of 0.18 angular second per year, from which 
we conclude that the expansion must have started about 
eight or nine hundred years ago. Was the mass of gas that 
forms the Crab Nebula exploded from some nova, or 

*We remind the reader once more that the giant "extragalactic 
nebulae" made up of stars, and the much smaller "gaseous nebulae" to be 
found in our own stellar system, are absolutely different things in spite of 
their similar names. 



186 The Birth and Death of the Sun 

rather, judging from the intensity of the effect, from some 
supernova, which flashed on our sky at that epoch? The 
study of Chinese manuscripts of the eleventh century re- 
veals that there actually was at that time a very brilliant 
stellar explosion, which took place in A.D. 1054 almost 
exactly in the same place where we now see this curious 
nebula. Thus, there is scarcely any doubt that the Crab 
Nebula is the result of a supernova explosion that was 
observed 886 years ago. 

Another interesting example is furnished by the so-called 
"Filamentary Nebula** in the constellation Cygnus (Plate 
X). This is shaped like the arc of a circle, and, together 
with some other nebulae of similar type, forms a rather 
regular loop, with an angular diameter of about 2 degrees 
(four moon diameters). The nebulae forming this loop 
move from their common centre with an angular velocity 
of 0.05 second per year, so that the expansion must have 
begun about 100,000 years ago. Most probably this is also 
the result of a supernova explosion, but unfortunately in 
the year 100,000 B.C. there were no astronomers, even 
Chinese ones, to record the appearance of the new star. 

The recent observations of G. P. Kuiper at the Yerkes 
Observatory have shown that this "blowing of smoke rings" 
is not the only consequence of stellar explosions. When 
Nova Hercules 1934 was telescopically examined a few 
years after its appearance, it became obvious that the star 
had probably been broken into two parts by the force of 
the explosion. The two fragments are now travelling away 
from each other with a relative velocity of about 0.25 
angular second a year, and will be separated by a visual 
distance equal to the visible diameter of the moon (0.5 
degree) by the year A.D. 9130. In Figure 47 we give the 



Can Our Sun Explode? 187 

observed relative distances of the two fragments of this 
stellar explosion. 



^/j^ 

3>tc.l2, WSf 


o.t- 

Ovjly ^iS* 


o.vV" 


Feb. 1957 



FIGURE 47 

The increasing separation of the two fragments formed by the explosion 
of Nova Hercules on December 12, 1934. 

WHAT CAUSES STELLAR EXPLOSIONS? 

What are the physical processes that cause the explosion 
of seemingly normal stars? We must confess that we do 
not know at present, and can only speculate about the 
different conditions that might possibly be responsible for 
these catastrophic events. 

The oldest, and probably the simplest, hypothesis is to 
the effect that the observed explosions are due to external 
causes, as, for example, a collision with some obstacle the 
star meets on its way through space. It is known, however, 
that, owing to the extremely sparse population of space, 
the chances of collisions between stars are negligibly small. 
In fact, it has been calculated that not more than two or 
three such collisions could have taken place in our stellar 
system in the past 2 billions of years. 

But w r e know that interstellar space contains very exten- 
sive rarefied gaseous material, evidently left over after the 
formation of the individual stars. These interstellar clouds, 
known as gaseous nebula, are often illuminated by the 
light of neighbouring stars, and appear as giant luminous 
nebulosities of very irregular and picturesque shape (see 



188 The Birth and Death of the Sun 

Plate XI). In other cases they are dark (see Plate XII), and 
can be observed only through their obscuration effect on 
the stars situated behind them. The two well-known dark 
holes in the Milky Way, named the "Coal Sacks" by astro- 
nomically inclined seamen, represent typical examples of 
such dark nebulosities. 

If a star, moving through space at a very great velocity, 
enters such a cloud of dilute material, it will burst into 
high luminosity in the very same way as does a meteorite 
that enters our terrestrial atmosphere. And, in fact, the 
kinetic energy of stellar motion, when thus transformed 
into heat, can easily supply the tremendous radiation 
characteristic of novae during the period of their high 
luminosity. If, for example, the motion of our Sun (whose 
present speed is 19 kilometres per second) were slowed 
down to half its present value by the friction of such a gas 
cloud, the liberated kinetic energy would suffice for a 
millionfold increase of its luminosity over a period of sev- 
eral weeks. 

This hypothesis, however, simple though it is, meets 
with serious difficulties in the attempt to explain the 
remarkable similarity of all observed nova explosions. For, 
since the gaseous nebulae that different stars might meet 
vary so widely in their densities and geometrical dimen- 
sions, it is hard to see how they could have such strikingly 
similar effects. It must also be noted that this purely kinetic 
hypothesis, though it accounts for enough energy to create 
ordinary novae, is absolutely inapplicable to supernovas, 
with their considerably larger energy liberation. 

If we try to solve the problem of stellar explosions in 
terms of nuclear transformations, which are so important 
in the normal life of the star, we must think of some 




PLATE XL The luminous gaseous nebula in Orion. This giant mass of 

gas is inside our Galaxy and probably owes its luminosity to the radiation 

of the surrounding stars. (See p. 188.) (Mt. Wilson photograph.) 




PLATE XII. A portion of the Milky Way near the constellation Aquila, 

showing its resolution into a large number of individual stars, The dark 

spot in the centre is not a "channel" but a dark gaseous nebula obscuring 

the view. (See p. 206.) (Mt. Wilson photograph.) 



Can Our Sun Explode? 189 

special thermonuclear reaction that will suddenly come 
into play when the central temperature of the evolving 
star reaches a certain critical value. A v.ery small amount 
of such an "explosive element" might indeed be enough 
to liberate the energy required for an ordinary nova and 
even for a supernova, but no possible reaction of this kind 
has as yet been found. 

So we must confess that we do not know why stars ex- 
plode, and that we cannot tell for certain whether our Sun 
is going to follow the example of Nova Hercules in the 
near or distant future. Let us hope it will not. 

SUPERNOVA AND THE "NUCLEAR STATE" OF 
MATTER 

In the particular case of supernovae, an entirely novel 
mechanism of explosion was proposed as a possibility by 
Zwicky, soon after he had proved the occurrence of these 
vast stellar catastrophes. In order to understand Zwicky's 
hypothesis, we must go back to our discussion of super- 
dense stars in Chapter VIII. We saw there that, after the 
consumption of all the hydrogen available for thermo- 
nuclear reactions, every massive star is bound to contract 
to a very small radius and a correspondingly very high 
density. 

In Figure 45 of that chapter we also gave a graphic 
representation of the fact that the radius of a collapsed 
star is a function of its mass, demonstrating that this finite 
radius decreases with the increasing mass. When he saw 
this diagram, the careful reader may already have noticed 
that the curve expressing this radius-mass relationship does 
not extend indefinitely in the direction of larger masses, 
but leads to a zero radius for a mass that is equal to 1.4 



190 The Birth and Death of the Sun 

Sun masses. This means that the minimum radius for all 
contracting stars heavier than 1.4 Suns is zero, or, in other 
words, that all sufficiently heavy stars are bound to have an 
unlimited contraction. The weight of the outside layers of 
these heavy stars is so great that the pressure of Fermi's 
electronic gas in the interior is never able to balance it, 
and no stable equilibrium with a finite value of the radius 
is possible.* 

What will happen to a very heavy star that is contracting, 
mathematically speaking, to a geometrical point? The an- 
swer to this question was first given by the young Russian 
physicist L. D. Landau, who pointed out that the contrac- 
tion must stop as soon as the distances between the sepa- 
rated electrons and atomic nuclei that make up stellar 
matter become equal to their diameters. At this stage of 
compression, the nuclei and electrons, being brought into 
direct contact, will stick together, as would separate drops 
of mercury so brought together, and will form in the 
stellar interior a continuous ''nuclear substance" (see Fig- 
ure 48). 

The hypothetical high "rigidity" of this form of matter 
must finally stop the progressive contraction of heavy stars, 
and in the resulting state of equilibrium the stellar interior 
will be occupied by a giant nucleus, quite analogous to 
ordinary atomic nuclei, but measuring many hundreds of 
kilometres in diameter. Being made up of atomic nuclei 
and electrons that have been torn apart by the crushing of 
originally neutral atoms, this stellar nucleus will be, on 

* The reader must not forget, of course, that all this pertains only to 
stars deprived of hydrogen and living on the gravitational energy liberated 
in contraction. In all young stars containing hydrogen, thermonuclear 
reactions produce sufficient energy to keep up a central temperature and 
gas pressure high enough to maintain stability. 



Can Our Sun Explode? 191 

the whole, neutral and will possess a density surpassing the 
density of water by a factor of several thousand billions.* 



A * 

Wm 







w 




FIGURE 48 
Formation of the "nuclear state" of matter by very high pressure 

(compare Figure 43). 

* In water the atomic nuclei are on the average io* 8 centimetre 
apart, whereas in the nuclear substance these distances are reduced to 
nuclear diameters, or io~ 12 centimetre. This linear compression by a 
factor of 10,000 will give an increase of density by a factor of io 12 , i.e., 
i ,000,000,000,000. 



192 The Birth and Death of the Sun 

A small dust particle made from such dense matter would 
weigh several tons! But, it must be clear, of course, that 
matter in this "nuclear state** can exist only under the tre- 
mendous pressures existing in the interior of heavy con- 
tracting stars. When brought out from these regions, it 
will immediately expand, splitting into separate nuclei and 
electrons, and forming the atoms of different stable chem- 
ical elements. 




FIGURE 49 
The hypothetical collapse of the central regions in a supernova. 

Let us now return to Dr. Zwicky's hypothesis concerning 
the catastrophic events observed in the supernovas: it is to 
the effect that what we witness here is the tremendously 

rapid collapse of heavy stars resulting from the format| A! 

HI 
of such "nuclear states*' of matter in their interiors. 1 he 

process probably begins with the neutralization of bare 
atomic nuclei in the stellar interior through their absorp- 
tion of free electrons that are squeezed too close to them 



Can Our Sun Explode? 193 

by outside pressure. This is then followed by the sticking 
together of the neutral particles thus formed into one solid 
block of nuclear matter. In such a collapsing process the 
radius of a star might decrease to one percent of its value 
within a few hours, and the enormous amount of gravita- 
tional energy liberated would be quite enough to explain 
the intense radiation of supernovas. Under the pressure 
of radiation coming from the interior of the star, its out- 
side layers will be blown away, to form the expanding 
shell that will surround the exploding star (Figure 49). 

In spite of the great attractiveness of this explanation 
of the supernova explosion, it remains so far only an inter- 
esting hypothesis, since no rigorous theoretical treatment 
of such collapse problems has yet been performed. But it 
may be hoped that in the course of the next few years a 
satisfactory solution of this last remaining puzzle of stellar 
evolution will finally be found. 



CHAPTER X 



The Formation of Stars and Planets 



STABS AS "GAS DROPS" 

WE HAVE mentioned several times that in the early 
stages of their development all stars are extremely 
rarefied and comparatively cool spheres of gas, which 
become hot and luminous as the result of their gravita- 
tional contraction. Once upon a time, at the dawn of the 
universe, the stars must have been so dilute that they 
occupied all available space, forming a practically con- 
tinuous gas. Later, under the action of some internal insta- 
bility^ this continuous gas must have broken up into a 
number of separate clouds or, so to speak, "gas drops" 
which contracted into the stars as we know them at present 
(Figure 50). 

What were the physical conditions underlying this 
break-up of the continuous cosmic gas, and why does not 
the same thing happen to the ordinary atmospheric air, 
for example? It would be odd indeed if the air filling a 
room were to collect itself into many "air drops" and 
leave a vacuum in between them. 

The difference between the two cases does not lie in 
any peculiar physical or chemical properties of the gas 
from which the stars were formed,* but is entirely due to 



* Of course, the primordial gas was much hotter than the air, and con- 
sisted of vapours from all the different elements. But this would not make 
an essential difference in its general properties as a gas. 

194 



The Formation of Stars and Planets 195 









FIGURE 50 
The formation of separate stars from a continuous gas. 



196 The Birth and Death of the Sun 

the vast extent of interstellar space as compared with the 
volume of an ordinary room or even with the thickness 
of the earth's atmosphere. If, inside a room, or in the free 
atmosphere surrounding our globe, a part of the gas occa- 
sionally begins to concentrate in a certain region, the 
increased gas pressure at that point immediately disperses 
the concentration and brings the density to its normal 
value. Thus, the germs of the "air drops" never have the 
chance to develop into more serious concentrations.* 

But, if such a germ is sufficiently large, it can be held 
together by the mutual gravitational attraction among its 
parts, and the forces of gravity will even cause its further 
concentration. The calculations of the British physicist 
and astronomer Sir James Jeans have shown that such germ 
formation must always take place if the gas is extended 
through a region of sufficiently large geometrical dimen- 
sions. In the case of atmospheric air, the diameter of a 
germ that could "hold itself together" would have to be 
many millions of kilometres, which explains why no "air 
drops" can be formed either in the room or in the thin 
atmospheric layer enveloping our globe. But in the dilute 
gas that long ago filled all infinite space, such concentra- 
tions must necessarily have taken place. 

When all the matter that now forms the separate stars 
was uniformly distributed throughout space, its average 
density was very low, amounting to only 0.000,000,000,000,- 

* We should note here, however, that even such small germs do play an 
important role in our atmosphere. The slight deviations from homogeneity 
in the air, due to this fluctuation of density, cause the scattering of the 
sunlight that passes through the atmosphere, and make possible the 
general illumination and blue colour of the sky above our heads. If the 
atmospheric air were absolutely homogeneous, the sky would always be 
black and the stars could be seen even in the daytime; neither would there 
t>e any beautiful sunsets. 



The Formation of Stars and Planets 197 

000,000,000, i times the density of water. At such low den- 
sities and at a temperature of several hundred degrees, 
the forces of gravity could break the gas into separate 
spheres, each with a diameter of about two or three light- 
years and a mass of about 1,000,000,000,000,000,000,- 
000,000,000,000 kilograms. When further contracted by 
the forces of gravity, these gas drops would become the 
ordinary stars as we see them now in the sky. 

It should be added that this process of star formation 
through the gravitational instability of large masses of gas 
could also lead, in some cases, to the creation of much 
larger bodies than the stars known to us. It can, however, 
be shown that the central temperatures and the nuclear 
energy production in the interiors of such "superstars" 
would make them absolutely unstable and cause their split- 
ting into a number of smaller bodies. 

DOES THE PROCESS OF STAR FORMATION CONTINUE 
AT PRESENT? 

According to the best estimates, the age of the stellar 
universe is 2 billion years, which should also give us 
roughly the time when the break-up of the continuous 
distribution of primordial gas must have taken place. But 
is this process of star formation quite completed by now, 
or are some new stars (not novae, but really new stars) 
being formed at the present time? 

The study of different types of stars belonging to our 
system indicates quite definitely that some of them must 
be considerably younger than the rest of the universe. We 
have seen, for example, in Chapter VII, that the so-called 
red giants represent comparatively early stages of stellar 
evolution. It seems hardly probable that these stars can be 



198 The Birth and Death of the Sun 

much older than a few million years, and we must con- 
clude that their formation must have taken place during 
geological times. The most striking example of a star in 
the very early stages of its evolution is one we have already 
discussed, the infrared star e Aurigas I, which is probably 
still in the original contractive stage. 

Then, too, the most brilliant stars of the main sequence, 
those known as blue giants, must also be relatively new 
stars. Indeed, owing to their extremely high luminosities, 
the total life expectancy of these stars must be compara- 
tively short, and in our present state of knowledge it must 
be concluded that they represent a fairly recent addition to 
our stellar system. Such stars as, for example, 29 Canis 
Majoris or AO Cassiopeiae produce 20,000 times more 
energy per gramme of their material than does our Sun, 
and are bound to run through all their original hydrogen 
content in not more than 5 million years. These stars were 
definitely not in the sky during the ages when giant rep- 
tiles crawled on the surface of our earth. 

There is, of course, no lack of the diffuse gaseous mate- 
rial (gaseous nebula) still left in interstellar space, and we 
must conclude that the process of star formation is still in 
progress, although probably on a much smaller scale than 
during the epoch when the main body of stars was formed. 

THE ORIGIN OF WHITE DWARFS 

When we compare the ages of different types of stars 
with the estimated age of the whole stellar universe, we 
also meet with cases opposite to those of the red and blue 
giants, and in which the stars seem much older than they 
possibly could be. We have seen in Chapter VIII that the 
so-called white dwarfs are the stars already depleted of 



The Formation of Stars and Planets 199 

their nuclear energy sources, and that they represent, in 
this sense, the evolutionary stage at which our Sun will 
arrive when it has exhausted all its original hydrogen con- 
tent. But we have also seen that stars of the size of our Sun 
need several billions of years to attain this state, and that 
our Sun itself has since its birth used up barely one of the 
original 35 percent of its hydrogen content. 

How does it happen, then, that such stars as the com- 
panion of Sirius, for example, have no more hydrogen in 
their interiors and are even now slowly dying? It is difficult 
to suppose that they did not have plenty of hydrogen from 
the very beginning, for the chemical elements in the uni- 
verse seem pretty well mixed and distributed; on the other 
hand, they can hardly be older than the stellar universe 
itself. In short, the stellar universe seems as yet too young 
to contain such old and decrepit stars as the white dwarfs^ 
and the presence of the companion of Sirius in the stellar 
family is no less surprising than would be the appearance 
of a white-bearded man in one of the cribs of a maternity 
ward. 

It seems to the author that the only reasonable explana- 
tion of the existence of white dwarfs of the observed mass 
in the present stage of the development of the stellar uni- 
verse is the hypothesis that these stars have never been 
young, and represent only the fragments formed by the 
collapse of heavier and more rapidly evolving stars. The 
very massive and luminous stars created at the very begin- 
ning of the stellar universe must have exhausted their 
hydrogen content and started their ultimate contraction 
long before the present time. We have seen in a previous 
chapter that the contraction of such stars, many times 
heavier than our Sun, leads most probably to a sudden col- 



200 The Birth and Death of the Sun 

lapse of their bodies (see Zwicky's explanation of super- 
novae), with a consequent split into several smaller pieces. 
These fragments, formed by stellar explosions in the dis- 
tant past f may account for the white dwarfs observed at 
the present time in our stellar system. 

WHAT ABOUT PLANETS? 

When people first began to think about the origin of 
the world along scientific lines, their main interest was 
concentrated upon problems concerned with the formation 
of our earth and the other planets of the solar system. And 
it is a curious thing that, even at present, when we know 
so much about the origin of different types of stars and 
seriously discuss questions relating to the birth of the 
entire universe, the problem of the earth's formation is 
not yet quite settled. 

More than a century ago the great German philosopher 
Immanuel Kant formulated the first scientifically accept- 
able hypothesis about the origin of our planetary system, 
a hypothesis that was further developed by the equally 
famous French mathematician Pierre Simon de Laplace. 
According to this hypothesis, the several planets were 
formed from gaseous rings detached by centrifugal force 
from the main body of the Sun during the early stages of 
its contraction (Figure 51). In view of our present knowl- 
edge this attractive and simple hypothesis will not stand 
up under serious criticism. 

First of all, mathematical analysis has shown that any 
gaseous ring that might be formed around the contracting 
and rotating Sun would never condense into a single 
planet but would rather give rise to a large number of 
small bodies analogous to the rings of Saturn. 



The Formation of Stars and Planets 201 







FIGURE 51 
The (incorrect) Kant-Laplace hypothesis of the formation of planets. 



202 The Birth and Death of the Sun 

The second, and still more serious, difficulty presented 
by the Kant-Laplace hypothesis consists in the fact that 98 
percent of the total rotational momentum of the solar sys- 
tem is associated with the motion of the major planets, and 
only 2 percent is accounted for by the rotation of the Sun 
itself. It is impossible to see how such a high percentage 
of rotational momentum could be concentrated in the 
ejected rings, leaving practically nothing with the original 
rotating body. It seems, therefore, necessary to assume (as 
was first done by Chamberlin and Moulton) that the ro- 
tational momentum was put into the system of planets 
from the outside and to consider the formation of the 
planets as due to an encounter of our Sun with some other 
stellar body of comparable size. 

We must imagine that once upon a time, when our Sun 
was a lonely body without its present family of planets, 
it met another similar body travelling through space. For 
the birth of planets no physical contact was necessary, since 
the mutual forces of gravity even at comparatively great 
distances can have caused on the bodies of both stars the 
formation of huge elevations extending toward each other 
(Figure 52). When these elevations, actually giant tidal 
waves, surpassed certain limiting heights, they must have 
broken up into several separate ''drops" along the line 
between the centres of the two stellar bodies. The motion 
of the two parent stars relative to each other must have 
given to these rudimentary gaseous planets a vigorous rota- 
tion, and when the parents parted they were each enriched 
by a system of rapidly rotating planets. The tidal waves 
on the surface of the stars must also have forced them to 
rotate slowly in the same direction as their planets, which 
explains why the rotation axis of our Sun so closely coin- 
cides with the axis of the planetary orbits. 



The Formation of Stars and Planets 



203 






t 





FIGURE 52 
The "hit-and-run" hypothesis of the formation of planets. 



204 The Birth and Death of the Sun 

It is interesting to think that somewhere in interstellar 
space moves a star responsible for the birth of our planetary 
system, and carrying along some of the half-brothers and 
half-sisters of our earth. But since the birth of our plane- 
tary system took place a few billions of years ago, our Sun's 
spouse must be very far away by now, and could be almost 
any star observed in the sky. 

This "hit-and-run theory" of the formation of our 
planetary system also leads to s6me difficulties, however, 
if we inquire into the chances of such a close encounter 
between two stars. From the tremendously great distances 
between stars and their comparatively small radii it is 
easy to calculate that, during the few billion years that 
have passed since their formation, the chance of such an 
encounter for each individual star is only one in several 
billions. Thus we should be forced to the conclusion that 
planetary systems are very rare phenomena, and that our 
Sun must be extremely lucky to have one. It may also 
mean that, among all the billions of stars forming our 
stellar system, the Sun and its spouse are probably the 
only ones to have a planetary family! 

It is true, of course, that no telescope yet constructed is 
strong enough to answer directly the question as to the 
possible existence of other planetary systems, even in the 
case of the nearest stars. But it would be extremely awkward 
if the planetary system of our Sun were to represent so 
rare a phenomenon, especially in view of the large ob- 
served number of double (and even sometimes triple) stars, 
the origin of which is not much easier to understand than 
the origin of the systems of smaller satellites. 

We can, however, escape all these difficulties if we sup- 
pose that the formation of planets took place during the 



The Formation of Stars and Planets 205 

early stages of the development of our universe, soon after 
the formation of the stars themselves. We shall see in the 
next two chapters that our universe is in a state of ever- 
progressing expansion, from which it follows that in the 
remote past the distances between individual stars must 
have been considerably smaller than they are at present. 
During that epoch, near-collisions between stars must have 
represented a much more common event, and each star 
was given a fair chance to acquire a planetary system of 
its own. Many of these stellar encounters may also have 
led (with the help of a third body) to the permanent bind- 
ing of the passing couples and the creation of what we 
now observe as binary systems. 



CHAPTER XI 



Island Universes 



THE MILKY WAY 

ON CLEAR nights, we can easily see a faint luminous 
band stretching across the sky from one horizon to 
the other. To the vivid imagination of ancient astronomers, 
this band presented itself as a flow of milk escaping from 
some heavenly Cow (though there does not seem to have 
been any constellation of that name), and it therefore 
received the name of the Galaxy or, in English, the Milky 
Way. The early telescopic observations of the famous 
astronomer Sir William Herschel reinforced this metaphor 
by showing that, just as ordinary milk consists of minute 
particles of fat suspended in a more or less transparent 
liquid, so does the celestial Milky Way consist of an 
immense number of very faint stars individually indistin- 
guishable by the naked eye (see Plate XII). 

The fact that the stars composing the Galaxy fall within 
a more or less regular belt that encircles the sky gave 
Herschel the ingenious idea that this collection of stars 
had the shape of a rather flattened disk, something like a 
thin watch, and that our Sun was situated somewhere in 
the interior of the space occupied by it. As must be clear 
at once from Figure 53, which represents HerscheFs view 
of the galactic system, we shall find comparatively few 
stars in the direction perpendicular to the main plane of 
the disk and a great number of them in the direction of 

206 



Island Universes 207 

this plane. Most of the stars seen in the direction of the 
plane are very distant from our point of observation; and 
their relative visual faintness, together with their large 
number, gives that impression of continuously distributed 
luminosity which is observed by the naked eye. This pic- 
ture of the stellar universe, proposed by Herschel more 




FIGURE 53 

A schematic view of the stellar system of the Milky Way, showing the 
excentric position of the Sun. 

than a century ago, formed a solid basis for all later studies 
of the universe on a large scale. 

THE NUMBER OF STARS IN THE SKY 

Notwithstanding the common expression, "as many as 
there are stars in the sky/' the number of stars actually 
seen by the naked eye is not at all large. In fact, the total 
number of such stars, including those of both the northern 
and the southern hemispheres, amounts to only a little 
more than 6000; and at any one time, taking into account 
the poor visibility near the horizon, hardly more than 2000 
can be seen. 

The situation changes, however, quite significantly when 



208 The Birth and Death of the Sun 

we count also those stars that can be seen through powerful 
telescopes, and the phrase of common speech mentioned 
above becomes more reasonable if we understand it in 
terms of the present astronomical evidence. The total 
number of stars in our galactic system, including the most 
distant and faint ones, is estimated by the Dutch astron- 
omer Kapteyn, to whom we owe the most careful study of 
the Milky Way, to be about 40 billions, which is quite a 
lot of stars. 

Of course, all the stars in the Milky Way do not have 
personal names, such as Sirius or Capella. It is not so much 
that one could not find enough names to go around among 
the members of this 4O-billion-strong family, for the num- 
ber of eight-letter words that could be formed with the 
twenty-six of the alphabet would suffice. It would simply 
take too long to christen every member of our Galaxy; 
at the rate of one new name per second, we should need 
about 1700 years to complete the list. 

THE DIMENSIONS OF OUR STELLAR SYSTEM 

The distance to Sirius is 52,000 billion miles, and it 
takes light, travelling at 186,000 miles per second, eight 
years to traverse it. But Sirius is comparatively near; to 
come to us from the most distant members of the galactic 
system, light often requires as much as several thousand 
years. Indeed, astronomers save themselves the trouble of 
dealing in such large numbers by expressing these stellar 
distances in light-years.* 

After careful measurements, Kapteyn came to the con- 
clusion that the 40 billions of stars in our Galaxy are dis- 

* A light-year is equivalent to 9,463,000,000,000 kilometres or 5900 billion 
miles. 



Island Universes 209 

tributed within a lens-shaped space measuring about 
100,000 light-years in diameter and 10,000 light-years in 
thickness. The limits of this lenticular Galaxy are, of 
course, not very sharp, since the distribution of stars be- 
comes more and more sparse as we go outward from the 
central regions. It is quite possible that a few stars may still 
be found at distances several times greater than those indi- 
cated above. 

Our own Sun, together with its system of planets, is 
situated not far from the rim of the galactic lens, rather 
close to the equatorial plane, and about 30,000 light-years 
from its centre. This centre of the Galaxy, which should 
be expected to show a much greater concentration of stars, 
and hence considerably greater intensity of light, is to be 
found in that part of the Milky Way that passes through 
the constellation Sagittarius (see the map of the stellar 
sky on the inside cover of the book). Unfortunately, some 
dark interstellar clouds,* formed by large masses of cool 
gas that were left over after the creation of the stars, hang 
in the space between the galactic centre and our Sun, 
making observation of this most interesting region quite 
impossible. 

THE MOTION OF STARS WITHIN THE GALAXY 

In ancient astronomy, the stars that composed the differ- 
ent constellations in the celestial sphere were called "fixed 
stars/* in contrast to the "wanderers," or "planets/* which 
move among the fixed stars with comparative rapidity. We 
know now that these so-called "fixed stars" also move 
through space, and indeed with velocities even greater 

* One of the so-called gaseous nebulae. See pp. 187-188 above and com- 
pare Plate X. 



210 The Birth and Death of the Sun 

than those of the planets. Owing, however, to the enor- 
mous distances that separate us from these stars, their high 
absolute velocities result in relatively minute angular 
changes of their observed positions. But photographs of 
the stellar sky taken several years apart do permit us now 
to note these slight changes of position, and to predict how 
our sky will look in the very distant future. 

In Figure 54, for instance, we give the changes that are 
destined to take place in the familiar constellation of the 
Great Bear, more commonly known as the Dipper. A 
period so short, astronomically, as a few hundred thousand 
years is enough to produce a complete change in the gen- 
eral appearance of the sky. We thus see that, when the 
Neanderthal caveman hunted bears and mammoths over 
the face of Europe tens of thousands of years ago, the stellar 
pattern above his head was quite different from what we 
know at present. It is a pity, therefore, that, when he 
covered the walls of his caves with artistic pictures of the 
chase, it never occurred to prehistoric man to draw an 
image of the stellar sky; it would most certainly have saved 
modern astronomers a lot of trouble. 

Incidentally, we may remark that, although the motions 
of the different stars through space are on the whole rather 
irregular and independent of each other, there are many 
instances in which the stars that happen to form a given 
constellation seem to be moving together. In the case of 
the Great Bear, for example (Figure 54), five of the seven 
stars are evidently moving in the same direction, and the 
estimate of their relative distances indicates, moreover, 
that they are situated rather near to each other. The other 
two stars, which are responsible for the dipper-shape of 



Island Universes 211 

the whole constellation, are obviously not connected with 
the system. They are moving in a quite different direction 



K 

\ 

* 









10Q,000 B.C. 



A.D. 



\ * \- 

A.D. 100,000 



FIGURE 54 

Changes in the constellation of the Great Bear (the Dipper) in 

200,000 years. 

and, at the time of prehistoric man, would probably not 
even have been thought to be related to the rest of the 



212 The Birth and Death of the Sun 

group. Another interesting example of the changes to be 
expected in a well-known grouping of stars is given by the 
constellation Scorpio, shown in Figure 55. 




FlGUBE 55 

The constellation Scorpio and the future changes (arrows) in the positions 
of its stars, 100,000 years hence. 

THE VELOCITIES OF STARS 

Knowing the angular displacements of stars due to their 
motion, and also their absolute distances from us, we can 
easily calculate their linear velocities perpendicular to the 
line of sight. These linear velocities average about 20 kilo- 
metres per second., although in some cases they are found 
to be as high as 100 kilometres per second. Our own Sun 
is moving with a velocity of 19 kilometres per second 
toward a point situated somewhere in the constellation 
Hercules. 

Although stellar velocities may seem very high from 



Island Universes 213 

man's point of view, they are rather small when compared 
with the giant distances that separate the stars scattered 
through space. If our Sun were moving directly toward 
one of its nearest neighbours, a Centauri, separated from 
us by only 4.3 light-years, it would take them about 70,000 
years to collide. But we need not fear so unpleasant an 
accident, for the stars are so thinly distributed through 
space that the chances of such a collision are negligibly 
small. In fact, it has been calculated that only a very few 
such collisions can have taken place in the whole stellar 
universe during the 2 billion years of its life. 

THE ROTATION OF THE GALAXY 

Besides the irregular random motion of the individual 
stars that form our Galaxy, astronomical observations have 
also found that this whole lenticular system is slowly rotat- 
ing around its central axis. According to the latest esti- 
mates, the rotation of the Galaxy amounts to about 7 
angular seconds per century, from which we may conclude 
that, during the whole of geological time, our Galaxy has 
made five or six complete turns. 

This may not seem like much, but one must not forget 
that, owing to the giant dimensions of the galactic lens, 
this angular rotation velocity actually corresponds to linear 
velocities on the periphery of many hundreds of kilo- 
metres per second. It is most probably this rotation that is 
responsible for the flattened shape of the Galaxy, just as 
the rotation of the earth is responsible for its ellipsoidal 
shape. 

THE AGE OF THE MILKY WAY 

If we remember that our Sun is only one of the numer- 



214 The Birth and Death of the Sun 

cms company of the galactic system, we must conclude that 
the age of the Galaxy cannot be less than the age of the 
Sun, and must amount to at least a few billions of years. 
The study of stellar motion permits us also to put an 
upper limit on the possible age of our Galaxy. It can be 
shown that, under the forces of mutual gravitational attrac- 
tion, a collection of stars moving within a limited space 
must sooner or later attain a definite distribution of veloci- 
ties that is quite analogous to the Maxwell distribution of 
gas molecules (compare Chapter II). Statistical calculations 
applied to the stars forming the system of the Milky Way 
indicate that in this case the Maxwell distribution of veloci- 
ties should be reached within a period of about 10 billion 
years. Since, according to astronomical evidence, such a 
distribution has not yet been reached by a large margin, 
we must conclude that the actual age of the stellar universe 
lies somewhere between 1.6 and 10 billion years. 

OTHER "GALAXIES" 

For a long time observational astronomy has known of 
the existence of a large number of elongated nebulous 
objects distributed more or less uniformly throughout the 
stellar sky. But only in comparatively recent times has it 
been established beyond doubt that these so-called elliptic 
or spiral nebula do not belong to our system of the Milky 
Way, but represent autonomous stellar systems, analo- 
gous to our own and situated at extremely great distances 
from it. 

The observed shapes of these remote stellar systems cor- 
respond exactly to what our own system must look like 
from the outside, according to the universally accepted 
view of Herschel. In Plates XIII, XIV, XV, and XVI we 




PLATE XIII, The central part of our nearest island universe, the spiral 
nebula in Andromeda, only about 680,000 light-years away, The stars in 
the toreground belong to our own Galaxy. (See p. 216.) (Mt. Wilson 

photograph, ) 




PLATE XIV. The spiral nebula in Coma Berenices, a distant island universe 

seen on edge. Note the ring of darker matter encircling this nebula. 

( See p. 220. ) ( Mt. Wilson photograph. ) 



Island Universes 215 

give the photographs of several stellar systems of this kind, 
taken through the powerful telescope of the Mount Wilson 
Observatory. These photographs make apparent the len- 
ticular shape of the extragalactic "nebulae" and also in- 
dicate the presence of somewhat irregular spiral arms 
winding around the central elongated bodies. Not all extra- 
galactic nebulae possess these spiral arms, however, and 
a number of them have regular shapes of more or less 
flattened ellipsoids. 



<*> 




Normal Spirals 



Barred Spirals 




FIGURE 56 
Hubble's classification of extragalactic "nebulae." 

In Figure 56 the reader will find a schematic represen- 
tation of the various observed shapes of these nebulae, 
based on the observations of the Mount Wilson astronomer, 
E. Hubble, to whom we owe most of our information 
concerning these distant island universes. When observed 
through not very strong telescopes, they seem to be continu- 
ous luminous masses of gas (hence their name "nebulae"); 
but the loo-inch telescope of the Mount Wilson Observa- 
tory reveals that the outer arms at least are actually made 
up of billions of separate stars, very similar to the mem- 



216 The Bir$iand Death of the Sun 

bers of our own Stella* system. But even in these powerful 
enlargements, the central bodies of the nebulae are not 
resolved into separate stars. Their stellar character may 
be proved only by somewhat more indirect evidence, which 
will be discussed in a following section. 

DISTANCES AND DIMENSIONS OF EXTRAGALACTIC 
NEBULA 

The distances separating us from the other island uni- 
verses are so immensely large that the ordinary astronom- 
ical methods for measuring distances (e.g., parallax esti- 
mates) completely fail us. This is why, until only rather 
recently, these objects were erroneously located somewhere 
among the stars of the Milky Way. 

The first measurements were made possible, in the case 
of the nebula in Andromeda (Plate XIIT), only after it was 
shown that its spirals consisted of numerous separate stars, 
which included among them several cepheid variables. We 
have already seen in Chapter VII that these peculiar stars 
are characterized by a regular pulsation, and that their 
pulsation periods are directly related to their luminosity. 
By observing the periods of cepheid variables in the spiral 
arms of the Andromeda Nebula, one could therefore com- 
pute their absolute luminosity; and by comparing their 
absolute luminosity with their observed brightness one 
could now estimate their distance by the application of the 
simple inverse-square law. 

All the cepheids that have been found in the Andromeda 
Nebula lead to about the same result, indicating a distance 
from us of 680,000 light-years. The geometrical dimensions 
of the Andromeda Nebula come out to about the same as, 
or slightly smaller than, those of our Milky Way, and its 



Island Universes 217 

total luminosity is estimated to equal 1.7 billion times that 
of our Sun. 

The Great Andromeda Nebula is one of the nearest 
neighbours of our galactic system, and so its tremendous 




Small Magellan'to Cloud 
Magellanic 



N.d C.7 

j ^A n<l vomeda 
Messier 32 




FIGURE 57 
Hie Galaxy and its nearest neighbours in space. 

distance gives us some inkling of the vastness of the empty 
spaces of the universe. Other neighbours include another 
spiral, two elliptic, and two irregularly shaped nebulae. 
Their respective distances and relative positions are sche- 
matically represented in Figure 57. 



218 The Birth and Death of the Sun 

In the neighbourhood of the Andromeda Nebula, ob- 
servation has revealed the presence of two "satellites" of 
this remote stellar world. These also represent large accu- 
mulations of stars, hundreds of millions of them, revolving 
around the Andromeda Nebula like a swarm of bees.* It 
would certainly be unfair if our Milky Way did not also 
have satellites of its own; and in fact it has two of them. 
Being comparatively close to us (85,000 and 95,000 light- 
years away), these can easily be seen by the naked eye. 
They were first described by the Portuguese explorer 
Ferdinand Magellan; thus, on our stellar maps we have 
two Magellanic clouds, just as on our terrestrial maps we 
have Magellanic Straits. 

Besides these near neighbours, telescopic observation 
has revealed a very large number of more distant stellar 
islands of the same kind. Varying slightly in shape and 
size, these "stellar otherworlds" are scattered throughout 
the vast spaces of the universe as far as the strongest tele- 
scopes permit us to see. According to Hubble, the large 
telescope of the Mount Wilson Observatory penetrates 
into regions of space 500 millions of light-years away, and 
finds there spiral nebulae quite similar to Andromeda's or 
our own Milky Way. The total number of the stellar 
islands that can be seen within this distance is about 100 
million, and there are probably still more, too far away even 
for the loo-inch telescope. 

EXTRAGALACTIC "NEBULsE" ARE NOT NEBULAE 

On page 215, we promised to give the reader proof of 
the statement that the so-called extragalactic "nebula" are 
not giant masses of continuous gas but consist of large 

* See Plate XVI for an example of a satellite of a spiral nebula. 




PLATE XV. Spiral nebula in Ursa Major, another distant island universe, 

seen from above. Note the clusters of stars in the arms. (See p. 220.) 

(Mt. Wilson photograph.) 




PLATE XVI. Spiral nebula in Canes Venatici, showing a satellite at tlie 
end of the lower arm. ( See p. 218. ) ( Mt. Wilson photograph, ) 



Island Universes 219 

numbers of stars similar to those of the Milky Way. As a 
matter of fact, the proof is rather simple. It is based on 
observations which show that the spectral character of the 
light emitted by these "nebulae" is very similar to that of 
the light emitted by our Sun. We know from the discussion 
in Chapter VI, therefore, that the surface temperature 
corresponding to such light emission cannot be much 
different from the surface temperature of the Sun and must 
amount to several thousand degrees. 

If these "nebulae" were really giant masses of continuous 
gas having the same surface temperature as our Sun, the 
total light emission would be proportional to their surface 
area, that is, to the square of their linear dimensions. And 
since the average diameter of these "nebulae" is about a 
billion times larger than the diameter of our Sun, we 
should expect that their total luminosity would be a billion 
billion times larger. But we have just seen that the actually 
observed luminosity of the Andromeda Nebula is consider- 
ably smaller than that, amounting to only 1.7 billion times 
that of the Sun. We must inevitably conclude, therefore, 
that the light comes not from the entire surface, but only 
from a large number of small luminous spots (see Figure 
53), the total surface area of which hardly comes to one- 
billionth of the total surface area of the nebula. This is just 
what we would expect if the "nebulae" were made up of 
separate normal stars. 

THE ROTATION OF EXTRAGALACTIC NEBULJE AND 
THE ORIGIN OF SPIRAL ARMS 

It has been mentioned that the statistical study of the 
motion of the stars of the Milky Way shows that our stellar 
system is slowly rotating around its central axis. A similar 



220 The Birth and Death of the Sun 

rotation has also been found in the case of other stellar 
systems. The Doppler effect on the two opposite ends of an 
extragalactic nebula seen on edge (see Plate XIV) always 
indicates that one end is approaching us while the other is 
receding. The Great Nebula of Andromeda, for example, 
makes one complete revolution in several hundred million 
years, spinning with about the same angular velocity as our 
Milky Way. 

It is easy to see that the rotation is responsible for the 
elliptical shape taken on by these stellar accumulations, but 
it is more than probable, too, that the spiral arms are also 
due to it. The current theory, proposed by Sir James Jeans, 
supposes that the spiral arms are formed by the material 
expelled from the very rapidly rotating equatorial plane 
of the nebulae (see Plate XV). Although Jeans's view seems 
to give a correct explanation of the origin of these interest- 
ing celestial forms, some difficulties have been encountered 
in the attempts to provide a more detailed picture of the 
process. In particular, the existence of two kinds of spiral 
arms, as indicated in Figure 56, still represents an unsolved 
problem of theoretical astronomy. 



CHAPTER XII 



The Birth of the Universe 



NEBULAE RUNNING AWAY 

THE study of the innumerable galaxies scattered 
through the vast spaces of the universe brought the 
foremost man in nebular research, Dr. E. Hubble, to an 
extremely interesting and puzzling conclusion. Measuring 
the radial velocities* of these distant stellar systems, he 
noticed that they almost all showed a definite tendency to 
recede from us rather than to approach us. 

This was not so true of the extragalactic nebulae closest 
to us, for these exhibited a rather arbitrary distribution of 
velocities, with almost as many of them approaching us as 
there were receding; in particular, the Great Andromeda 
Nebula is moving toward us at a velocity of 30 kilometres 
per second. But even in these cases the approach velocities 
are always somewhat smaller than the velocities of reces- 
sion, showing a general tendency of the stellar islands to 
increase their distance from our Galaxy. 

Also, as we go further and further out toward the more 
distant stellar islands, the recession velocity becomes greater 
and greater, completely overbalancing any contrary effect 
of the irregularity of individual systems (see Figure 58). 

* The radial velocities of these distant objects, that is, the velocities 
along the line of sight, can be directly estimated from the observed Dop- 
pier shift of the lines in their spectra. Because of the enormous distances, 
the proper motion of extragalactic nebulae, perpendicular to the line of 
sight, cannot be measured. 

221 



222 The Birth and Death of the Sun 







V 



WE 



FIGURE 58 

Extragalactic nebulas running away from us. Note the direction and the 
length of the velocities. 



The Birth of the Universe 223 

Without a single exception, all the very distant stellar 
islands are running away from the earth, and the farther 
they already are the faster they go. Hubble's measurements 
demonstrate that these recession velocities increase in direct 
proportion to the distance, varying from a few hundred 
miles per second for the neighbouring nebulae up to 
60,000 miles per second (one-third the velocity of light!) 
for the most distant but still visible ones. 

AN EXPANDING UNIVERSE 

But is it not too much to suggest that our poor little 
earth, with its handful of inquisitive astronomers, frightens 
all these giant stellar worlds to such an extent that they 
rush away in all possible directions? Does this point of 
view not represent a return to the long-abandoned Ptole- 
maic system of the world, with its geocentric conception? 

Not at all, for the extragalactic nebulae are not running 
away from our Galaxy particularly, but in reality from one 
another. If we paint a number of more or less equidistant 
dots on the surface of a rubber balloon, which we then 
blow up (Figure 59), the distance from any given dot to all 
the others will regularly increase, so that an insect sitting 
on one of the dots will receive the definite impression that 
all the other dots are "running away" from it. Moreover, 
the recession velocities of the different dots on the expand- 
ing balloon will be directly proportional to their distances 
from the insect's observation point. 

This illustration should make it quite clear that the 
phenomenon observed by Hubble may be interpreted as 
due to a general uniform expansion of the space occupied 
by the extragalactic nebula. We must point out that only 
the distances between different stellar islands, and not their 



224 The Birth and Death of the Sun 

proper geometrical dimensions, increase in this process of 
expansion. Two billion years from now, all the stellar 
islands will have about their present size, but they will be 
twice as far from one another. On the other hand, accord- 
ing to these estimates, 2 billion years ago the distances 




FIGURE 59 

The dots run away from one another when the rubber balloon is 

expanding. 

between the stellar islands must have been so small that 
the nebula constituted a practically undifferentiated col- 
lection of stars uniformly distributed throughout the uni- 
verse (Figure 60). 

We see, then, that the process in which the separate 
galaxies are formed is somewhat analogous to the process 
that has led to the formation of individual stars, but with 
the difference that, whereas the stars were formed from or- 
dinary gas consisting of molecules, the formation of galaxies 



The Birth of the Universe 225 




' " " % * 04* % * 




FIGURE 60 

Formation of island universes, through the expansion of space, from the 
uniform distribution of stars. 



226 The Birth and Death of the Sun 

corresponds to the "coagulation" of a "stellar gas," the 
particles of which are represented by separate stars. 

Before the separate galaxies were pulled away from one 
another by the progressive expansion of the universe, very 
strong gravitational interactions must have taken place 
among those giant groups of stars. In a way very similar to 
that which leads to the formation of planetary systems in 
the case of individual stars (Chapter X), such interactions 
must have supplied the newborn stellar islands with a 
certain amount of angular momentum, and may perhaps 
also have drawn from their bodies those long ribbons of 
"stellar gas*' which we now observe as their spiral arms. 

WHICH ARE OLDER: STARS OR GALAXIES? 

We have just suggested that the galaxies were formed 
from a continuously distributed multitude of stars, which 
of course presupposes that stars are older than galaxies. But 
is this correct? Why cannot one suppose, as was done by 
Sir James Jeans, that the process actually went the other 
way around? According to him, the primordial gas filling 
the universe was first broken up into giant gaseous nebulae, 
and the process of star formation began only when these 
nebulae became entirely separated from one another. What 
can be said against this alternative hypothesis? 

The question of the relative ages of stars and nebulae is 
not unlike the famous problem concerning the hen and 
the egg; it is unfortunately rather complicated, and can 
hardly be discussed without going into much too much 
detail. We shall have to content ourselves, therefore, with 
saying that, according to recent investigations by the 
author and his colleague Edward Teller, all the observa- 
tional evidence indicates that the stars already existed when 



The Birth of the Universe 227 

the process of the formation of galaxies was just beginning. 
This conclusion possesses definite advantages over Jeans's 
point of view, and permits us not only to give a satisfactory 
explanation of the processes underlying the formation of 
galaxies, but also to calculate their distances and dimen- 
sions in fair agreement with the observations. The reader 
who wishes to learn more about this important contro- 
versy in cosmogonic theory must be referred to the special 
literature devoted to these problems. 

THE EARLY STAGES OF EXPANSION AND THE 
CREATION OF RADIOACTIVE ELEMENTS 

If we now look backward in time, reversing the process 
of progressive expansion, we are obliged to conclude that, 
a long, long time ago, before the galaxies or even the sepa- 
rate stars were formed, both the density and the tempera- 
ture of the primordial gas that filled the universe must 
have been extremely high. Only with the progressive 
expansion did the density and the temperature fall suffi- 
ciently low to permit the degradation of the primordial 
gas and the formation of separate stellar bodies. Theoreti- 
cally, the densities and temperatures corresponding to the 
very earliest evolutionary stage of the expanding universe 
were higher than anything we can imagine, and . . . 

''Enough!" the reader has by now certainly exclaimed. 
"After all, this book is supposed to be based on certain 
physical realities. But all this talk of the universe's being 
formed from a superdense and superhot gas sounds very 
much like metaphysical speculation! 

There is, however, a good physical reality that strongly 
supports, if it does not actually prove the truth of, these 
seemingly metaphysical speculations about the very first 



228 The Birth and Death of the Sun 

stages of the development of our universe. This reality 
consists in the existence of the ordinary radioactive ele- 
ments, such as uranium and thorium, which are unstable 
and must, therefore, have been formed within a certain 
finite time interval from now. The life periods of these 
particular radioactive elements (4.5 billion years for 
uranium and 16 billions for thorium), together with their 
comparative abundance at the present time, strongly sug- 
gest that their origin dates no further back than a couple 
of billion years. This coincides roughly with the probable 
date of the creation of the universe from the primordial 
superdense gas, as given by the observational evidence on 
the present rate of expansion. 

Furthermore, the recent investigations of the young 
German physicist Carl von Weizsacker have definitely 
proved that the formation of such heavy elements as 
uranium and thorium could have taken place only under 
the physical conditions of enormously high densities and 
temperatures densities several billions of times larger 
than that of water and temperatures of several billions of 
degrees Centigrade. As such extreme conditions could not 
be found even in the central regions of the hottest stars, 
we are forced to look for them in the early superdense and 
superhot stages of the universe. 

These diverse facts add up to give us a clear picture, 
according to which the formation of radioactive elements 
must have taken place during the "prehistoric" stages of 
the universe. Thus, the luminous hands of our wrist- 
watches are fed by energy that was squeezed into atomic 
nuclei in the epoch preceding the formation of the stars 
and of the universe as we know it at present. 



The Birth of the Universe 229 

THE INFINITY OF SPACE 

How large was the universe when, instead of being so 
very dilute, as it is now, its density surpassed the density 
of water by a factor of many billions? Was it perhaps so 
small that it could have been squeezed in a fist, if there had 
been fists at that time? The answer to this question depends 
on whether our universe is finite or infinite. If the uni- 
verse has finite dimensions, let us say 10 times as great as 
the distance to the most remote visible nebula, its diameter 
at the time the radioactive elements were formed must 
have been only 10 times larger than the orbit of Neptune! 
But if the universe is infinite, it would also have been 
infinite no matter how strongly it was squeezed. 

The problems of the finite and infinite properties of 
space, and the closely related questions about spatial curva- 
ture, belong to the domain of the general theory of rela- 
tivity and, strictly speaking, do not enter into the scope of 
the present book.* We shall, therefore, have to be satisfied 
with the observation that, according to the most recent 
investigations, our space seems to be infinite and rapidly 
expanding into infinity. So much the better! 

* A discussion of curved spaces and the problems of spatial expansion 
may be found in the author's book, Mr. Tompkins in Wonderland (Mac- 
millan, 1940). 



Conclusion 



BEFORE closing this book and turning to a more 
amusing kind of mystery story, the reader would 
probably like to refresh his mind on its main conclusions 
and to have reviewed in a few sentences and in more strictly 
chronological order the picture it presented of the evolu- 
tion of our universe in the light of modern science. 

The story begins with space uniformly filled with an 
unbelievably hot and dense gas, in which the processes of 
the nuclear transformation of the various elements went 
on as easily as an egg is cooked in boiling water. In this 
"prehistoric" kitchen of the universe, the proportions of 
the different chemical elements the great abundance of 
iron and oxygen and the rarity of gold and silver were 
established. To this early epoch also belongs the formation 
of the I6ng-lived radioactive elements, which even at the 
present time have not yet quite decayed. 

Under the action of the tremendous pressure of this hot 
compressed gas, the universe began to expand, the density 
and the temperature of matter slowly declining all the 
while. At a certain stage of the expansion, the continuous 
gas broke up into separate irregular clouds of different 
sizes, which soon took on the regular spherical shapes of 
individual stars. The stars were still very large, much larger 
than they are now, and not very hot. But the progressive 
process of gravitational contraction diminished their diam- 
eters and raised their temperatures. The frequent mutual 
collisions among the members of this primitive stellar 
family led to the formation of numerous planetary systems, 

230 



Conclusion 231 

and in one of these encounters our earth was born. 

While the stars grew hotter and hotter, and their planets 
being small and unable to develop the high central tem- 
peratures necessary for thermonuclear reactions covered 
themselves with solid crusts, the "stellar gas" uniformly 
filling all space continued to expand, and the distances 
between the stars began to approach their present values. 

At another stage of the expansion, corresponding to the 
average concentration still to be found within individual 
galaxies, the "stellar gas" broke up into separate giant 
clouds of stars. While these stellar islands were still close to 
one another, their mutual gravitational interaction led in 
many cases to the formation of the odd-looking spiral arms 
and supplied them with a certain amount of rotational 
momentum. 

By that time most of the stars that made up these reced- 
ing stellar islands had become sufficiently hot in their 
interior regions to start off various thermonuclear reactions 
between hydrogen and other light elements. First deu- 
terium, then lithium, beryllium, and, finally, boron were 
turned into "ashes" (nuclear "ash" being the well-known 
gas helium); and, passing through these different phases of 
"red giant" development, the stars approached the main 
and longest part of their evolution. When no other light 
elements were left, the stars began to transform their 
hydrogen into helium through the catalytic action of the 
phoenix-like elements, carbon and nitrogen. Our Sun is in 
this stage now. 

But, sooner or later, all the stellar supply of hydrogen 
must be finally exhausted. The massive and luminous stars 
arrive first at this critical point in evolution, and begin to 
contract, setting free their gravitational energy. In many 



232 The Birth and Death of the Sun 

cases such contraction leads to general instability of the 
stellar bodies, and they burst, in brilliant explosions, into 
several smaller fragments. Two billion years after the "crea- 
tive process" began, we find many of these hydrogen-de- 
pleted stellar fragments; they possess extremely high den- 
sities and very low luminosities and are known as "white 
dwarfs." 

But our Sun, which uses its hydrogen supply very 
sparingly, is still going strong and plans to live ten times 
longer than it has already. It is, however, gradually be- 
coming hotter and hotter, and threatens to burn up 
everything on the surface of the earth several billion years 
hence, before it has passed through the maximum stage of 
its luminosity and has begun to contract. 

While the old and spendthrift stars die, a number of 
new stars are being formed from the gaseous material left 
over after the original process of stellar creation. But as 
time passes, most of the stars belonging to the innumerable 
stellar islands grow older and older. 

And the year 12,000,000,000 after the Creation of the 
Universe, or A.D. 10,000,000,000, will find infinite space 
sparsely filled with still receding stellar islands populated 
by dead or dying stars. 



Chronology 

of the most important steps in the solution of problems 
concerning the constitution, energy production, and evo- 
lution of stars. 

1. Contraction hypothesis (Helmholtz) 1854 

2. Discovery of radioactivity (Becquerel) 1896 

3. Classification of stars into three fundamental 
groups (Russell) 1 9 1 3 

4. The theory of stellar interiors (Eddington) 1917 etseq. 

5. Artificial transformation of elements (Ruther- 
ford) 1919 

6. White dwarfs as collapsed stars (Fowler) 1926 

7. The quantum theory of nuclear transforma- 
tions (Gamow; Gurney and Condon) 1928 

8. Thermonuclear reactions as the sources of 
stellar energy (Atkinson and Houtermans) 1929 

9. Cyclic nuclear reactions in stars (Weizsacker) 1937 
. v Evolution of stars with thermonuclear energy 

production (Gamow) 

11. Carbon-nitrogen cycle in the Sun (Bethe; 
Weizsacker) 

12. The reactions of light elements in red giants 
(Gamow and Teller) 1939 



233 



Index 



Absolute zero, temperature, 5, 23, 27 
Age 

earth, 9, 10, 11, 12 

stellar system, 11, 213, 214 

Sun, 9, 10, 11, 12 
Alchemy 

medieval, 18, 19 

modern, 67, 68 

of the Sun, 101 ff. 
Alpha (a) decay 

process of, 60 

quantum theory of, 64, 65 
Alpha (a) rays 

bombardment by, 43, 68 

discovery of, 59 

energy of, 62 
Andromeda, nebula of, 216, 217, 

218 

Aston, F. W., 45 
Atkinson, R., 102 
Atom 

chemical notion of, 21 

complexity of, 32, 33 

mass of, 30 

model of, 41 

philosophical notion of, 17, 18 

size of, 30 
Atomic mass, 30 
Atomic model, 41 
Atomic number, 45 
Atomic weight, 21 
Atom-smashers, 76-81 
Aungas ( e ), 143, 144 



Baade, W., 177 
Barrier, potential, 64, 65 
Becquerel, H., 57, 58 
Beta (j8) decay 

process of, 61 

theory of, 65, 66, 67 
Bethe, H., 112, 113 
Binaries, 131 
Blackett, P., 68, 69, 71 
Blue giants, 128 
Bohr, N., 52, 53, 55 
Brahe, Tycho, 176 
Broglie, Louis de, 54 
Brown, R., 24 
Brownian motion, 24, 25 



Canis Major. See Great Dog 
Capella, 141 

Carbon-nitrogen cycle, 113, 114, 115 
Cepheid variables. See Pulsating 

stars 

Chadwick, J., 82 
Chain-reactions, nuclear, 113 
Chamberlin, T. C., 202 
Chandrasekhar, S., 170, 171 
Chemical binding, 49, 50 
Chemical elements 

abundance of, 147, 148 

notion of, 18, 19 

periodic properties of, 48, 49 
Chemical formulae, 20 
Chemical reactions, 20, 21 
Cloud-chamber, 68, 69, 70 
"Coal sacks," 188 
Cockcroft, J., 74, 75, 76 
Collapse of matter, 160-4 
Colour of stars. See Stars 
Condon, E. U., 65 
Contraction hypothesis, 13 
Crab nebula, 185, 186 
Critchfield, C., 135 
Crushed state of matter, 162, 163, 

164 

Curie, P. and M., 59 
Cyclotron, 79, 80, 81 

Dalton, J., 21 
Decay 

a (alpha), 59 

j9 (beta), 61 

periods, 63 
Democritus, 17, 18 
Density 

red giants, 141-4 

stars, 130, 131 

Sun, 6, 7 

white dwarfs, 173 
Deuterium, 47, 48 

formation in stars, 135 
Deuterons, bombardment by, 8 
Dirac, P. A. M., 67 
Distance 

of the nebulae, 216-8 

of the stars, 123 
Doppler effect, 131, 154 
Double stars. See Binaries 



235 



236 



Index 



Dwarfs, red, 128. See also White 
dwarfs 



Earth 

age, 9, 10, 11, 12 

origin, 200-5 
Aurigae, 143, 144 
Eclipsing variables, 153 
Eddington, Sir A., 7, 111, 132, 155 
Einstein, A., 173 
Einstein shift. See Red shift 
Electromagnetic radiation, 51 
Electron 

charge, 35, 36, 37, 38 

discovery, 34, 35, 39 

mass, 39, 40, 41 

positive, 67 

Electronic shells of atoms, 48, 49, 50 
Electrostatic generator, 76, 77, 78, 

79 

Elements. See Chemical elements 
Energy 

chemical, 12, 50 

equipartition of, 25 

of molecular motion, 23, 24, 25, 26 

radiated by Sun, 4 

subatomic, 15, 62, 63 

unit of, 3 

^g, 3 
Evolution 

galaxies, 223-7 

stars, 135-40 

Sun, 116-20 
Explosions, stellar. See Novae and 

Supernovae 
Extragalactic nebulas. See Island 



Faraday, M., 34 
Fermi, E., 83, 165 
Fermi gas, 165 
Fission, nuclear, 84 
Fowler, R. H., 173 
Fraunhofer lines, 126 



Galaxy 

definition, 206 

rotation, 213, 214 

shape, 207 

size, 208, 209 
Galvani, L., 34 
Gamma (7) rays, 62 
Gamow, G., 64, 65, 74, 89, 116, 118, 
145, 152, 158, 169, 226 



Gas 

Fermi, 165 

ordinary, 22 

Gaseous nebulae, 187, 188 
Giants, blue, 128. See also Red 

giants 

Gravitational contraction, 13, 14, 15 
Gravitational instability, 197 
Great Bear (Ursa Major), 210, 211 
Great Dog (Canis Major), eye of, 

122, 123 
Gurney, R. W., 65, 90 

Hafstad, L., 76 
Hahn, O., 84, 93 
Harvard spectral classes, 126 
Heat, kinetic theory of, 22, 23 
Heavy water. See Deuterium 
Heisenberg, W., 54, 55 
Helmholtz, H. von, 13 
Herschel, Sir W., 206, 207, 214 
"Hit-and-run" hypothesis, 202, 203, 

204 

Houtermans, F., 102 
Hubble, E., 215,218,, i 

Inert gases, 50 
Ion, 35 
lonization 

by atomic projectiles, 69, 71 

thermal, 103 
Island universes 

distance, 216-8 

recession, 221-3 

size, 216-8 

types, 215 
Isotopes, 45, 46, 47, 48 

Jeans, Sir J., 196, 226 
Jupiter, as the largest stone, 167, 
168 

Kant-Laplace hypothesis, 200, 201, 

202 

Kapteyn, 208 

Kelvin scale of temperature, 27 
Kepler, J., 176 

Kinetic theory of heat, 22, 23 
Kothari, D. S., 167, 170 
Kuiper, G. P., 186 

Landau, L., 190 

Largest stone, 165, 166, 167, 168 
Lawrence, E. O., 79, 80 
"Leaking-out" theory of ct-decay, 64, 
65 



Index 



237 



Light-quanta, 53 
Light-year, 208 

Magellanic clouds, 218 
Main sequence of stars, 128 
Mass 

of atoms and molecules, 30 

of electrons, 39 

of stars, 130, 131 

of Sun. 7 
Mass-luminosity relation, 131, 132, 

l &> J 39 

Mass-radius relation, 168, 169, 170 
Maxwell, Clerk, 32 
Maxwell distribution, 30, 31, 32, 

105, 106 

Meh-Nad-Saha, 126 
Meitner, L., 84, 93 
Mendelyeev, D., 48 
Milky Way. See Galaxy 
Millikan, R. A., 35 
Molecular beams, 29 
Molecular velocities, 27, 28, 29 
Molecules 

notion of, 9 

size, 30 

Moulton, F. R., 202 
Multiplicative nuclear reactions, 
92-6 

Nebuize 

extragalactic. Sec Island universes 

gaseous, 187, 188 

planetary, 185 
Neutrons 

bombardment by, 83, 84, 91, 92 

discovery and properties of, 81, 82 

instability of, 91 
Novae 

phenomenon of, 175, 176 

physical processes in, 183, 184, 

185 
Nuclear bombardment, 43, 68, 74, 

75 7 6 83,84,91,92 
Nuclear energy, 15, 16 
Nuclear state of matter, 189, 190, 

191 
Nucleus 

atomic, 43, 44 

stellar, 190 
Number of stars in sky, 207, 208 

Opacity of stellar matter, 116, 117 
Origin 

of earth and planets, 200-5 

of elements, 227, 228 



Origin (Continued) 
or "nebulae," 223-7 
of stars, 194-8 
of white dwarfs, 198, 199, 200 

Periodicity of sunspots, 8, 9 
Periodic system of elements, 48, 49 
Period-luminosity relation, 155 
Perrin, J., 26 
Photoelectric effect, 37 
Planck, M., 52 
Planetary nebulae, 185 
Planets, origin of, 200-5 
Positive electron. See Electron, posi- 
tive 

Potential barrier. See Barrier, po- 
tential 

Prenova stage of stars, 182 
Pressure 

critical, 167 

interior of earth, 167 

interior of Jupiter, 167 

interior of Sun, 6 
Prominences, solar, 8, 9 
Protons, bombardment by, 74, 75, 76 
Prutkov, Kuzma, i 
Pulsating stars 

classification, 156, 157 

properties, 153, 154, 155 

tentative theory of, 155, 156 

Quantum 
laws, 53 
mechanics, 54 
of energy, 53 
states, 54 

Radiation 

a (alpha), 60 

ft (beta), 61 

electromagnetic, 51 

7 (gamma), 62 

of the Sun, 4, 12 

Radioactive families, 59, 60, 61, 62 
Radioactivity, discovery of, 57, 58, 

59 

Radium, 59 
Radius 

of atoms and molecules, 30 

of Galaxy, 208 

of red giants, 141-4 

of white dwarfs, 173 
Rate of thermonuclear reactions, 

107, 108 
Red dwarfs, 128 



238 



Inde* 



Red giants 
definition, 130 
energy sources of, 145-50 
evolution of, 150, 151, 152 
interior of, 144, 145 
properties, 141, 142, 143, 144 

Red shift, 173 

Relativity, theory of, 173, 229 

Resonance disintegration, 89, 90, 91 

Russell, H. N., 128 

Russell diagram, 127-31 

Rutherford, Sir E., 41, 59, 68, 73, 82 

Scattering of a-particles, 43 

Schrodinger, E., 54 

Shapley, H., 156 

Shells, electronic. See Electronic 

shells 
Sirius 

main star, 123 

satellite, 172 
Solar prominences, 8, 9 
Solar reaction, 111-5 
Solar spectra, 124, 125, 126 
Spectral classification of stars, 126, 

127 
Stars 

colours and temperatures, 124, 

i*5> '33 

diameters, 127 

distances, 123 

energy sources, 132, 133, 134, 135 

evolution, 135-40 

luminosities, 123, 124, 131, 132 

masses, 131, 132 

motion, 209-13 

number in sky, 207, 208 

origin, 194-8 
Statistics, 30, 31, 32 
Stern, O., 27 
Subatomic energy, 15, 16 
Subatomic motor, 108, 109 
Sun 

age, 9, 10, 11, 12 

density, 6, 7 

energy sources, 113, 114, 115 

evolution, 116-20 

interior, 7 

mass, j 

radiation, 4, 12 

size, 7 



Sun (Con tinned) 
surface, 8 
temperature 
central, 6 
surface, 4, 5 
Sunspots, 8, 9 
Supernovae 
discovery of, 
frequency of, 177 

Teller, E., 145, 226 
Temperature 

absolute zero, 5, 23, 27 

stars, 124, 125, 133 

Sun's interior, 6 

Sun's surface, 4, 5 
Thermionic emission, 39 
Thermonuclear reactions, 102, 103, 

104 

Thomson, Sir J. J., 39 
Transformation of elements, 67, 68, 

7*> 73> 74 

Transparency of nuclear walls, 65 
Tuve, M., 76 

Uncertainty principle, 55, 56 
Universe, expanding, 223-6 
Urey, H. C, 47 

Van de Graff, 77 
Velocity 

molecules, 27, 28, 29 

nebuLe, 221, 222, 223 

stars, 209-13 

Waves, de Broglie, 54 
Weizsacker, C. von, 113, 228 
White dwarfs % 

definition, 131 

densities, 173 

hydrogen content, 169, 170 

masses, 173 

origin, 198, 199, 200 

radii, 173 

Wilson chamber. See Cloud-cham- 
ber 

Zero, absolute. See Absolute zero 
Zero-point motion, 160 
Zwicky, F., 177, 178, 179, 189