Author: Sir James Jeans, M. A., D. Sc., Sc. D., LL. D., F. R. S.
[p. 92] 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 [p. 93] 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 seashore 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 [p. 94] 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.
[p. 95] 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 x 10-8 cms.), while that of the simpler hydrogen molecule is only just over [p. 96] a hundred-millionth of an inch (2.7 x 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 x 1025 molecules, each weighing 1.06 x 10-24 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 [p. 97] 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 x 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 [p. 98] 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[1].
[p. 99] 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 [p. 100] 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 gun- powder 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 [p. 101] 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 [p. 102] 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 [p. 103] 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 [p. 104] 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 H20.
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 ©, nitrogen (N), oxygen (O), sodium (Na), magnesium (Mg), aluminium (Al), [p. 105] silicon (Si), phosphorus §, sulphur (S), chlorine (CI), 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 [p. 106] 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 [p. 107] 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 [p. 108] 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 [p. 109] about 2 x 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 x 10-13 cms. 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.
[p. 110] 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 [p. 111] 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 [p. 112] 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 C´, 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 a-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 anα-particle is left [p. 113] 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).
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[^2].
[p. 114] 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 [p. 115] light into its constituent wave-lengths[2], 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 x 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 x 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.
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 [p. 116] 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 radioactive 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.
[p. 117]
¶ 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 underworld 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 [p. 118] 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 [p. 119] 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 [p. 120] 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 extraordinarity 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 [p. 121] 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 :
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 electro- magnetic 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 [p. 122] 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[3]. 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.
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 [p. 123] 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.
[p. 124] 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 3 or 3 stairs up. The change from one position to another is generally [p. 125] 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 arid 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 [p. 126] 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[4], 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.
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 [p. 127] precise type of radiation needed to work any atomic or molecular penny-in-the-slot mechanism[5].
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 rearrange [p. 128] 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 [p. 129] 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 [p. 130] in the hydrogen atom are shewn in fig. 10. The smallest orbit of all, of diameter 1, is marked l1; 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 l1 orbit. Such an orbit would be represented in fig. 10 by a circle four yards in diameter.
All orbits, whether elliptic or circular, which have [p. 131] 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 x 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 x 10-12 ergs of energy in the process, and so becoming temporarily a reservoir of energy holding 16 x 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 [p. 13] 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 x 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 x 10-12 ergs of energy in the form of radiation in so doing. Einstein shewed that, if this were not so, then Planck’s wellestablished “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 [p. 133] 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 [p. 134] 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 i£-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. [p. 135] 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 [p. 136] 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 [p. 137] 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 [p. 138] length is below this limit[^7]. 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.
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 [p. 139] 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 x 10-10 cms. These wave-lengths are only about a hundred-thou- sandth 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 [p. 140] sufficiently high temperatures contains an abundant supply both of quanta of high energy, and of particles moving with high speeds.
Temperature-radiation. We speakin 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 gasfilled 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[6].
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 [p. 141] 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[7].
For instance, an ordinary atom with a diameter of about 4 x 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 [p. 142] 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 x 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[8]. This of course explains why no temperature we can command on earth has any appreciable effect in expediting or inhibiting radio-active disintegration.
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 [p. 143] [p. 144</pequeño>] 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.
| Wave-lengths (cms.) | Nature of Radiation | Effect on Atom | Temperature (degress abs.) | Where found |
|---|---|---|---|---|
| 7500 x 10-8 to 3750 x 10-8 |
Visible light | Disturbs outermost electrons | 3,850° to 7,700° |
Stellar atmospeheres |
| 250 x 10-8 to 10-8 |
X-rays | Disturbs inner electrons | 115,000° to 29,000,000° |
Stellar interiors |
| 5 x 10-9 to 10-9 |
Soft γ-rays | Strip off all or neraly all electrons | 58,000,000° to 290,000,000° |
Central regions of dense stars |
| 4 x 10-10 | γ-rays of Radium-B | Disturbs nuclear arrangement | 720,000,000° | ? |
| 5 x 10-11 | Shortest γ-rays | – | 5,800,000,000° | |
| 1.3 x 10-13 | Highly penetrating radiation (?) | Annihilation or creation of proton and accompanying electron | 2,200,000,000,000° |
Since 1902, various investigators, Rutherford, Cooke, McLennan, Burton, Kolhorster 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, Kolhorster, 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 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 [p. 145] 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, [p. 146] 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 x 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 x 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 l.66 x 10-24 grammes. Every physicist recognises this weight at once, for the best determinations give the weight of the hydrogen atom as 1.662 x 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.
[p. 147] 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 [p. 148] 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 [p. 149] 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.
¶ Footnotes
[^2] These were called δ-rays by Bumstead.
This is expressed in the mathematical formula 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 “ergs.” Thus an “erg” is the energy of motion of a body of 2 grammes weight (so that ) moving with a speed of one centimetre a second. As an example, the energy of an express train of 300 tons’ weight (3 x 108 gms.) moving at 60 miles an hour (2682 cms. a second) is 1079 x 1014 ergs ; a cannon-ball or shell weighing a ton and moving at 1520 feet a second has precisely the same energy. ↩︎
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 reader whose interest is limited to astronomy may prefer to proceed at once to Chapter III. ↩︎
To be precise, if v is the frequency of the radiation, its quantum of energy is hv, 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 x 10-27 ergs x seconds. ↩︎
In the form of an equation :
↩︎The wave-length λ of the radiation and the associated temperature T (measured in Centigrade degrees absolute) are connected through the well-known relation :
λT = 0.28S5 cm. degree. ↩︎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 l/3000_r_ degrees. ↩︎
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. ↩︎