_Exploring the Atom_
So far our exploration of the universe has been in the direction from
man to bigger things than man; we have been exploring ranges of space
which dwarf man and his home in space into utter insignificance. Yet
we have explored only about half the total range of the universe;
an almost equal range awaits exploration in the direction of the
infinitely small. We appreciate only half of the infinite richness of
the world around us until we extend our survey down to the smallest
units of matter. This survey has been first the task, and now the
brilliant achievement, of modern physics.
It may perhaps be asked why an account of modern astronomy should
concern itself with this other end of the universe. The answer is
that the stars are something more than huge inert masses; they are
machines in action, generating and emitting the radiation by which we
see them. We shall best understand their mechanism by studying the ways
in which radiation is generated and emitted on earth, and this takes
us right into the heart of modern atomic physics. In the present book
we naturally cannot attempt to cover the whole of this new field of
knowledge; we shall concern ourselves only with those parts which are
important for the interpretation of astronomical results.
ATOMIC THEORY
As far back as the fifth century before Christ, Greek philosophy was
greatly exercised by the question of whether in the last resort the
ultimate substance of the universe was continuous or discontinuous. We
stand on the sea-shore, and all around us see stretches of sand which
appear at first to be continuous in structure, but which a closer
examination shews to consist of separate hard particles or grains. In
front rolls the ocean, which also appears at first to be continuous in
structure, and this we find we cannot divide into grains or particles
no matter how we try. We can divide it into drops, but then each drop
can be subdivided into smaller drops, and there seems to be no reason,
on the face of things, why this process of subdivision should not be
continued for ever. The question which agitated the Greek philosophers
was, in effect, whether the water of the ocean or the sand of the
sea-shore gave the truest picture of the ultimate structure of the
substance of the universe.
The school of Democritus, Leucippus and Lucretius believed in the
ultimate discontinuity of matter; they taught that any substance, after
it had been subdivided a sufficient number of times, would be found
to consist of hard discrete particles which did not admit of further
subdivision. For them the sand gave a better picture of ultimate
structure than the water, because, or so they thought, sufficient
subdivision would cause the water to display the granular properties
of sand. And this intuitional conjecture is amply confirmed by modern
science.
The question is, in effect, settled as soon as a thin layer of a
substance is found to shew qualities essentially different from those
of a slightly thicker layer. A layer of yellow sand swept uniformly
over a red floor will make the whole floor appear yellow if there is
enough sand to make a layer at least one grain thick. If, however,
there is only half this much sand, the redness of the floor inevitably
shews through; it is impossible to spread sand in a uniform layer only
half a grain thick. This sudden change in the properties of a layer of
sand is of course a consequence of the granular structure of sand.
Similar changes are found to occur in the properties of thin layers of
liquid. A teaspoonful of soup will cover the bottom of a soup plate,
but a single drop of soup will only make an untidy splash. In some
cases it is possible to measure the exact thickness of layer at which
the properties of liquids begin to change. In 1890 Lord Rayleigh found
that thin films of olive oil floating on water changed their properties
entirely as soon as the thickness of the film was reduced to below a
millionth of a millimetre (or a 25,000,000th part of an inch). The
obvious interpretation, which is confirmed in innumerable ways, is that
olive oil consists of discrete particles—analogous to the “grains” in a
pile of sand—each having a diameter somewhere in the neighbourhood of a
25,000,000th part of an inch.
Every substance consists of such “grains.” They are called molecules,
and the familiar properties of matter are those of layers many
molecules thick; the properties of layers less than a single molecule
thick are known only to the physicist in his laboratory.
MOLECULES
How are we to break up a piece of substance into its ultimate grains,
or molecules? It is easy for the scientist to say that, by subdividing
water for long enough, we shall come to grains which cannot be
subdivided any further; the plain man would like to see it done.
Fortunately the process is one of extreme simplicity. Take a glass of
water, apply gentle heat underneath, and the water begins to evaporate.
What does this mean? It means that the water is being broken up into
its separate ultimate grains or molecules. If the glass of water
could be placed on a sufficiently sensitive spring balance, we should
see that the process of evaporation does not proceed continuously,
layer after layer, but jerkily, molecule by molecule. We should find
the weight of the water changing by jumps, each jump representing
the weight of a single molecule. The glass may contain any integral
number of molecules but never fractional numbers—if the fractions
of a molecule exist, at any rate they do not come into play in the
evaporation of a glass of water.
THE GASEOUS STATE. The molecules which break loose from the surface
of the water as it evaporates form a gas—water-vapour or steam. A
gas consists of a vast number of molecules which fly about entirely
independently of one another, except at the rare instants at which two
collide, and so interfere with each other’s motion. The extent to which
the molecules interfere with one another must obviously depend on their
sizes; the larger they are, the more frequent their collisions will be,
and the more they will interfere with one another’s motion. Actually
the extent of this interference provides the best means of estimating
the sizes of molecules. They prove to be exceedingly small, being for
the most part about a hundred-millionth of an inch in diameter, and,
as a general rule, the simpler molecules have the smaller diameters,
as we should expect. The molecule of water has a diameter of 1·8
hundred-millionths of an inch (4·6 × 10⁻⁸ cms.), while that of the
simpler hydrogen molecule is only just over a hundred-millionth of
an inch (2·7 × 10⁻⁸ cms.). The fact that a number of different lines
of investigation all attribute the same diameters to these molecules
provides an excellent proof of the reality of their existence.
As molecules are so exceedingly small, they must also be exceedingly
numerous. A pint of water contains 1·89 × 10⁴⁵ molecules, each weighing
1·06 × 10⁻² ounces. If these molecules were placed end to end, they
would form a chain capable of encircling the earth over 200 million
times. If they were scattered over the whole land surface of the earth,
there would be nearly 100 million molecules to every square inch of
land. If we think of the molecules as tiny seeds, the total amount of
seed needed to sow the whole earth at the rate of 100 million molecules
to the square inch could be put into a pint pot.
These molecules move with very high speeds; in the ordinary air of
an ordinary room, the average molecular speed is about 500 yards a
second. This is roughly the speed of a rifle-bullet, and is rather more
than the ordinary speed of sound. As we are familiar with this latter
speed from everyday experience, it is easy to form some conception of
molecular speeds in a gas. It is not a mere accident that molecular
speeds are comparable with the speed of sound. Sound is a disturbance
which one molecule passes on to another when it collides with it,
rather like relays of messengers passing a message on to one another,
or Greek torch-bearers handing on their lights. Between collisions the
message is carried forward at exactly the speed at which the molecules
travel. If these all travelled with precisely the same speed and in
precisely the same direction, the sound would of course travel with
just the speed of the molecules. But many of them travel on oblique
courses, so that although the average speed of individual molecules in
ordinary air is about 500 yards a second, the net forward velocity of
the sound is only about 370 yards a second.
At high temperatures the molecules may have even greater speeds; the
molecules of steam in a boiler may move at 1000 yards a second.
It is the high speed of molecular motion that is responsible for the
great pressure exerted by a gas; any surface in contact with the gas
is exposed to a hail of molecules each moving with the speed of a
rifle-bullet. For instance, the piston in a locomotive cylinder is
bombarded by about 14 × 10²⁸ molecules every second. This incessant
fusillade of innumerable tiny bullets urges the piston forward in the
cylinder, and so propels the train. With each breath we take, swarms of
millions of millions of millions of molecules enter our bodies, each
moving at about 500 yards a second, and nothing but their incessant
hammering on the walls of our lungs keeps our chests from collapsing.
Perhaps the best general mental picture we can form of a gas is that of
an incessant hail of shot or rifle-bullets flying indiscriminately in
all directions, and running into one another at frequent intervals. In
ordinary air each molecule collides with some other molecule about 3000
million times every second, and travels an average distance of about
1/160,000 inch between successive collisions. If we compress a gas to
a greater density, more molecules are crowded into a given space, so
that collisions become more frequent and the molecules travel shorter
distances between collisions. If, on the contrary, we reduce the
pressure of the gas, and so lessen its density, collisions become less
frequent and the distance of travel of a molecule between successive
collisions—the “free-path” as it is called—is increased. In the lowest
vacua which are at present obtainable in the laboratory, a molecule
can travel over 100 yards without colliding with any other molecule,
although there are still 600,000 million molecules to the cubic inch.
Under astronomical conditions still lower vacua may occur. In some
nebulae molecules of gas may travel millions of miles without a
collision, so few are the molecules to a given volume of space.
It might be thought that the flying molecules would soon be brought to
rest by their collisions; rifle-bullets undoubtedly would, but not the
molecule bullets of a gas, for reasons now to be explained.
ENERGY. The amount of the charge of powder used to fire a rifle-bullet
gives a measure of the “energy of motion” which is imparted to the
bullet. To fire a bullet of double weight requires twice as much
powder, because the energy of motion of a bullet, or indeed of any
other moving body, is proportional to its weight. But to fire the same
bullet with double speed does not merely require double the charge of
powder. Four times as much powder is needed, because the energy of
motion of a moving body is proportional to the _square_ of its speed.
The experienced motorist is familiar with this; if our brakes stop
our car in 20 feet when we are travelling 20 miles an hour, they will
not stop it in 40 feet when travelling at 40 miles an hour; we need
80 feet. Double speed requires four times the distance to pull up in,
because double speed represents fourfold energy of motion. In general,
the energy of motion of any moving body whatever is proportional both
to the weight of the body and to the square of its speed[8].
[8] This is expressed in the mathematical formula _½mv²_ for the energy
of motion of a body of weight _m_ moving with a speed _v_. If _m_ is
measured in grammes, and _v_ in centimetres per second, the energy of
motion of the body is said to be _½mv²_ “ergs.” Thus an “erg” is the
energy of motion of a body of 2 grammes weight (so that _½m_= 1) moving
with a speed of one centimetre a second. As an example, the energy of
an express train of 300 tons’ weight (3 × 10⁸ gms.) moving at 60 miles
an hour (2682 cms. a second) is 1079 × 10¹⁴ ergs; a cannon-ball or
shell weighing a ton and moving at 1520 feet a second has precisely the
same energy.
One of the great achievements of nineteenth-century physics was to
establish the general principle known as the “conservation of energy.”
Energy can exist in a number of forms, and can change about almost
endlessly from one form to another, but it can never be utterly
destroyed. The energy of a moving body is not lost when the body is
brought to rest, it merely takes some other form. When a bullet is
brought to rest by hitting a target, part of its energy of motion goes
into heating up the target, and part into heating up, or perhaps even
melting, the bullet. In its new guise of heat, there is just as much
energy as there was in the original motion of the bullet.
In accordance with the same principle, energy cannot be created; all
existing energy must have existed from all time, although possibly
in some form entirely different from its present form. For instance,
gunpowder contains a large amount of energy stored up in the form
of chemical energy; we have to take precautions to prevent this
bottled-up energy suddenly breaking free and doing damage, as, for
instance, by exploding the vessel in which it is contained, kicking
things up into the air, and so forth. A rifle is in effect a device for
setting free the energy contained in a measured charge of gunpowder,
and directing as much as possible of it into the form of energy of
motion of a bullet. When we fire a bullet at a target, a specified
amount of energy (determined by the charge of powder we have used)
is transformed from chemical energy, residing in the powder, first
into energy of motion, residing in the bullet (and to a minor degree
in the recoil of the rifle), and then finally into heat-energy,
residing partly in the spent bullet and partly in the target. Here
we have energy taking three different forms in rapid succession. All
the life of the universe may be regarded as manifestations of energy
masquerading in various forms, and all the changes in the universe
as energy running about from one of these forms to the other, but
always without altering its total amount. Such is the great law of
conservation of energy.
Among the commoner forms of energy may be mentioned electric energy,
as exemplified by the energy of a charged accumulator or of a
thundercloud: mechanical energy, as exemplified in the coiled spring
of a watch or the raised weight of a clock: chemical energy, as
exemplified by the energy stored up in gunpowder or in coal, wood and
oil: energy of motion, as exemplified by the motion of a bullet, and
finally heat-energy, which, as we have seen, is exemplified by the heat
which appears when the motion of a rifle-bullet is checked.
HEAT. Let us examine further into heat as a possible form of energy.
When we want to warm a room, we light a fire and set free some of the
chemical energy which is stored up in coal or wood, or we turn on an
electric heater and let the electric current transport to us some of
the energy which is being set free by the burning of coal in a distant
power-station. But what, in the last resort, is heat, and how does it
come to be a mode of energy?
Heat, whether of a gas, a liquid or a solid, is merely the energy of
motion of individual molecules. When we heat up the air of a room
we simply make its molecules move faster, and the total heat of the
substance is the total energy of all the molecules of which it is
composed. In pumping up a bicycle tyre, we drive the piston of the
pump forward in opposition to the impact of innumerable millions of
molecules of air inside the pump. In kicking the opposing molecules out
of its way, the piston increases their speed of motion. The resulting
increase in the energy of motion of the molecules is simply an increase
of heat. We could verify this by inserting a thermometer, or, still
more simply, by putting our hand on the pump; it feels hot.
The molecules of a solid are not possessed of much energy, and so do
not move very fast—so slowly indeed that they seldom change their
relative positions, the neighbouring molecules gripping them so firmly
that their feeble energy of motion cannot extricate them. If we warm
the solid up, the molecules acquire more energy, and so begin to move
faster. After a time they are moving with such speeds that they can
laugh at the restraining pulls from their neighbours; each molecule has
enough energy of motion to go where it pleases, and we have a crowd
of molecules moving freely as independent units, jostling one another
and pushing their way past one another; the substance has assumed the
liquid state. To make the picture definite, ice has melted and become
water; the frozen grip is relaxed, and the molecules flow freely past
one another. Each still exerts forces on its neighbours, but these
are no longer strong enough to preclude all motion. Heat the liquid
further, thus further increasing the energy of motion of the molecules,
and these begin to break loose entirely from their bonds and fly about
freely in space forming a gas or vapour. If we go on supplying heat,
the whole substance will in time assume the gaseous state. Heating the
gas still further merely causes the molecule-bullets to fly faster; it
increases their energy of motion.
The average energy of motion of the molecules in a gas is proportional
to the temperature of the gas—indeed, this is the way in which
temperature is defined. The temperature must not, however, be measured
on the Fahrenheit or Centigrade scale in ordinary use, but on what is
called the “absolute” scale, which has its zero at -273° Centigrade, or
-469° Fahrenheit. This “absolute” zero, being the temperature of a body
which has no further heat to lose, is the lowest temperature possible.
We can approach to within about one degree of it in the laboratory, and
find that it freezes air, hydrogen and even helium, the most refractory
gas of all, solid. A thermometer placed out in interstellar space, far
from any star, would probably shew a temperature of only about four
degrees above absolute zero, while still lower temperatures must be
reached out beyond the limits of the galactic system.
MOLECULAR COLLISIONS. We may now try to picture a collision between
two molecule-bullets in a gas. Lead bullets colliding on a battlefield
would probably change most of their energy of motion into heat-energy;
they would become hotter, or perchance even melt. But how can the
molecule-bullets transform their energy of motion into heat-energy?
For them heat and energy of motion are not two different forms of
energy, they are one and the same thing; their heat is their energy
of motion. The total energy must be conserved, and there is no
new disguise that it can assume. So it comes about that when two
molecule-bullets collide, the most that can happen is that they may
exchange a certain amount of energy of motion. If their energies of
motion before collision were, say, 7 and 5 respectively, their energies
after collision may be 6 and 6, or 8 and 4, or 9 and 3, or any other
combination which adds up to 12.
It is the same at every collision; energy can neither be lost nor
transformed, and so the bullets on the molecular battlefield go on
flying for ever, happily hitting only one another, and doing no harm
to one another when they hit. Their energies of motion go up and down,
down and up, according as they make lucky hits or the reverse, but the
most they have to fear are fluctuations and never total loss of energy;
their motion is perpetual.
ATOMS
In the gaseous state, each separate molecule retains all the chemical
properties of the solid or liquid substance from which it originated;
molecules of steam, for instance, moisten salt or sugar, or combine
with thirsty substances such as unslaked lime or potassium chloride,
just as water does.
Is it possible to break up the molecules still further? Lucretius
and his predecessors would, of course, have said: “No.” A simple
experiment, which, however, was quite beyond their range, will speedily
shew that they were wrong.
On sliding the two wires of an ordinary electric bell circuit into a
tumbler of water, down opposite sides, bubbles of gas will be found to
collect on the wires, and chemical examination shews that the two lots
of gas have entirely different properties. They cannot, then, both be
water-vapour, and in point of fact neither of them is; one proves to
be hydrogen and the other oxygen. There is found to be twice as much
hydrogen as oxygen, whence we conclude that the electric current has
broken up each molecule of water into two parts of hydrogen and one of
oxygen. These smaller units into which a molecule is broken are called
“atoms.” Each molecule of water consists of two atoms of hydrogen (H)
and one atom of oxygen (O); this is expressed in its chemical formula
H₂O.
All the innumerable substances which occur on earth—shoes, ships,
sealing-wax, cabbages, kings, carpenters, walruses, oysters, everything
we can think of—can be analysed into their constituent atoms, either
in this or in other ways. It might be thought that a quite incredible
number of different kinds of atoms would emerge from the rich variety
of substances we find on earth. Actually the number is quite small. The
same atoms turn up again and again, and the great variety of substances
we find on earth result, not from any great variety of atoms entering
into their composition, but from the great variety of ways in which
a few types of atoms can be combined—just as in a colour-print three
colours can be combined so as to form almost all the colours we meet in
nature, not to mention other weird hues such as never were on land or
sea.
Analysis of all known terrestrial substances has, so far, revealed only
90 different kinds of atoms. Probably 92 exist, there being reasons
for thinking that two, or possibly even more, still remain to be
discovered. Even of the 90 already known, the majority are exceedingly
rare, most common substances being formed out of the combinations of
about 14 different atoms, say hydrogen (H), carbon (C), nitrogen (N),
oxygen (O), sodium (Na), magnesium (Mg), aluminium (Al), silicon (Si),
phosphorus (P), sulphur (S), chlorine (Cl), potassium (K), calcium
(Ca), and iron (Fe).
In this way, the whole earth, with its endless diversity of substances,
is found to be a building built of standard bricks—the atoms. And
of these only a few types, about 14, occur at all abundantly in the
structure, the others appearing but rarely.
SPECTROSCOPY. Just as a bell struck with a hammer emits a
characteristic note, so every atom put in a flame or in an electric
arc or discharge-tube, emits a characteristic light. When Newton
passed sunlight through a prism, he found it to be a blend of all the
colours of the rainbow. In the same way the modern spectroscopist, with
infinitely more refined instruments, can analyse any light into all
the constituent colours which enter into its composition. The rainbow
of colours so produced—the “spectrum”—is crossed by the pattern of
light or dark lines or bands which the astronomer utilises to determine
the speeds of recession or approach of the stars. From an examination
of this pattern the skilled spectroscopist can at once announce the
type of atom from which the light emanates, so much so that one of
the most delicate tests for the presence of certain substances is the
spectroscopic test.
This spectroscopic method of analysis is by no means confined to
terrestrial substances. In 1814 Fraunhofer repeated Newton’s analysis
of sunlight, and found its spectrum to be crossed by certain dark
lines, still known as Fraunhofer lines. The spectroscopist has no
difficulty in interpreting these dark lines; they indicate the presence
in the sun of the common terrestrial elements, hydrogen, sodium,
calcium, and iron. For reasons which we shall see later (p. 125 below),
the atoms of these substances drink up the light of precisely those
colours which the Fraunhofer lines shew to be absent from the solar
spectrum. This spectrum is now known to be incomparably more intricate
than Fraunhofer thought, but practically all the lines which occur in
it can be assigned to atoms known on earth, and the same is true of
the spectra of all the stars in the sky. It is tempting to jump to the
generalisation that the whole universe is built solely of the 90 or 92
types of atoms found on earth, but at present there is no justification
for this. The light we receive from the sun and stars comes only from
the outermost layers of their surfaces, and so conveys no information
at all as to the types of atoms to be found in the stars’ interiors.
Indeed we have no knowledge of the types of atoms which occur in the
interior of our own earth.
THE STRUCTURE OF THE ATOM. Until quite recently, atoms were regarded
as the permanent bricks of which the whole universe was built. All
the changes of the universe were supposed to amount to nothing more
drastic than a re-arrangement of permanent indestructible atoms; like a
child’s box of bricks, these built many buildings in turn. The story of
twentieth-century physics is primarily the story of the shattering of
this concept.
It was towards the end of the last century that Crookes, Lenard, and,
above all, Sir J. J. Thomson first began to break up the atom. The
structures which had been deemed the unbreakable bricks of the universe
for more than 2000 years, were suddenly shown to be very susceptible to
having fragments chipped off. A mile-stone was reached in 1895, when
Thomson shewed that these fragments were identical, no matter what type
of atom they came from; they were of equal weight and they carried
equal charges of negative electricity. On account of this last property
they were called “electrons.” The atom cannot, however, be built up of
electrons and nothing else, for as each electron carries a negative
charge of electricity, a structure which consisted of nothing but
electrons would also carry a negative charge. Two negative charges of
electricity repel one another, as also do two positive charges, while
two charges, one of positive and one of negative electricity, attract
one another. This makes it easy to determine whether any body or
structure carries a positive or a negative charge of electricity, or no
charge at all. Observation shews that a complete atom carries no charge
at all, so that somewhere in the atom there must be a positive charge
of electricity, of amount just sufficient to neutralise the combined
negative charges of all the electrons.
In 1911 experiments by Sir Ernest Rutherford and others revealed
the architecture of the atom. As we shall soon see (p. 112 below),
nature herself provides an endless supply of small particles charged
with positive electricity, and moving with very high speeds, in the
α-particles shot off from radio-active substances. Rutherford’s method
was in brief to fire these into atoms and observe the result. And the
surprising result he obtained was that the vast majority of these
bullets passed straight through the atom as though it simply did not
exist. It was like shooting at a ghost.
Yet the atom was not all ghostly. A tiny fraction—perhaps one in
10,000—of the bullets were deflected from their courses as if they
had met something very substantial indeed. A mathematical calculation
shewed that these obstacles could only be the missing positive charges
of the atoms.
A detailed study of the paths of these projectiles proved that the
whole positive charge of an atom must be concentrated in a single very
small space, having dimensions of the order of only a millionth of a
millionth of an inch. In this way, Rutherford was led to propound the
view of atomic structure which is generally associated with his name.
He supposed the chemical properties and nature of the atom to reside
in a weighty, but excessively minute, central “nucleus” carrying a
positive charge of electricity, around which a number of negatively
charged electrons described orbits. It was of course necessary to
suppose the electrons to be in motion in the atom, otherwise the
attraction of positive for negative electricity would immediately draw
them into the central nucleus—just as gravitational attraction would
cause the earth to fall into the sun, were it not for the orbital
motion of the former. In brief Rutherford supposed the atom to be
constructed like the solar system, the heavy central nucleus playing
the part of the sun and the electrons acting the parts of the planets.
The speeds with which these electrons fly round their tiny orbits are
terrific. The average electron revolves around its nucleus several
thousand million million times every second, with a speed of hundreds
of miles a second. Thus the smallness of their orbits does not prevent
the electrons moving with higher orbital speeds than the planets, or
even the stars themselves.
By clearing a space around the central nucleus, and so preventing other
atoms from coming too near to it, these electronic orbits give size to
the atom. The volume of space kept clear by the electrons is enormously
greater than the total volume of the electrons; roughly, the ratio of
volumes is that of the battlefield to the bullets. The atom, with a
radius of about 2 × 10⁻⁸ cms., has about 100,000 times the diameter,
and so about a thousand million million times the volume, of a single
electron, which has a radius of only about 2 × 10⁻¹³cms. The nucleus,
although it generally weighs 3000 or 4000 times as much as all the
electrons in the atom together, is at most comparable in size with, and
may be even smaller than, a single electron.
We have already commented on the extreme emptiness of astronomical
space. Choose a point in space at random, and the odds against its
being occupied by a star are enormous. Even the solar system consists
overwhelmingly of empty space; choose a spot inside the solar system
at random, and there are still immense odds against its being occupied
by a planet or even by a comet, meteorite or smaller body. And now we
see that this emptiness extends also to the space of physics. Even
inside the atom we choose a point at random, and the odds against there
being anything there are immense; they are of the order of at least
millions of millions to one. We saw how six specks of dust inside
Waterloo Station represented—or rather over-represented—the extent to
which space was crowded with stars. In the same way a few wasps—six for
the atom of carbon—flying around in Waterloo Station will represent
the extent to which the atom is crowded with electrons—all the rest is
emptiness. As we pass the whole structure of the universe under review,
from the giant nebulae and the vast interstellar and internebular
spaces down to the tiny structure of the atom, little but vacant space
passes before our mental gaze. We live in a gossamer universe; pattern,
plan and design are there in abundance, but solid substance is rare.
ATOMIC NUMBERS. The number of electrons which fly round in orbits in
an atom is called the “atomic number” of the atom. Atoms of all atomic
numbers from 1 to 92 have been found, except for two missing numbers
85 and 87. As already mentioned, it is highly probable that these also
exist, and that there are 92 “elements” whose atomic numbers occupy the
whole range of atomic numbers from 1 to 92 continuously.
The atom of atomic number unity is of course the simplest of all. It
is the hydrogen atom, in which a solitary electron revolves around
a nucleus whose charge of positive electricity is exactly equal in
amount, although opposite in sign, to the charge on the negative
electron.
Next comes the helium atom of atomic number 2, in which two electrons
revolve about a nucleus which has four times the weight of the hydrogen
nucleus, although carrying only twice its electric charge. After this
comes the lithium atom of atomic number 3, in which three electrons
revolve around a nucleus having six times the weight of the hydrogen
atom and three times its charge. And so it goes on, until we reach
uranium, the heaviest of all atoms known on earth, which has 92
electrons describing orbits about a nucleus of 238 times the weight of
the hydrogen nucleus.
RADIO-ACTIVITY
While it was still engaged in breaking up the atom into its
component factors, physical science was beginning to discover that
the nuclei themselves were neither permanent nor indestructible.
In 1896, Becquerel had found that various substances containing
uranium possessed the remarkable property, as it then appeared,
of spontaneously affecting photographic plates in their vicinity.
This observation led to the discovery of a new property of matter,
namely radio-activity. All the results obtained from the study of
radio-activity in the few following years were co-ordinated in the
hypothesis of “spontaneous disintegration” which Rutherford and Soddy
advanced in 1903. According to this hypothesis in its present form,
radio-activity indicates a spontaneous break-up of the nuclei of the
atoms of radio-active substances. These atoms are so far from being
permanent and indestructible that their very nuclei crumble away with
the mere lapse of time, so that what was once the nucleus of a uranium
atom is transformed, after sufficient time, into the nucleus of a lead
atom.
The process of transformation is not instantaneous; it proceeds
gradually and by distinct stages. During its progress, three types of
product are emitted, which are designated α-rays, β-rays, and γ-rays.
These were originally described as rays because they have the power
of penetrating through a certain thickness of air, metal, or other
substance. Their true nature was discovered later. It is well known
that magnetic forces such as, for instance, occur in the space between
the poles of a magnet, cause a moving particle charged with electricity
to deviate from a straight course; it deviates in one direction or the
other according as it is charged with positive or negative electricity.
On passing the various rays emitted by radio-active substances through
the space between the poles of a powerful magnet, the α-rays were found
to consist of particles charged with positive electricity, and the
β-rays to consist of particles charged with negative electricity. But
the most powerful magnetic forces which could be employed failed to
cause the slightest deviation in the paths of the γ-rays, from which
it was concluded that either the γ-rays were not material particles
at all, or that, if they were, they carried no electric charges. The
former of these alternatives was subsequently proved to be the true one.
α-PARTICLES. The positively charged particles which constitute α-rays
are generally described as α-particles. In 1909 Rutherford and Royds
allowed α-particles to penetrate through a thin glass wall of less than
a hundredth of a millimetre thickness into a chamber from which they
could not escape—a sort of mouse-trap for α-particles. They found that
so long as the number of α-particles in the vessel went on increasing,
an accumulation of helium was forming. In this way it was established
that the positively charged α-particles are simply nuclei of helium
atoms.
These particles move with enormous speeds, which depend upon the nature
of the radio-active substance from which they have been shot out.
The fastest of all, those emitted by Thorium Cʹ, move with a speed
of 12,800 miles a second; even the slowest, those from Uranium 1,
have a speed of 8800 miles a second, which is about 30,000 times the
ordinary molecular velocity in air. Particles moving with these speeds
knock all ordinary molecules out of their way; this explains the great
penetrating power of the α-rays.
β-PARTICLES. By examining their motion under magnetic forces, the
β-rays were found to consist of negatively charged electrons, exactly
similar to those which revolve orbitally in all atoms. As an α-particle
carries a positive charge equal in amount to that of two electrons,
an atom which has ejected an α-particle is left with a deficiency of
positive charge, or what comes to the same thing, with a negative
charge, equal to that of two electrons. Consequently it is natural,
and indeed almost inevitable, that the ejections of α-particles should
alternate with an ejection of negatively charged electrons, so that
the balance of positive and negative electricity in the atom may be
maintained. The β-particles move with even greater speeds than the
α-particles, many approaching to within a few per cent. of the velocity
of light (186,000 miles a second).
[Illustration: PLATE XIII _C. T. R. Wilson_
The tracks of α- and β-particles]
One of the most beautiful devices known to physical science, the
invention of Professor C. T. R. Wilson, makes it possible to study the
motions of the α- and β-particles as they thread their way through
a gas, colliding with its molecules on their way. A chamber through
which the particles are made to travel is filled with water-vapour in
such a condition that the passage of an electrically charged particle
leaves behind it a trail of condensations which can be photographed.
As an example, Plate XIII shews a photograph taken by Professor Wilson
himself, in which the trails of both α- and β-particles appear on
the same plate. As the α-particles weigh about 7400 times as much as
the β-particles, they naturally create more disturbance in the gas,
and so leave broader and more pronounced tracks; also they pursue
a comparatively straight course while the lighter β-particles are
deflected from their courses by many of the molecules they meet. The
plate shews four α-particle tracks and one (much fainter) β-ray track.
The knobby-looking projections which may be seen on one of the α-ray
tracks are of interest; they represent the short paths of electrons
knocked out of atoms by the passage of the α-particle[9].
[9] These were called δ-rays by Bumstead.
γ-RAYS. The γ-rays are not material particles at all; they prove to be
merely radiation of a very special kind, which we shall now discuss.
RADIATION
Disturb the surface of a pond with a stick and a series of ripples
starts from the stick and travels, in a series of ever-expanding
circles, over the surface of the pond. As the water resists the motion
of the stick, we have to work to keep the pond in a state of agitation.
The energy of this work is transformed, in part at least, into the
energy of the ripples. We can see that the ripples carry energy about
with them, because they cause a floating cork or a toy boat to rise
up against the earth’s gravitational pull. Thus the ripples provide a
mechanism for distributing over the surface of the pond the energy that
we put into the pond through the medium of the moving stick.
Light and all other forms of radiation are analogous to water-ripples
or waves, in that they distribute energy from a central source. The
sun’s radiation distributes through space the vast amount of energy
which is generated inside the sun. We hardly know whether there is any
actual wave-motion in light or not, but we know that both light and all
other types of radiation are propagated in such a form that they have
some of the properties of a succession of waves.
We have seen how the different colours of light which in combination
constitute sunlight can be separated out by passing the light through
a prism. An alternative instrument, the diffraction grating, analyses
light into its constituent wave-lengths[10], and these are found to
correspond to the different colours of the rainbow. This shews that
different colours of light represent different wave-lengths, and at
the same time provides a means of measuring the actual wave-lengths
of light of different colours. These prove to be very minute. The
reddest light we can see, which is that of longest wave-length, has a
wave-length of only 3/100,000 inch (7·5 × 10⁻⁵ cms.); the most violet
light we can see has a wave-length only half of this, or 0·000015 inch.
Light of all colours travels with the same uniform speed of 186,000
miles, or 3 × 10¹⁰ centimetres, a second. The number of waves of red
light which pass any fixed point in a second is accordingly no fewer
than four hundred million million. This is called the “frequency” of
the light. Violet light has the still higher frequency of eight hundred
million million; when we see violet light, eight hundred million
million waves of light enter our eyes each second.
[10] The wave-length in a system of ripples is the distance from the
crest of one ripple to that of the next, and the term may be applied to
all phenomena of an undulatory nature.
The spectrum of analysed sunlight appears to the eye to stretch from
red light at one end to violet light at the other, but these are not
its true limits. If certain chemical salts are placed beyond the violet
end of the visible spectrum, they are found to shine vividly, shewing
that even out here energy is being transported, although in invisible
form.
Regions of invisible radiation stretch indefinitely from both ends of
the visible spectrum. From one end—the red—we can pass continuously
to waves of the type used for wireless transmission, which have
wave-lengths of the order of hundreds, or even thousands, of yards.
From the violet end, we pass through waves of shorter and ever
shorter wave-length—all the various forms of ultra-violet radiation.
At wave-lengths of from about a hundredth to a thousandth of the
wave-length of visible light, we come to the familiar X-rays, which
penetrate through inches of our flesh, so that we can photograph
the bones inside. Far out even beyond these, we come to the type of
radiation which constitutes the γ-rays, its wave-length being of the
order of 1/10,000,000,000 inch, or only about a hundred-thousandth part
of the wave-length of visible light. Thus the γ-rays may be regarded as
invisible radiation of extremely short wave-length. We shall discuss
the exact function they serve later. For the moment let us merely
remark that in the first instance they served the extremely useful
function of fogging Becquerel’s photographic plates, thus leading to
the detection of the radio-active property of matter.
Thus we see that the break-up of a radio-active atom may be compared
to the discharge of a gun; the α-particle is the shot fired, the
β-particles are the smoke, and the γ-rays are the flash. The atom
of lead which finally remains is the unloaded gun, and the original
radio-active atom, of uranium or what not, was the loaded gun. And
the special peculiarity of radio-active guns is that they go off
spontaneously and of their own accord. All attempts to pull the trigger
have so far failed, or at least have led to inconclusive results; we
can only wait, and the gun will be found to fire itself in time.
[Illustration: PLATE XIV Fig. 1]
[Illustration: _P. M. S. Blackett_ Fig. 2
Collisions of α-particles with Nitrogen Atoms
In fig. 1 the α-particle merely rebounds from a nitrogen atom. In fig.
2 it drives out a proton and then joins itself to the atom]
ATOMIC NUCLEI
With the unimportant exceptions of potassium and rubidium (of atomic
numbers 19 and 37), the property of radio-activity occurs only in
the most complex and massive of atoms, being indeed confined to
those of atomic numbers above 83. Yet, although the lighter atoms
are not liable to spontaneous disintegration in the same way as the
heavy radio-active atoms, their nuclei are of composite structure,
and can be broken up by artificial means. In 1920, Rutherford, using
radio-active atoms as guns, fired α-particles at light atoms and found
that direct hits broke up their nuclei. There is, however, found to
be a significant difference between the spontaneous disintegration of
the heavy radio-active atoms, and the artificial disintegration of the
light atoms; in the former case, apart from the ever-present β-rays
and γ-rays, only α-particles are ejected, while in the latter case
α-particles were not ejected at all, but particles of only about a
quarter their weight, which proved to be identical with the nuclei of
hydrogen atoms.
These sensational events in the atomic under-world can be photographed
by Professor C. T. R. Wilson’s condensation method already explained.
Plate XIV shews two collisions of an α-particle with a nitrogen
atom photographed by Mr P. M. S. Blackett. The straight lines are
merely the quite uneventful tracks of ordinary α-particles similar to
those already shewn in Plate XIII. But one α-particle track in each
photograph suddenly branches, so that the complete figure is of a
=Y=-shape.
There is little room for doubt that in fig. 1 the branch occurs
because the α-particle has collided with a nitrogen atom; the stem of
the =Y= is the track of the α-particle before the collision; the two
upper branches are the tracks of the α-particle and the nitrogen atom
after the collision, the latter now moving with enormous speed and
hitting everything out of its way. By taking simultaneous photographs
in two directions at right angles, as shewn in the Plate, Mr Blackett
was able to reconstruct the whole collision, and the angles were found
to agree exactly with those which dynamical theory would require on
this interpretation of the photograph.
The occurrence photographed in fig. 2 is of a different type from that
seen in fig. 1, for the angles do not agree with those which dynamical
theory would require if the upper branches of the =Y= were the tracks
of the α-particles and the nitrogen atom as in fig. 1. The stem of the
=Y= is still an ordinary α-particle track, but the long faint upper
branch is the track of a particle smaller than an α-particle, namely
a particle of quarter-weight shot out of the nucleus, whilst the
shorter and clearer branch is that of the nitrogen atom moving along in
company with the α-particle, which it has captured. It would take too
much space to describe in full the beautiful method by which Blackett
has established this interpretation of his photographs, but there is
little room for doubt that in fig. 2 he has actually succeeded in
photographing the break-up of the nucleus of an atom of nitrogen.
ISOTOPES. Two atoms have the same chemical properties if the charges
of positive electricity carried by their nuclei are the same. The
amount of this charge fixes the number of electrons which can revolve
around the nucleus, this number being of course exactly that needed to
neutralise the electric field of the nucleus, and this in turn fixes
the atomic number of the element. But Dr Aston has shewn that atoms
of the same chemical element, say neon or chlorine, may have nuclei
of different weights. The various forms which the atoms of the same
chemical element can assume are known as isotopes, being of course
distinguished by their different weights. Aston further made the highly
significant discovery that the weights of all atoms are, to a very
close approximation, multiples of a single definite weight. This unit
weight is approximately equal to the weight of the hydrogen atom, but
is more nearly equal to a sixteenth of the weight of the oxygen atom.
The weight of any type of atom, measured in terms of this unit, is
called the “atomic weight” of the atom.
PROTONS AND ELECTRONS. In conjunction with the results of Rutherford’s
artificial disintegration of atomic nuclei, Aston’s results have led
to the general acceptance of the hypothesis that the whole universe is
built up of only two kinds of ultimate bricks, namely, electrons and
protons. Each proton carries a positive charge of electricity exactly
equal in amount to the negative charge carried by an electron, but has
about 1840 times the weight of the electron. Protons are supposed to
be identical with the nucleus of the hydrogen atom, all other nuclei
being composite structures in which both protons and electrons are
closely packed together. For instance, the nucleus of the helium atom,
or α-particle, consists of four protons and two electrons, these giving
it approximately four times the weight of the hydrogen atom, and a
resultant charge equal to twice that of the nucleus of the hydrogen
atom.
Yet this is not quite the whole story. If it were, every complete atom
would consist of a certain number _N_ of protons, together with just
enough electrons, namely _N_, to neutralise the electric charges on the
_N_ protons, so that its ingredients would be precisely the same as
those of _N_ hydrogen atoms. Thus the weight of every atom would be an
exact multiple of the weight of a hydrogen atom. Experiment shews this
not to be the case.
ELECTROMAGNETIC ENERGY. To get at the whole truth, we have to recognise
that, in addition to containing material electrons and protons,
the atom contains yet a third ingredient which we may describe as
electromagnetic energy. We may think of this, although with something
short of absolute scientific accuracy, as bottled radiation.
It is a commonplace of modern electromagnetic theory that radiation
of every kind carries weight about with it, weight which is in every
sense as real as the weight of a ton of coal. A ray of light causes an
impact on any surface on which it falls, just as a jet of water does,
or a blast of wind, or the fall of a ton of coal; with a sufficiently
strong light one could knock a man down just as surely as with the jet
of water from a fire-hose. This is not a mere theoretical prediction.
The pressure of light on a surface has been both detected and measured
by direct experiment. The experiments are extraordinarily difficult
because, judged by all ordinary standards, the weight carried by
radiation is exceedingly small; all the radiation emitted from a 50
horse-power searchlight working continuously for a century weighs only
about a twentieth of an ounce.
It follows that any substance which is emitting radiation must at the
same time be losing weight. In particular, the disintegration of any
radio-active substance must involve a decrease of weight, since it is
accompanied by the emission of radiation in the form of γ-rays. The
ultimate fate of an ounce of uranium may be expressed by the equation:
{ 0·8653 ounce lead,
1 ounce uranium = { 0·1345 ” helium,
{ 0·0002 ” radiation.
The lead and helium together contain just as many electrons and just as
many protons as did the original ounce of uranium, but their combined
weight is short of the weight of the original uranium by about one part
in 4000. Where 4000 ounces of matter originally existed, only 3999 now
remain; the missing ounce has gone off in the form of radiation.
This makes it clear that we must not expect the weights of the
various atoms to be exact multiples of the weight of the hydrogen
atom; any such expectation would ignore the weight of the bottled-up
electromagnetic energy which is capable of being set free and going
off into space in the form of radiation as the atom changes its make
up. The weight of this energy is relatively small, so that the weights
of the atoms may be expected to be approximately integral multiples of
that of the hydrogen atom, and this expectation is confirmed, but they
will not be so exactly. The exact weight of our atomic building is not
simply the total weight of all its bricks; something must be added for
the weight of the mortar—the electromagnetic energy—which keeps the
bricks bound together.
Thus the normal atom consists of protons, electrons, and energy, each
of which contributes something to its weight. When the atom re-arranges
itself, either spontaneously or under bombardment, protons and
electrons may be shot off in the form of material particles (α- and
β-rays) and energy may also be set free in the form of radiation. This
radiation may either take the form of γ-rays, or, as we shall shortly
see, of other forms of visible and invisible radiation. The final
weight of the atom will be obtained by deducting from its original
weight not only the weight of all the ejected electrons and protons,
but also the weight of all the energy which has been set free as
radiation.
QUANTUM THEORY
The series of concepts which we now approach are difficult to grasp and
still more difficult to explain, largely, no doubt, because our minds
receive no assistance from our everyday experience of nature[11]. It
becomes necessary to speak mainly in terms of analogies, parables and
models which can make no claim to represent ultimate reality; indeed it
is rash to hazard a guess even as to the direction in which ultimate
reality lies.
[11] The reader whose interest is limited to astronomy may prefer to
proceed at once to Chapter III.
The laws of electricity which were in vogue up to about the end of the
nineteenth century—the famous laws of Maxwell and Faraday—required that
the energy of an atom should continually decrease, through the atom
scattering energy abroad in the form of radiation, and so having less
and less left for itself. These same laws predicted that all energy set
free in space should rapidly transform itself into radiation of almost
infinitesimal wave-length. Yet these things simply did not happen,
making it obvious that the then prevailing electrodynamical laws had to
be given up.
CAVITY-RADIATION. A crucial case of failure was provided by what is
known as “cavity-radiation.” A body with a cavity in its interior
is heated up to incandescence; no notice is taken of the light and
heat emitted by its outer surface, but the light imprisoned in the
internal cavity is let out through a small window and analysed into
its constituent colours by a spectroscope or diffraction grating. It
is this radiation that is known as “cavity-radiation.” It represents
the most complete form of radiation possible, radiation from which
no colour is missing, and in which every colour figures at its full
strength. No known substance ever emits quite such complete radiation
from its surface, although many approximate to doing so. We speak of
such bodies as “full radiators.”
The nineteenth-century laws of electromagnetism predicted that the
whole of the radiation emitted by a full radiator or from a cavity
ought to be found at or beyond the extreme violet end of the spectrum,
independently of the precise temperature to which the body had been
heated. In actual fact the radiation is usually found piled up at
exactly the opposite end of the spectrum, and in no case does it ever
conform to the predictions of the nineteenth-century laws, or even
begin to think of doing so.
In the year 1900, Professor Planck of Berlin discovered experimentally
the law by which “cavity-radiation” is distributed among the different
colours of the spectrum. He further shewed how his newly discovered law
could be deduced theoretically from a system of electromagnetic laws
which differed very sensationally from those then in vogue.
Planck imagined all kinds of radiation to be emitted by systems of
vibrators which emitted light when excited, much as tuning forks emit
sound when they are struck. The old electrodynamical laws predicted
that each vibration should gradually come to rest and then stop, as
the vibrations of a tuning fork do, until the vibrator was in some way
excited again. Rejecting all this, Planck supposed that a vibrator
could change its energy by sudden jerks, and in no other way; it might
have one, two, three, four or any other integral number of units of
energy, but no intermediate fractional numbers, so that gradual changes
of energy were rendered impossible. The vibrator, so to speak, kept
no small change, and could only pay out its energy a shilling at a
time until it had none left. Not only so, but it refused to receive
small change, although it was prepared to accept complete shillings.
This concept, sensational, revolutionary and even ridiculous, as many
thought it at the time, was found to lead exactly to the distribution
of colours actually observed in cavity-radiation.
In 1917, Einstein put the concept into the more precise form which
now prevails. According to a theory previously advanced by Professor
Niels Bohr of Copenhagen, an atomic or molecular structure does not
change its configuration, or dissipate away its energy, by gradual
stages. Gradualness is driven out of physics, and discontinuity takes
its place. An atomic structure has a number of possible states or
configurations which are entirely distinct and detached one from
another, just as a weight placed on a staircase has only a possible
number of positions; it may be 3 stairs up, or 4 or 5, but cannot
be 3¼ or 3¾ stairs up. The change from one position to another is
generally effected through the medium of radiation. The system can
be pushed upstairs by absorbing energy from radiation which falls on
it, or may move downstairs to a state of lower energy and emit energy
in the form of radiation in so doing. Only radiation of a certain
definite colour, and so of a certain precise wave-length, is of any
account for effecting a particular change of state. The problem of
shifting an atomic system is like that of extracting a box of matches
from a penny-in-the-slot machine; it can only be done by a special
implement, to wit a penny, which must be of precisely the right size
and weight—a coin which is either too small _or too large_, too
light _or too heavy_, is doomed to fail. If we pour radiation of the
wrong wave-length on to an atom, we may reproduce the comedy of the
millionaire whose total wealth will not procure him a box of matches
because he has not a loose penny, or we may reproduce the tragedy of
the child who cannot obtain a slab of chocolate because its hoarded
wealth consists of farthings and half-pence, but we shall not disturb
the atom. When mixed radiation is poured on to a collection of atoms,
these absorb the radiation of just those wave-lengths which are needed
to change their internal states, and none other; radiation of all other
wave-lengths passes by unaffected.
This selective action of the atom on radiation is put in evidence in a
variety of ways; it is perhaps most simply shewn in the spectra of the
sun and stars. Dark lines similar to those which Fraunhofer observed in
the solar spectrum are observed in the spectra of practically all stars
(see Plate VIII, p. 51), and we can now understand why this must be.
Light of every possible wave-length streams out from the hot interior
of a star, and bombards the atoms which form its atmosphere. Each atom
drinks up that radiation which is of precisely the right wave-length
for it, but has no interaction of any kind with the rest, so that the
radiation which is finally emitted from the star is deficient in just
the particular wave-lengths which suit the atoms. Thus the star shews
an _absorption spectrum_ of fine lines. The positions of these lines
in the spectrum shew what types of radiation the stellar atoms have
swallowed, and so enable us to identify the atoms from our laboratory
knowledge of the tastes of different kinds of atoms for radiation. But
what ultimately decides which types of radiation an atom will swallow,
and which it will reject?
Planck had already supposed that radiation of each wave-length has
associated with it a certain amount of energy, called the “quantum,”
which depends on the wave-length and on nothing else. The quantum is
supposed to be proportional to the “frequency” (p. 115), or number
of vibrations of the radiation per second[12], and so is _inversely_
proportional to the wave-length of the radiation—the shorter the
wave-length, the greater the energy of the quantum, and conversely. Red
light has feeble quanta, violet light has energetic quanta, and so on.
[12] To be precise, if _v_ is the frequency of the radiation, its
quantum of energy is _h__v_, where _h_ is a universal constant of
nature, known as Planck’s constant. This constant is of the physical
nature of energy multiplied by time; its numerical value is:
6·55 × 10⁻²⁷ ergs × seconds.
Einstein now supposes that radiation of a given type can effect an
atomic or molecular change, only if the energy needed for the change
is precisely equal to that of a single quantum of the radiation. This
is commonly known as Einstein’s law; it determines the precise type
of radiation needed to work any atomic or molecular penny-in-the-slot
mechanism[13].
[13] In the form of an equation:
_E_₁ - _E_₂ = _h_ν,
where _E_₁, _E_₂ are the energies of the material system before and
after the change, ν is the frequency of the radiation, and _h_ is
Planck’s constant already specified.
We notice that work which demands one powerful quantum cannot be
performed by two, or indeed by any number whatever, of feeble quanta.
A small amount of violet (high-frequency) light can accomplish what
no amount of red (low-frequency) light can effect—a circumstance with
which every photographer is painfully familiar; we can admit as much
red light as we please without any damage being done, but even the
tiniest gleam of violet light spoils our plates.
The law prohibits the killing of two birds with one stone, as well as
the killing of one bird with two stones; the whole quantum is used up
in effecting the change, so that no energy from this particular quantum
is left over to contribute to any further change. This aspect of the
matter is illustrated by Einstein’s photochemical law: “in any chemical
reaction which is produced by the incidence of light, the number of
molecules which are affected is equal to the number of quanta of light
which are absorbed.” Those who manage penny-in-the-slot machines are
familiar with a similar law: “the number of articles sold is exactly
equal to the number of coins in the machine.”
If we think of energy in terms of its capacity for doing damage, we
see that radiation of short wave-length can work more destruction
in atomic structures than radiation of long wave-length. Radiation
of sufficiently short wave-length may not only re-arrange molecules
or atoms; it may break up any atom on which it happens to fall, by
shooting out one of its electrons, giving rise to what is known as
photoelectric action. Again there is a definite limit of frequency,
such that light whose frequency is below this limit does not produce
any effect at all, no matter how intense it may be; whereas as soon as
we pass to frequencies above this limit, light of even the feeblest
intensity starts photoelectric action at once. Again the absorption
of one quantum breaks up only one atom, and further ejects only one
electron from the atom. If the radiation has a frequency above this
limit, so that its quantum has more energy than the minimum necessary
to remove a single electron from the atom, the whole quantum is still
absorbed, the excess energy now being used in endowing the ejected
electron with motion.
ELECTRON ORBITS. These concepts are based upon Bohr’s supposition
that only a limited number of orbits are open to the electrons in
an atom, all others being prohibited for reasons which we still do
not fully understand, and that an electron is free to move from one
permitted orbit to another under the stimulus of radiation. Bohr
himself investigated the way in which the various permitted orbits
are arranged. Modern investigations indicate the need for a good deal
of revision of his simple concepts, but we shall discuss these in
some detail, partly because Bohr’s picture of the atom still provides
the best working mechanical model we have, and partly because an
understanding of his simple theory is absolutely essential to the
understanding of the far more intricate theories which are beginning to
replace it.
The hydrogen atom, as we have already seen, consists of a single
proton as central nucleus, with a single electron revolving around
it. The nucleus, with about 1840 times the weight of the electron,
stands practically at rest unagitated by the motion of the latter,
just as the sun remains practically undisturbed by the motion of the
earth round it. The nucleus and electron carry charges of positive and
negative electricity, and therefore attract one another; this is why
the electron describes an orbit instead of flying off in a straight
line, again like the earth and sun. Furthermore, the attraction between
electric charges of opposite sign, positive and negative, follows,
as it happens, precisely the same law as gravitation, the attraction
falling off as the inverse square of the distance between the two
charges. Thus the nucleus-electron system is similar in all respects
to a sun-planet system, and the orbits which an electron can describe
around a central nucleus are precisely identical with those which a
planet can describe about a central sun; they consist of a system of
ellipses each having the nucleus in one focus (p. 46).
Yet the general concepts of quantum-dynamics prohibit the electron from
moving in all these orbits indiscriminately. According to Bohr, the
electron of the hydrogen atom can move in a certain number of circular
orbits whose diameters are proportional to the squares of the natural
numbers 1, 4, 9, 16, 25, ...; it can also move in a series of elliptic
orbits whose greatest diameters are respectively equal to the diameters
of the possible circular orbits, although these elliptic orbits are
still further limited by the condition that their eccentricities
must have certain definite values. All other orbits are in some way
prohibited.
The smallest orbits which the electron can describe in the hydrogen
atom are shewn in fig. 10. The smallest orbit of all, of diameter 1,
is marked 1₁; beyond this come two orbits of diameter 4 marked 2₁ 2₂;
then three orbits of diameter 9 marked 3₁, 3₂, 3₃; and four orbits of
diameter 16 marked 4₁, 4₂, 4₃, 4₄. The diagram stops here for want
of space, but the available orbits go on indefinitely. Even under
laboratory conditions, electrons may move in orbits of a hundred times
the diameter of that marked 1₁. Under the more rarefied conditions of
stellar atmospheres the hydrogen atom may swell out to even greater
dimensions, and stellar spectra provide evidence of orbits having over
a thousand times the dimensions of the 1₁ orbit. Such an orbit would be
represented in fig. 10 by a circle four yards in diameter.
[Illustration: Fig. 10. The arrangement of electron orbits in the
hydrogen atom (Bohr’s model).]
All orbits, whether elliptic or circular, which have the same diameter,
have also the same energy, but the energy changes when an electron
crosses over from any orbit to another of a different diameter. Thus,
to a certain limited extent, the atom constitutes a reservoir of
energy. Its changes of energy are easily calculated; for example, the
two orbits of smallest diameters in the hydrogen atom differ in energy
by 16 × 10⁻¹² ergs. If we pour radiation of the appropriate wave-length
on to an atom in which the electron is describing the smallest orbit
of all, it crosses over to the next orbit, absorbing 16 × 10⁻¹² ergs
of energy in the process, and so becoming temporarily a reservoir of
energy holding 16 × 10⁻¹² ergs. If the atom is in any way disturbed
from outside, it may of course discharge the energy at any time, or it
may absorb still more energy and so increase its store.
If we know all the orbits which are possible for an atom of any
type, it is easy to calculate the changes of energy involved in the
various transitions between them. As each transition absorbs or
releases exactly one quantum of energy, we can immediately deduce the
frequencies of the light emitted or absorbed in these transitions.
In brief, given the arrangement of atomic orbits, we can calculate
the spectrum of the atom. In practice the problem of course takes the
converse form: given the spectrum, to find the structure of the atom
which emits it. Bohr’s model of the hydrogen atom is a good model
at least to this extent—that the spectrum it would emit reproduces
the hydrogen spectrum almost exactly. Yet the agreement is not quite
perfect, and it is now generally accepted that Bohr’s scheme of orbits
is inadequate to account for actual spectra. We continue to discuss
Bohr’s scheme, not because the atom is actually built that way, but
because it provides a good enough working model for our present purpose.
An essential, although at first sight somewhat unexpected, feature of
the whole theory is that even if the hydrogen atom charged with its 16
× 10⁻¹² ergs of energy is left entirely undisturbed, the electron must,
after a certain time, lapse back spontaneously to its original smaller
orbit, ejecting its 16 × 10⁻¹² ergs of energy in the form of radiation
in so doing. Einstein shewed that, if this were not so, then Planck’s
well-established “cavity-radiation” law could not be true. Thus a
collection of hydrogen atoms in which the electrons describe orbits
larger than the smallest possible orbit is similar to a collection of
uranium or other radio-active atoms, in that the atoms spontaneously
fall back to their states of lower energy as the result merely of the
passage of time.
The electron orbits in more complicated atoms have much the same
general arrangement as in the hydrogen atom, but are different in size.
In the hydrogen atom the electron normally falls, after sufficient
time, to the orbit of lowest energy and stays there. It might be
thought by analogy that in more complicated atoms in which several
electrons are describing orbits, all the electrons would in time
fall into the orbit of lowest energy and stay there. Such does not
prove to be the case. There is never room for more than one electron
in the same orbit. This is a special aspect of a general principle
which appears to dominate the whole of physics. It has a name—“the
exclusion-principle”—but this is about all as yet; we have hardly
begun to understand it. In another of its special aspects it becomes
identical with the old familiar corner-stone of science which asserts
that two different pieces of matter cannot occupy the same space at
the same time. Without understanding the underlying principle, we
can accept the fact that two electrons not only cannot occupy the
same space, but cannot even occupy the same orbit. It is as though
in some way the electron spread itself out so as to occupy the whole
of its orbit, thus leaving room for no other. No doubt this must not
be accepted as a literal picture of things, and yet it seems not
improbable that the orbits of lowest energy in the hydrogen atom are
possible orbits just because the electron can completely fill them, and
that adjacent orbits are impossible because the electron would fill
them ¾ or 1½ times over, and similarly for more complicated atoms.
In this connection it is perhaps significant that no single known
phenomenon of physics makes it possible to say that at a given instant
an electron is at such or such a point in an orbit of lowest energy;
such a statement appears to be quite meaningless, and the condition of
an atom is apparently specified with all possible precision by saying
that at a given instant an electron is in such an orbit, as it would
be, for instance, if the electron had spread itself out into a ring.
We cannot say the same of other orbits. As we pass to orbits of higher
energy, and so of greater diameter, the indeterminateness gradually
assumes a different form, and finally becomes of but little importance.
Whatever form the electron may assume while it is describing a little
orbit near the nucleus, by the time it is describing a very big
orbit far out it has become a plain material particle charged with
electricity.
Thus, whatever the reason may be, electrons which are describing orbits
in the same atom must all be in different orbits. The electrons in
their orbits are like men on a ladder; just as no two men can stand on
the same rung, so no two electrons can ever follow one another round in
the same orbit. The neon atom, for instance, with 10 electrons, is in
its normal state of lowest energy when its 10 electrons each occupy one
of the 10 orbits whose energy is lowest. For reasons which the quantum
theory has at last succeeded in elucidating, there are, in every atom,
two orbits in which the energy is equal and lower than in any other
orbit. After this come eight orbits of equal but substantially higher
energy, then 18 orbits of equal but still higher energy, and so on.
As the electrons in each of these various groups of orbits all have
equal energy, they are commonly spoken of, in a graphic but misleading
phraseology, as rings of electrons. They are designated the _K_-ring,
the _L_-ring, the _M_-ring and so on. The _K_-ring, which is nearest
to the nucleus, has room for two electrons only. Any further electrons
are pushed out into the _L_-ring, which has room for eight electrons,
all describing orbits which are different but of equal energy. If still
more electrons remain to be accommodated they must go into the _M_-ring
and so on.
In their normal states, the hydrogen atom has one electron in its
_K_-ring, while the helium atom has two, the _L_, _M_, and higher rings
being unoccupied. The atom of next higher complexity, the lithium
atom, has three electrons, and as only two can be accommodated in its
_K_-ring, one has to wander round in the outer spaces of the _L_-ring.
In beryllium with four electrons, two are driven out into the _L_-ring.
And so it goes on, until we reach neon with 10 electrons, by which time
the _L_-ring as well as the inner _K_-ring is full up. In the next
atom, sodium, one of the 11 electrons is driven out into the still
more remote _M_-ring, and so on. Provided the electrons are not being
excited by radiation or other stimulus, each atom sinks in time to a
state in which its electrons are occupying its orbits of lowest energy,
one in each.
So far as our experience goes, an atom, as soon as it reaches this
state, becomes a true perpetual motion machine, the electrons
continuing to move in their orbits (at any rate on Bohr’s theory)
without any of the energy of their motion being dissipated away,
either in the form of radiation or otherwise. It seems astonishing and
quite incomprehensible that an atom in such a state should not be able
to yield up its energy still further, but, so far as our experience
goes, it cannot. And this property, little though we understand it,
is, in the last resort, responsible for keeping the universe in
being. If no restriction of this kind intervened, the whole material
energy of the universe would disappear in the form of radiation in
a few thousand-millionth parts of a second. If the normal hydrogen
atom were capable of emitting radiation in the way demanded by the
nineteenth-century laws of physics, it would, as a direct consequence
of this emission of radiation, begin to shrink at the rate of over a
metre a second, the electron continually falling to orbits of lower and
lower energy. After about a thousand-millionth part of a second the
nucleus and the electron would run into one another, and the whole atom
would probably disappear in a flash of radiation. By prohibiting any
emission of radiation except by complete quanta, and by prohibiting any
emission at all when there are no quanta available for dissipation, the
quantum theory succeeds in keeping the universe in existence as a going
concern.
It is difficult to form even the remotest conception of the realities
underlying all these phenomena. The recent branch of physics known as
“wave-mechanics” is at present groping after an understanding, but
so far progress has been in the direction of co-ordinating observed
phenomena rather than in getting down to realities. Indeed it may
be doubted whether we shall ever properly understand the realities
ultimately involved; they may well be so fundamental as to be beyond
the grasp of the human mind.
It is just for this reason that modern theoretical physics is so
difficult to explain, and so difficult to understand. It is easy to
explain the motion of the earth round the sun in the solar system.
We see the sun in the sky; we feel the earth under our feet, and the
concept of motion is familiar to us from everyday experience. How
different when we try to explain the analogous motion of the electron
round the proton in the hydrogen atom! Neither you nor I have any
direct experience of either electrons or protons, and no one has so
far any inkling of what they are really like. So we agree to make a
sort of model in which the electron and proton are represented by the
simplest things known to us, tiny hard spheres. The model works well
for a time and then suddenly breaks in our hands. In the new light of
the wave-mechanics, the hard sphere is seen to be hopelessly inadequate
to represent the electron. A hard sphere has always a definite position
in space; the electron apparently has not. A hard sphere takes up a
very definite amount of room, an electron—well, it is probably as
meaningless to discuss how much room an electron takes up as it is
to discuss how much room a fear, an anxiety or an uncertainty takes
up, but if we are pressed to say how much room an electron takes
up, perhaps the best answer is that it takes up the whole of space.
A hard sphere moves from one point to the next; our model electron,
jumping from orbit to orbit in the model hydrogen atom certainly
does not behave like any hard sphere of our waking experience, and
the real electron—if there is any such thing as a real electron in
an atom—probably even less. Yet as our minds have so far failed to
conceive any better picture of the atom than this very imperfect model,
we can only proceed by describing phenomena in terms of it.
THE MECHANICAL EFFECTS OF RADIATION
The more compact an electrical structure is, the greater the amount of
energy necessary to disturb it; and, as this energy must be supplied
in the form of a single quantum, the greater the energy of the quantum
must be, and so the shorter the wave-length of the radiation. A very
compact structure can only be disturbed by radiation of very short
wave-length.
A ship heading into a rough sea runs most risk of damage, and its
passengers most risk of discomfort, when its length is about equal to
the length of the waves. Short waves disturb a short ship and long
waves a long ship, but a long swell does little harm to either. But
this provides no real analogy with the effects of radiation, since
the wave-length of radiation which breaks up an electrical structure
is hundreds of times the size of the structure. The nautical analogy
to such radiation is a very long swell indeed. As a rough working
guide we may say that an electrical structure will only be disturbed
by radiation whose wave-length is about equal to 860 times the
dimensions of the structure, and will only be broken up by radiation
whose wave-length is below this limit[14]. In brief, the reason why
blue light affects photographic plates, while red light does not, is
that the wave-length of blue light is less, and that of red light is
greater, than 860 times the diameter of the molecule of silver bromide;
we must get below the “860-limit” before anything begins to happen.
[14] The mathematician will readily see the reason for this rule, which
is, in brief, as follows: the energy needed to separate two electric
charges + _e_ and - _e_, at a distance _r_ apart, is _e_²/_r_, and the
energy needed to re-arrange or break up a structure of electrons and
protons of linear dimensions _r_ will generally be comparable with
this. If λ is the wave-length of the requisite radiation, the energy
made available by the absorption of this radiation is the quantum
_hC_/λ. Combining this with the circumstance that the value of _h_ is
very approximately
_e_²
860 —————,
_C_
we find that the requisite wave-length of radiation is about 860 times
the dimensions of the structure to be broken up.
When an atom discharges its reservoir of stored energy, the light
it emits has necessarily the same wave-length as the light which it
absorbed in originally storing up this energy; the two quanta of energy
being equal, their wave-lengths are the same. It follows that the light
emitted by any electrical structure will also have a wave-length of
about 860 times the dimensions of the structure. Ordinary visible light
is emitted mainly by atoms, and so has a wave-length equal to about 860
atomic diameters. Indeed it is just because it has this wave-length
that the light acts on the atoms of our retina, and so is visible.
Radiation of this wave-length disturbs only the outermost electrons
in an atom, but radiation of much shorter wave-length may have much
more devastating effects; X-radiation, for instance, may break up the
far more compact inner rings of electrons, the _K_-ring, _L_-ring,
etc., of the atomic structure. Radiation of still shorter wave-length
may even disturb the protons and electrons of the nucleus. For the
nuclei, like the atoms themselves, are structures of positive and
negative electrical charges, and so must behave similarly with respect
to the radiation falling upon them, except for the wide difference
in the wave-length of the radiation. Ellis and others have found
that the γ-radiation emitted during the disintegration of the atoms
of the radio-active element radium-B has wave-lengths of 3·52, 4·20,
4·80, 5·13, and 23 × 10⁻¹⁰ cms. These wave-lengths are only about a
hundred-thousandth part of those of visible light, the reason being
that the atomic nucleus has only about a hundred-thousandth part the
dimensions of the complete atom. Radiation of such wave-lengths ought
to be just as effective in re-arranging the nucleus of radium-B as that
of 100,000 times longer wave-length is effective in re-arranging the
hydrogen atom.
Since the wave-length of the radiation absorbed or emitted by an atom
is inversely proportional to the quantum of energy, the quantum needed
to “work” the atomic nucleus must have something like 100,000 times the
energy of that needed to “work” the atom. If the hydrogen atom is a
penny-in-the-slot machine, nothing less than five-hundred-pound notes
will work the nuclei of the radio-active atoms.
The radio-active nuclei, like those of nitrogen and oxygen, could
probably be broken up by a sufficiently intense bombardment, although
the experimental evidence on this point is not very definite. If so,
each bombarding particle would have to bring to the attack an energy
of motion equal at least to that of one quantum of the radiation in
question, this requiring it to move with an enormously high speed.
Matter at sufficiently high temperatures contains an abundant supply
both of quanta of high energy, and of particles moving with high speeds.
TEMPERATURE-RADIATION. We speak in ordinary life of a red-heat or a
white-heat, meaning the heat to which a substance must be raised to
emit red or white light respectively. The filament in a carbon-filament
lamp is said to be raised to a red-heat, that in a gas-filled lamp to
a yellow-heat. It is not necessary to specify the substance we are
dealing with; if carbon emits a red light at a temperature of 3000°,
then tungsten or any other substance, raised to this same temperature,
will emit exactly the same red light as the carbon, and the same is
true for other colours of radiation. Thus each colour, and so also
each wave-length of radiation, has a definite temperature associated
with it, this being the temperature at which this particular colour
is most abundant in the spectroscopic analysis of the light emitted
by a hot body. As soon as this particular temperature begins to be
approached, but not before, radiation of the wave-length in question
becomes plentiful; at temperatures well below this it is quite
inappreciable[15].
[15] The wave-length λ of the radiation and the associated temperature
_T_ (measured in Centigrade degrees absolute) are connected through the
well-known relation:
λ_T_ = 0·2855 cm. degree.
Just as we speak of a red-heat or a white-heat, we might, although we
do not do so, quite legitimately speak of an X-ray heat or a γ-ray
heat. The shorter the wave-length of the radiation, the higher the
temperature specially associated with it. Thus as we make a substance
hotter and hotter, it emits light of ever shorter wave-length, and
runs in succession through the whole rainbow of colours—red, orange,
yellow, green, blue, indigo, violet. We cannot command a sufficient
range of temperature to perform the complete experiment in the
laboratory, but nature performs it for us in the stars.
THE EFFECTS OF HEAT. We have already seen that radiation of
short wave-length is needed to break up an electric structure of
small dimensions. As short wave-lengths are associated with high
temperatures, it now appears that the smaller an electrical structure
is, the greater the heat needed to break it up. And we can calculate
the temperature at which an electric structure of given dimensions will
first begin to break up under the influence of heat[16].
[16] On combining the relation just given between _T_ and λ with
that implied in the rough law of the “860-limit,” we find that a
structure whose dimensions are _r_ cms. will begin to be broken up by
temperature-radiation when the temperature first approaches ¹/₃₀₀₀_r_
degrees.
For instance, an ordinary atom with a diameter of about 4 × 10⁻⁸ cms.
will first be broken up at temperatures of the order of thousands
of degrees. To take a definite example, yellow light of wave-length
0·00006 cm. is specially associated with the temperature 4800 degrees;
this temperature represents an average “yellow-heat.” At temperatures
well below this, yellow light only occurs when it is artificially
created. But stars, and all other bodies, at a temperature of 4800
degrees emit yellow light naturally, and show lines in the yellow
region of their spectrum, because yellow light removes the outermost
electron from the atoms of calcium and similar elements. The electrons
in the calcium atom begin to be disturbed when a temperature of 4800
degrees begins to be approached, but not before. This temperature
is not approached on earth (except in the electric arc and other
artificial conditions), so that terrestrial calcium atoms are generally
at rest in their states of lowest energy.
To take another instance, the shortest wave-length of radiation emitted
in the transformation of uranium is about 0·5 × 10⁻¹⁰ cms., and this
corresponds to the enormously high temperature of 5,800,000,000
degrees. When some such temperature begins to be approached, but not
before, the constituents of the radio-active nuclei ought to begin to
re-arrange themselves, just as the constituents of the calcium atom do
when a temperature of 4800 degrees is approached[17]. This of course
explains why no temperature we can command on earth has any appreciable
effect in expediting or inhibiting radio-active disintegration.
[17] If we suppose that re-arrangements of an electric structure
can also be effected by bombarding it with material particles, the
temperature at which bombardment by electrons, nuclei, or molecules
first becomes effective is about the same as that at which radiation of
the effective wave-length would first begin to be appreciable; the two
processes begin at approximately the same temperature.
The table on p. 144 shews the wave-lengths of the radiation necessary
to effect various atomic transformations. The last two columns shew
the corresponding temperatures, and the kind of place, so far as we
know, where this temperature is to be found, these latter entries
anticipating certain results which will be given in detail in Chapter
V below (p. 288). In places where the temperature is far below that
mentioned in the last column but one, the transformation in question
cannot be affected by heat, and so can only occur spontaneously. Thus
it is entirely a one-way process. The available radiation not being
of sufficiently short wave-length to work the atomic slot machine,
the atoms absorb no energy from the surrounding radiation and so are
continually slipping back into states of lower energy, if such exist.
HIGHLY PENETRATING RADIATION
The shortest wave-lengths we have so far had under discussion are those
of the γ-rays, but the last line of the table refers to radiation
with a wave-length of only about a four-hundredth part of that of the
shortest of γ-rays.
Since 1902, various investigators, Rutherford, Cooke, McLennan, Burton,
Kolhörster and Millikan in particular, have found that the earth’s
atmosphere is continually being traversed by radiation which has
enormously higher penetrating power than any known γ-rays. By sending
up balloons to great heights, Hess, Kolhörster, and later Millikan and
Bowen, have shewn that the radiation is noticeably more intense at
great heights, thus proving that it comes into the earth’s atmosphere
from outside. If the radiation had its origin in the sun and stars, the
main part of the radiation received on earth would come from the sun,
and the radiation would be more intense by day than by night. This is
found not to be the case, so that the radiation cannot come from the
stars, and so must originate in nebulae or cosmic masses other than
stars. Millikan is confident that its sources lie outside the galactic
system.
_The Mechanical Effects of Radiation_
+------------+-----------+----------------+-------------+-----------+
|Wave-lengths| Nature of | Effect on Atom | Temperature | Where |
| (cms.) | Radiation | | (deg. abs.) | found |
+------------+-----------+----------------+-------------+-----------+
|7500 × 10⁻⁸ | Visible | Disturbs | 3,850°| Stellar |
| to | light | outermost | to |atmospheres|
|3750 × 10⁻⁸ | | electrons | 7,700°| |
| | | | | |
| 250 × 10⁻⁸ | X-rays | Disturbs inner | 115,000°| Stellar |
| to | | electrons | to | interiors |
| 10⁻⁸ | | | 29,000,000°| |
| | | | | |
| 5 × 10⁻⁹ | Soft | Strip off all | 58,000,000°| Central |
| to | γ-rays | or nearly all | to |regions of |
| 10⁻⁹ | | electrons | 290,000,000°|dense stars|
| | | | | |
| 4 × 10⁻¹⁰| γ-rays of |Disturbs nuclear| 720,000,000°| ? |
| | radium-B | arrangement | | |
| | | | | |
| 5 × 10⁻¹¹| Shortest | —— | 5.8 × 10⁹ °| |
| | γ-rays | | | |
| | | | | |
| 1·3 × 10⁻¹²| Highly |Annihilation or | 2.2 × 10¹² °| |
| |penetrating| creation of | | |
| | radiation | proton and | | |
| | (?) | accompanying | | |
| | | electron | | |
+------------+-----------+----------------+-------------+-----------+
The amount of the radiation is very great. Even at sea-level, where
it is least, Millikan and Cameron find that it breaks up about 1·4
atoms in every cubic centimetre of air each second. It must break up
millions of atoms in each of our bodies every second—and we do not
know what its physiological effects may be. The total energy of the
radiation received on earth is just about a tenth of that of the total
radiation, light and heat together, received from all the stars. This
does not mean that light and heat are ten times as abundant as this
radiation in the universe as a whole. For if the radiation originates
in extra-galactic regions, then the stars which send us light and heat
are comparatively near, while the sources of the highly penetrating
radiation are far more remote. On taking an average through the whole
of space, including the vast stretches of internebular space, it seems
likely that the highly penetrating radiation is far more plentiful than
stellar light and heat, and so is the most abundant form of radiation
in the whole universe.
It is the most penetrating form of radiation known. Ordinary light will
hardly pass through metals or solid substances at all; only a tiny
fraction emerges through the thinnest of gold-leaf. On account of their
shorter wave-length, and so of their more energetic quanta, X-rays will
pass through foils of a few millimetres thickness of gold or of lead.
The most highly penetrating γ-rays from radium-B will pass through
inches of lead. The radiation we have just been discussing varies in
penetrating power; the most penetrating part of it will pass through 16
feet of lead.
It is not altogether clear whether the radiation is of the nature of
very short γ-radiation or is of a corpuscular nature, like β-radiation;
it may even be a mixture of both. Its penetrating power far exceeds
that of any known β-radiation, so that if it is corpuscular, the
corpuscles must be moving with very nearly the velocity of light.
If, as seems far more likely, the radiation is, in part at least, of
the nature of γ-radiation, then it ought to be possible to determine
its wave-length from its penetrating power. Until quite recently
different theories on the relation between the two have been in the
field. The latest theory of all, that of Klein and Nishina, which
is more perfect and more complete than any of the earlier theories,
assigns to the most penetrating part of the radiation the amazingly
short wave-length of 1·3 × 10⁻¹³ cms., as indicated in the table on p.
144.
We perhaps get the clearest conception of what this means if we apply
the 860-rule; this shews that the radiation would break up an electric
structure whose dimensions are only about 10⁻¹⁶ cms. No structure
formed of electrons and protons can possibly be as small as this, for
the radius of a single electron is about 2 × 10⁻¹³ cms. The radiation
is of about the wave-length needed to break up the proton itself, the
smallest and most compact structure known to science.
Approaching the problem from another angle, the numerical relations
already given shew that a quantum of radiation of this wave-length
must have energy equal to 0·0015 erg, and so must have a weight of
about 1·66 × 10⁻²⁴ grammes. Every physicist recognises this weight at
once, for the best determinations give the weight of the hydrogen atom
as 1·662 × 10⁻²⁴ grammes. The quantum of highly penetrating radiation
has, then, just about the weight, and just about the energy, that would
result from a complete hydrogen atom suddenly being annihilated and
having all its energy set free as radiation.
It can hardly be supposed that all the highly penetrating radiation
received on earth has its origin in the annihilation of hydrogen atoms.
If for no other reason, there are probably not enough hydrogen atoms
in the universe for such a hypothesis to be tenable. The hydrogen atom
consists of a proton and an electron, and its weight is roughly the
same as the combined weight of a proton and an electron selected from
any atom in the universe, so that, to a near enough approximation, the
quantum of highly penetrating radiation has the wave-length and energy
which would result from a proton and electron in any atom whatever
coalescing and annihilating one another. We have seen how the weights
of the different known types of atoms approximate to integral multiples
of the weight of the hydrogen atom, or to be more precise, differ by
almost exactly equal steps, each of which is about equal to the weight
of the hydrogen atom. The weight of the quantum of highly penetrating
radiation is equal to the change of weight represented by a single
step, so that the quantum could be produced by any transformation which
degraded the weight of an atom by a single step. In the most general
case possible, this degradation of weight must, so far as we can see,
arise from the coalescence of a proton and electron, with the resulting
annihilation of both.
While this seems far and away the most probable source of this
radiation, it is not the only conceivable source. For instance, the
most abundant isotope of xenon, of atomic number 54 and atomic weight
129, is built up of 129 protons, 75 nuclear electrons and 54 orbital
electrons. The sudden building up of such an atom out of 129 protons
and 129 electrons would involve a loss of weight just about equal to
the weight of the hydrogen atom. If the building took place absolutely
simultaneously, so that the whole of the liberated energy was emitted
catastrophically as a single quantum, this quantum would have about
the same wave-length and penetrating power as the observed highly
penetrating radiation. Some time ago Millikan suggested the formation
of other complex atoms out of simpler constituents as a possible source
of the radiation, but it now appears that the schemes he propounded
would not result in radiation of sufficiently short wave-length, at any
rate if the modern Klein-Nishina theory is correct.
On the physical evidence alone, such schemes cannot be dismissed as
impossible, but they must be treated as suspect on account of their
high improbability. The xenon atom with its 258 constituent parts is
a highly complicated structure, and it is exceedingly hard to believe
that all these 258 parts could be hammered into a fully-formed atom by
a single instantaneous act, accompanied by the catastrophic emission
of only one quantum of radiation. If atoms ever are built up out of
simpler constituents—and there is no evidence whatever that this
process ever occurs in nature—it seems so much more likely that the
aggregation would take place by distinct stages, and that the radiation
would be emitted in a number of small quanta rather than in one large
quantum. Moreover, any such hypothesis has to explain the numerical
agreement of the calculated weight of the observed quanta of radiation
with the known weight of the hydrogen atom as a pure coincidence. Not
only so, but also we have to suppose that atoms of xenon, and possibly
others of approximately the same atomic weight, are formed far more
frequently than atoms of other atomic weights. Indeed the amount of the
highly penetrating radiation received on earth is so great that if it
were evidence of the creation of xenon, a large part of the universe
ought already to consist of xenon, mixed perhaps with elements of
nearly equal atomic weight. So far is this from being the case, that
xenon and its neighbours in the atomic weight table are among the
rarest of elements. For these reasons, and on the general principle
that the simpler and more natural hypothesis is always to be given
preference in science, we may say that the annihilation of electrons
and protons forms a more probable and more acceptable origin for the
observed highly penetrating radiation.
We may leave the problem in this state of uncertainty for the present,
because it will appear later that astronomy has some evidence to give
on the question.