Chapter II: Exploring the Atom (2)

The series of concepts which we now approach are difficult to grasp and still more difficult to explain, largely, no doubt, because our minds receive no assistance from our everyday experience of nature[11]. It becomes necessary to speak mainly in terms of analogies, parables and models which can make no claim to represent ultimate reality; indeed it is rash to hazard a guess even as to the direction in which ultimate reality lies.

[11] The reader whose interest is limited to astronomy may prefer to proceed at once to Chapter III.

The laws of electricity which were in vogue up to about the end of the nineteenth century—the famous laws of Maxwell and Faraday—required that the energy of an atom should continually decrease, through the atom scattering energy abroad in the form of radiation, and so having less and less left for itself. These same laws predicted that all energy set free in space should rapidly transform itself into radiation of almost infinitesimal wave-length. Yet these things simply did not happen, making it obvious that the then prevailing electrodynamical laws had to be given up.

CAVITY-RADIATION. A crucial case of failure was provided by what is known as “cavity-radiation.” A body with a cavity in its interior is heated up to incandescence; no notice is taken of the light and heat emitted by its outer surface, but the light imprisoned in the internal cavity is let out through a small window and analysed into its constituent colours by a spectroscope or diffraction grating. It is this radiation that is known as “cavity-radiation.” It represents the most complete form of radiation possible, radiation from which no colour is missing, and in which every colour figures at its full strength. No known substance ever emits quite such complete radiation from its surface, although many approximate to doing so. We speak of such bodies as “full radiators.”

The nineteenth-century laws of electromagnetism predicted that the whole of the radiation emitted by a full radiator or from a cavity ought to be found at or beyond the extreme violet end of the spectrum, independently of the precise temperature to which the body had been heated. In actual fact the radiation is usually found piled up at exactly the opposite end of the spectrum, and in no case does it ever conform to the predictions of the nineteenth-century laws, or even begin to think of doing so.

In the year 1900, Professor Planck of Berlin discovered experimentally the law by which “cavity-radiation” is distributed among the different colours of the spectrum. He further shewed how his newly discovered law could be deduced theoretically from a system of electromagnetic laws which differed very sensationally from those then in vogue.

Planck imagined all kinds of radiation to be emitted by systems of vibrators which emitted light when excited, much as tuning forks emit sound when they are struck. The old electrodynamical laws predicted that each vibration should gradually come to rest and then stop, as the vibrations of a tuning fork do, until the vibrator was in some way excited again. Rejecting all this, Planck supposed that a vibrator could change its energy by sudden jerks, and in no other way; it might have one, two, three, four or any other integral number of units of energy, but no intermediate fractional numbers, so that gradual changes of energy were rendered impossible. The vibrator, so to speak, kept no small change, and could only pay out its energy a shilling at a time until it had none left. Not only so, but it refused to receive small change, although it was prepared to accept complete shillings. This concept, sensational, revolutionary and even ridiculous, as many thought it at the time, was found to lead exactly to the distribution of colours actually observed in cavity-radiation.

In 1917, Einstein put the concept into the more precise form which now prevails. According to a theory previously advanced by Professor Niels Bohr of Copenhagen, an atomic or molecular structure does not change its configuration, or dissipate away its energy, by gradual stages. Gradualness is driven out of physics, and discontinuity takes its place. An atomic structure has a number of possible states or configurations which are entirely distinct and detached one from another, just as a weight placed on a staircase has only a possible number of positions; it may be 3 stairs up, or 4 or 5, but cannot be 3¼ or 3¾ stairs up. The change from one position to another is generally effected through the medium of radiation. The system can be pushed upstairs by absorbing energy from radiation which falls on it, or may move downstairs to a state of lower energy and emit energy in the form of radiation in so doing. Only radiation of a certain definite colour, and so of a certain precise wave-length, is of any account for effecting a particular change of state. The problem of shifting an atomic system is like that of extracting a box of matches from a penny-in-the-slot machine; it can only be done by a special implement, to wit a penny, which must be of precisely the right size and weight—a coin which is either too small _or too large_, too light _or too heavy_, is doomed to fail. If we pour radiation of the wrong wave-length on to an atom, we may reproduce the comedy of the millionaire whose total wealth will not procure him a box of matches because he has not a loose penny, or we may reproduce the tragedy of the child who cannot obtain a slab of chocolate because its hoarded wealth consists of farthings and half-pence, but we shall not disturb the atom. When mixed radiation is poured on to a collection of atoms, these absorb the radiation of just those wave-lengths which are needed to change their internal states, and none other; radiation of all other wave-lengths passes by unaffected.

This selective action of the atom on radiation is put in evidence in a variety of ways; it is perhaps most simply shewn in the spectra of the sun and stars. Dark lines similar to those which Fraunhofer observed in the solar spectrum are observed in the spectra of practically all stars (see Plate VIII, p. 51), and we can now understand why this must be. Light of every possible wave-length streams out from the hot interior of a star, and bombards the atoms which form its atmosphere. Each atom drinks up that radiation which is of precisely the right wave-length for it, but has no interaction of any kind with the rest, so that the radiation which is finally emitted from the star is deficient in just the particular wave-lengths which suit the atoms. Thus the star shews an _absorption spectrum_ of fine lines. The positions of these lines in the spectrum shew what types of radiation the stellar atoms have swallowed, and so enable us to identify the atoms from our laboratory knowledge of the tastes of different kinds of atoms for radiation. But what ultimately decides which types of radiation an atom will swallow, and which it will reject?

Planck had already supposed that radiation of each wave-length has associated with it a certain amount of energy, called the “quantum,” which depends on the wave-length and on nothing else. The quantum is supposed to be proportional to the “frequency” (p. 115), or number of vibrations of the radiation per second[12], and so is _inversely_ proportional to the wave-length of the radiation—the shorter the wave-length, the greater the energy of the quantum, and conversely. Red light has feeble quanta, violet light has energetic quanta, and so on.

[12] To be precise, if _v_ is the frequency of the radiation, its quantum of energy is _h__v_, where _h_ is a universal constant of nature, known as Planck’s constant. This constant is of the physical nature of energy multiplied by time; its numerical value is:

6·55 × 10⁻²⁷ ergs × seconds.

Einstein now supposes that radiation of a given type can effect an atomic or molecular change, only if the energy needed for the change is precisely equal to that of a single quantum of the radiation. This is commonly known as Einstein’s law; it determines the precise type of radiation needed to work any atomic or molecular penny-in-the-slot mechanism[13].

[13] In the form of an equation:

_E_₁ - _E_₂ = _h_ν,

where _E_₁, _E_₂ are the energies of the material system before and after the change, ν is the frequency of the radiation, and _h_ is Planck’s constant already specified.

We notice that work which demands one powerful quantum cannot be performed by two, or indeed by any number whatever, of feeble quanta. A small amount of violet (high-frequency) light can accomplish what no amount of red (low-frequency) light can effect—a circumstance with which every photographer is painfully familiar; we can admit as much red light as we please without any damage being done, but even the tiniest gleam of violet light spoils our plates.

The law prohibits the killing of two birds with one stone, as well as the killing of one bird with two stones; the whole quantum is used up in effecting the change, so that no energy from this particular quantum is left over to contribute to any further change. This aspect of the matter is illustrated by Einstein’s photochemical law: “in any chemical reaction which is produced by the incidence of light, the number of molecules which are affected is equal to the number of quanta of light which are absorbed.” Those who manage penny-in-the-slot machines are familiar with a similar law: “the number of articles sold is exactly equal to the number of coins in the machine.”

If we think of energy in terms of its capacity for doing damage, we see that radiation of short wave-length can work more destruction in atomic structures than radiation of long wave-length. Radiation of sufficiently short wave-length may not only re-arrange molecules or atoms; it may break up any atom on which it happens to fall, by shooting out one of its electrons, giving rise to what is known as photoelectric action. Again there is a definite limit of frequency, such that light whose frequency is below this limit does not produce any effect at all, no matter how intense it may be; whereas as soon as we pass to frequencies above this limit, light of even the feeblest intensity starts photoelectric action at once. Again the absorption of one quantum breaks up only one atom, and further ejects only one electron from the atom. If the radiation has a frequency above this limit, so that its quantum has more energy than the minimum necessary to remove a single electron from the atom, the whole quantum is still absorbed, the excess energy now being used in endowing the ejected electron with motion.

ELECTRON ORBITS. These concepts are based upon Bohr’s supposition that only a limited number of orbits are open to the electrons in an atom, all others being prohibited for reasons which we still do not fully understand, and that an electron is free to move from one permitted orbit to another under the stimulus of radiation. Bohr himself investigated the way in which the various permitted orbits are arranged. Modern investigations indicate the need for a good deal of revision of his simple concepts, but we shall discuss these in some detail, partly because Bohr’s picture of the atom still provides the best working mechanical model we have, and partly because an understanding of his simple theory is absolutely essential to the understanding of the far more intricate theories which are beginning to replace it.

The hydrogen atom, as we have already seen, consists of a single proton as central nucleus, with a single electron revolving around it. The nucleus, with about 1840 times the weight of the electron, stands practically at rest unagitated by the motion of the latter, just as the sun remains practically undisturbed by the motion of the earth round it. The nucleus and electron carry charges of positive and negative electricity, and therefore attract one another; this is why the electron describes an orbit instead of flying off in a straight line, again like the earth and sun. Furthermore, the attraction between electric charges of opposite sign, positive and negative, follows, as it happens, precisely the same law as gravitation, the attraction falling off as the inverse square of the distance between the two charges. Thus the nucleus-electron system is similar in all respects to a sun-planet system, and the orbits which an electron can describe around a central nucleus are precisely identical with those which a planet can describe about a central sun; they consist of a system of ellipses each having the nucleus in one focus (p. 46).

Yet the general concepts of quantum-dynamics prohibit the electron from moving in all these orbits indiscriminately. According to Bohr, the electron of the hydrogen atom can move in a certain number of circular orbits whose diameters are proportional to the squares of the natural numbers 1, 4, 9, 16, 25, ...; it can also move in a series of elliptic orbits whose greatest diameters are respectively equal to the diameters of the possible circular orbits, although these elliptic orbits are still further limited by the condition that their eccentricities must have certain definite values. All other orbits are in some way prohibited.

The smallest orbits which the electron can describe in the hydrogen atom are shewn in fig. 10. The smallest orbit of all, of diameter 1, is marked 1₁; beyond this come two orbits of diameter 4 marked 2₁ 2₂; then three orbits of diameter 9 marked 3₁, 3₂, 3₃; and four orbits of diameter 16 marked 4₁, 4₂, 4₃, 4₄. The diagram stops here for want of space, but the available orbits go on indefinitely. Even under laboratory conditions, electrons may move in orbits of a hundred times the diameter of that marked 1₁. Under the more rarefied conditions of stellar atmospheres the hydrogen atom may swell out to even greater dimensions, and stellar spectra provide evidence of orbits having over a thousand times the dimensions of the 1₁ orbit. Such an orbit would be represented in fig. 10 by a circle four yards in diameter.

All orbits, whether elliptic or circular, which have the same diameter, have also the same energy, but the energy changes when an electron crosses over from any orbit to another of a different diameter. Thus, to a certain limited extent, the atom constitutes a reservoir of energy. Its changes of energy are easily calculated; for example, the two orbits of smallest diameters in the hydrogen atom differ in energy by 16 × 10⁻¹² ergs. If we pour radiation of the appropriate wave-length on to an atom in which the electron is describing the smallest orbit of all, it crosses over to the next orbit, absorbing 16 × 10⁻¹² ergs of energy in the process, and so becoming temporarily a reservoir of energy holding 16 × 10⁻¹² ergs. If the atom is in any way disturbed from outside, it may of course discharge the energy at any time, or it may absorb still more energy and so increase its store.

If we know all the orbits which are possible for an atom of any type, it is easy to calculate the changes of energy involved in the various transitions between them. As each transition absorbs or releases exactly one quantum of energy, we can immediately deduce the frequencies of the light emitted or absorbed in these transitions. In brief, given the arrangement of atomic orbits, we can calculate the spectrum of the atom. In practice the problem of course takes the converse form: given the spectrum, to find the structure of the atom which emits it. Bohr’s model of the hydrogen atom is a good model at least to this extent—that the spectrum it would emit reproduces the hydrogen spectrum almost exactly. Yet the agreement is not quite perfect, and it is now generally accepted that Bohr’s scheme of orbits is inadequate to account for actual spectra. We continue to discuss Bohr’s scheme, not because the atom is actually built that way, but because it provides a good enough working model for our present purpose.

An essential, although at first sight somewhat unexpected, feature of the whole theory is that even if the hydrogen atom charged with its 16 × 10⁻¹² ergs of energy is left entirely undisturbed, the electron must, after a certain time, lapse back spontaneously to its original smaller orbit, ejecting its 16 × 10⁻¹² ergs of energy in the form of radiation in so doing. Einstein shewed that, if this were not so, then Planck’s well-established “cavity-radiation” law could not be true. Thus a collection of hydrogen atoms in which the electrons describe orbits larger than the smallest possible orbit is similar to a collection of uranium or other radio-active atoms, in that the atoms spontaneously fall back to their states of lower energy as the result merely of the passage of time.

The electron orbits in more complicated atoms have much the same general arrangement as in the hydrogen atom, but are different in size. In the hydrogen atom the electron normally falls, after sufficient time, to the orbit of lowest energy and stays there. It might be thought by analogy that in more complicated atoms in which several electrons are describing orbits, all the electrons would in time fall into the orbit of lowest energy and stay there. Such does not prove to be the case. There is never room for more than one electron in the same orbit. This is a special aspect of a general principle which appears to dominate the whole of physics. It has a name—“the exclusion-principle”—but this is about all as yet; we have hardly begun to understand it. In another of its special aspects it becomes identical with the old familiar corner-stone of science which asserts that two different pieces of matter cannot occupy the same space at the same time. Without understanding the underlying principle, we can accept the fact that two electrons not only cannot occupy the same space, but cannot even occupy the same orbit. It is as though in some way the electron spread itself out so as to occupy the whole of its orbit, thus leaving room for no other. No doubt this must not be accepted as a literal picture of things, and yet it seems not improbable that the orbits of lowest energy in the hydrogen atom are possible orbits just because the electron can completely fill them, and that adjacent orbits are impossible because the electron would fill them ¾ or 1½ times over, and similarly for more complicated atoms. In this connection it is perhaps significant that no single known phenomenon of physics makes it possible to say that at a given instant an electron is at such or such a point in an orbit of lowest energy; such a statement appears to be quite meaningless, and the condition of an atom is apparently specified with all possible precision by saying that at a given instant an electron is in such an orbit, as it would be, for instance, if the electron had spread itself out into a ring. We cannot say the same of other orbits. As we pass to orbits of higher energy, and so of greater diameter, the indeterminateness gradually assumes a different form, and finally becomes of but little importance. Whatever form the electron may assume while it is describing a little orbit near the nucleus, by the time it is describing a very big orbit far out it has become a plain material particle charged with electricity.

Thus, whatever the reason may be, electrons which are describing orbits in the same atom must all be in different orbits. The electrons in their orbits are like men on a ladder; just as no two men can stand on the same rung, so no two electrons can ever follow one another round in the same orbit. The neon atom, for instance, with 10 electrons, is in its normal state of lowest energy when its 10 electrons each occupy one of the 10 orbits whose energy is lowest. For reasons which the quantum theory has at last succeeded in elucidating, there are, in every atom, two orbits in which the energy is equal and lower than in any other orbit. After this come eight orbits of equal but substantially higher energy, then 18 orbits of equal but still higher energy, and so on. As the electrons in each of these various groups of orbits all have equal energy, they are commonly spoken of, in a graphic but misleading phraseology, as rings of electrons. They are designated the _K_-ring, the _L_-ring, the _M_-ring and so on. The _K_-ring, which is nearest to the nucleus, has room for two electrons only. Any further electrons are pushed out into the _L_-ring, which has room for eight electrons, all describing orbits which are different but of equal energy. If still more electrons remain to be accommodated they must go into the _M_-ring and so on.

In their normal states, the hydrogen atom has one electron in its _K_-ring, while the helium atom has two, the _L_, _M_, and higher rings being unoccupied. The atom of next higher complexity, the lithium atom, has three electrons, and as only two can be accommodated in its _K_-ring, one has to wander round in the outer spaces of the _L_-ring. In beryllium with four electrons, two are driven out into the _L_-ring. And so it goes on, until we reach neon with 10 electrons, by which time the _L_-ring as well as the inner _K_-ring is full up. In the next atom, sodium, one of the 11 electrons is driven out into the still more remote _M_-ring, and so on. Provided the electrons are not being excited by radiation or other stimulus, each atom sinks in time to a state in which its electrons are occupying its orbits of lowest energy, one in each.

So far as our experience goes, an atom, as soon as it reaches this state, becomes a true perpetual motion machine, the electrons continuing to move in their orbits (at any rate on Bohr’s theory) without any of the energy of their motion being dissipated away, either in the form of radiation or otherwise. It seems astonishing and quite incomprehensible that an atom in such a state should not be able to yield up its energy still further, but, so far as our experience goes, it cannot. And this property, little though we understand it, is, in the last resort, responsible for keeping the universe in being. If no restriction of this kind intervened, the whole material energy of the universe would disappear in the form of radiation in a few thousand-millionth parts of a second. If the normal hydrogen atom were capable of emitting radiation in the way demanded by the nineteenth-century laws of physics, it would, as a direct consequence of this emission of radiation, begin to shrink at the rate of over a metre a second, the electron continually falling to orbits of lower and lower energy. After about a thousand-millionth part of a second the nucleus and the electron would run into one another, and the whole atom would probably disappear in a flash of radiation. By prohibiting any emission of radiation except by complete quanta, and by prohibiting any emission at all when there are no quanta available for dissipation, the quantum theory succeeds in keeping the universe in existence as a going concern.

It is difficult to form even the remotest conception of the realities underlying all these phenomena. The recent branch of physics known as “wave-mechanics” is at present groping after an understanding, but so far progress has been in the direction of co-ordinating observed phenomena rather than in getting down to realities. Indeed it may be doubted whether we shall ever properly understand the realities ultimately involved; they may well be so fundamental as to be beyond the grasp of the human mind.

It is just for this reason that modern theoretical physics is so difficult to explain, and so difficult to understand. It is easy to explain the motion of the earth round the sun in the solar system. We see the sun in the sky; we feel the earth under our feet, and the concept of motion is familiar to us from everyday experience. How different when we try to explain the analogous motion of the electron round the proton in the hydrogen atom! Neither you nor I have any direct experience of either electrons or protons, and no one has so far any inkling of what they are really like. So we agree to make a sort of model in which the electron and proton are represented by the simplest things known to us, tiny hard spheres. The model works well for a time and then suddenly breaks in our hands. In the new light of the wave-mechanics, the hard sphere is seen to be hopelessly inadequate to represent the electron. A hard sphere has always a definite position in space; the electron apparently has not. A hard sphere takes up a very definite amount of room, an electron—well, it is probably as meaningless to discuss how much room an electron takes up as it is to discuss how much room a fear, an anxiety or an uncertainty takes up, but if we are pressed to say how much room an electron takes up, perhaps the best answer is that it takes up the whole of space. A hard sphere moves from one point to the next; our model electron, jumping from orbit to orbit in the model hydrogen atom certainly does not behave like any hard sphere of our waking experience, and the real electron—if there is any such thing as a real electron in an atom—probably even less. Yet as our minds have so far failed to conceive any better picture of the atom than this very imperfect model, we can only proceed by describing phenomena in terms of it.

THE MECHANICAL EFFECTS OF RADIATION

The more compact an electrical structure is, the greater the amount of energy necessary to disturb it; and, as this energy must be supplied in the form of a single quantum, the greater the energy of the quantum must be, and so the shorter the wave-length of the radiation. A very compact structure can only be disturbed by radiation of very short wave-length.

A ship heading into a rough sea runs most risk of damage, and its passengers most risk of discomfort, when its length is about equal to the length of the waves. Short waves disturb a short ship and long waves a long ship, but a long swell does little harm to either. But this provides no real analogy with the effects of radiation, since the wave-length of radiation which breaks up an electrical structure is hundreds of times the size of the structure. The nautical analogy to such radiation is a very long swell indeed. As a rough working guide we may say that an electrical structure will only be disturbed by radiation whose wave-length is about equal to 860 times the dimensions of the structure, and will only be broken up by radiation whose wave-length is below this limit[14]. In brief, the reason why blue light affects photographic plates, while red light does not, is that the wave-length of blue light is less, and that of red light is greater, than 860 times the diameter of the molecule of silver bromide; we must get below the “860-limit” before anything begins to happen.

[14] The mathematician will readily see the reason for this rule, which is, in brief, as follows: the energy needed to separate two electric charges + _e_ and - _e_, at a distance _r_ apart, is _e_²/_r_, and the energy needed to re-arrange or break up a structure of electrons and protons of linear dimensions _r_ will generally be comparable with this. If λ is the wave-length of the requisite radiation, the energy made available by the absorption of this radiation is the quantum _hC_/λ. Combining this with the circumstance that the value of _h_ is very approximately

_e_²
860 —————,
_C_

we find that the requisite wave-length of radiation is about 860 times the dimensions of the structure to be broken up.

When an atom discharges its reservoir of stored energy, the light it emits has necessarily the same wave-length as the light which it absorbed in originally storing up this energy; the two quanta of energy being equal, their wave-lengths are the same. It follows that the light emitted by any electrical structure will also have a wave-length of about 860 times the dimensions of the structure. Ordinary visible light is emitted mainly by atoms, and so has a wave-length equal to about 860 atomic diameters. Indeed it is just because it has this wave-length that the light acts on the atoms of our retina, and so is visible.

Radiation of this wave-length disturbs only the outermost electrons in an atom, but radiation of much shorter wave-length may have much more devastating effects; X-radiation, for instance, may break up the far more compact inner rings of electrons, the _K_-ring, _L_-ring, etc., of the atomic structure. Radiation of still shorter wave-length may even disturb the protons and electrons of the nucleus. For the nuclei, like the atoms themselves, are structures of positive and negative electrical charges, and so must behave similarly with respect to the radiation falling upon them, except for the wide difference in the wave-length of the radiation. Ellis and others have found that the γ-radiation emitted during the disintegration of the atoms of the radio-active element radium-B has wave-lengths of 3·52, 4·20, 4·80, 5·13, and 23 × 10⁻¹⁰ cms. These wave-lengths are only about a hundred-thousandth part of those of visible light, the reason being that the atomic nucleus has only about a hundred-thousandth part the dimensions of the complete atom. Radiation of such wave-lengths ought to be just as effective in re-arranging the nucleus of radium-B as that of 100,000 times longer wave-length is effective in re-arranging the hydrogen atom.

Since the wave-length of the radiation absorbed or emitted by an atom is inversely proportional to the quantum of energy, the quantum needed to “work” the atomic nucleus must have something like 100,000 times the energy of that needed to “work” the atom. If the hydrogen atom is a penny-in-the-slot machine, nothing less than five-hundred-pound notes will work the nuclei of the radio-active atoms.

The radio-active nuclei, like those of nitrogen and oxygen, could probably be broken up by a sufficiently intense bombardment, although the experimental evidence on this point is not very definite. If so, each bombarding particle would have to bring to the attack an energy of motion equal at least to that of one quantum of the radiation in question, this requiring it to move with an enormously high speed. Matter at sufficiently high temperatures contains an abundant supply both of quanta of high energy, and of particles moving with high speeds.

TEMPERATURE-RADIATION. We speak in ordinary life of a red-heat or a white-heat, meaning the heat to which a substance must be raised to emit red or white light respectively. The filament in a carbon-filament lamp is said to be raised to a red-heat, that in a gas-filled lamp to a yellow-heat. It is not necessary to specify the substance we are dealing with; if carbon emits a red light at a temperature of 3000°, then tungsten or any other substance, raised to this same temperature, will emit exactly the same red light as the carbon, and the same is true for other colours of radiation. Thus each colour, and so also each wave-length of radiation, has a definite temperature associated with it, this being the temperature at which this particular colour is most abundant in the spectroscopic analysis of the light emitted by a hot body. As soon as this particular temperature begins to be approached, but not before, radiation of the wave-length in question becomes plentiful; at temperatures well below this it is quite inappreciable[15].

[15] The wave-length λ of the radiation and the associated temperature _T_ (measured in Centigrade degrees absolute) are connected through the well-known relation:

λ_T_ = 0·2855 cm. degree.

Just as we speak of a red-heat or a white-heat, we might, although we do not do so, quite legitimately speak of an X-ray heat or a γ-ray heat. The shorter the wave-length of the radiation, the higher the temperature specially associated with it. Thus as we make a substance hotter and hotter, it emits light of ever shorter wave-length, and runs in succession through the whole rainbow of colours—red, orange, yellow, green, blue, indigo, violet. We cannot command a sufficient range of temperature to perform the complete experiment in the laboratory, but nature performs it for us in the stars.

THE EFFECTS OF HEAT. We have already seen that radiation of short wave-length is needed to break up an electric structure of small dimensions. As short wave-lengths are associated with high temperatures, it now appears that the smaller an electrical structure is, the greater the heat needed to break it up. And we can calculate the temperature at which an electric structure of given dimensions will first begin to break up under the influence of heat[16].

[16] On combining the relation just given between _T_ and λ with that implied in the rough law of the “860-limit,” we find that a structure whose dimensions are _r_ cms. will begin to be broken up by temperature-radiation when the temperature first approaches ¹/₃₀₀₀_r_ degrees.

For instance, an ordinary atom with a diameter of about 4 × 10⁻⁸ cms. will first be broken up at temperatures of the order of thousands of degrees. To take a definite example, yellow light of wave-length 0·00006 cm. is specially associated with the temperature 4800 degrees; this temperature represents an average “yellow-heat.” At temperatures well below this, yellow light only occurs when it is artificially created. But stars, and all other bodies, at a temperature of 4800 degrees emit yellow light naturally, and show lines in the yellow region of their spectrum, because yellow light removes the outermost electron from the atoms of calcium and similar elements. The electrons in the calcium atom begin to be disturbed when a temperature of 4800 degrees begins to be approached, but not before. This temperature is not approached on earth (except in the electric arc and other artificial conditions), so that terrestrial calcium atoms are generally at rest in their states of lowest energy.

To take another instance, the shortest wave-length of radiation emitted in the transformation of uranium is about 0·5 × 10⁻¹⁰ cms., and this corresponds to the enormously high temperature of 5,800,000,000 degrees. When some such temperature begins to be approached, but not before, the constituents of the radio-active nuclei ought to begin to re-arrange themselves, just as the constituents of the calcium atom do when a temperature of 4800 degrees is approached[17]. This of course explains why no temperature we can command on earth has any appreciable effect in expediting or inhibiting radio-active disintegration.

[17] If we suppose that re-arrangements of an electric structure can also be effected by bombarding it with material particles, the temperature at which bombardment by electrons, nuclei, or molecules first becomes effective is about the same as that at which radiation of the effective wave-length would first begin to be appreciable; the two processes begin at approximately the same temperature.

The table on p. 144 shews the wave-lengths of the radiation necessary to effect various atomic transformations. The last two columns shew the corresponding temperatures, and the kind of place, so far as we know, where this temperature is to be found, these latter entries anticipating certain results which will be given in detail in Chapter V below (p. 288). In places where the temperature is far below that mentioned in the last column but one, the transformation in question cannot be affected by heat, and so can only occur spontaneously. Thus it is entirely a one-way process. The available radiation not being of sufficiently short wave-length to work the atomic slot machine, the atoms absorb no energy from the surrounding radiation and so are continually slipping back into states of lower energy, if such exist.

HIGHLY PENETRATING RADIATION

The shortest wave-lengths we have so far had under discussion are those of the γ-rays, but the last line of the table refers to radiation with a wave-length of only about a four-hundredth part of that of the shortest of γ-rays.

Since 1902, various investigators, Rutherford, Cooke, McLennan, Burton, Kolhörster and Millikan in particular, have found that the earth’s atmosphere is continually being traversed by radiation which has enormously higher penetrating power than any known γ-rays. By sending up balloons to great heights, Hess, Kolhörster, and later Millikan and Bowen, have shewn that the radiation is noticeably more intense at great heights, thus proving that it comes into the earth’s atmosphere from outside. If the radiation had its origin in the sun and stars, the main part of the radiation received on earth would come from the sun, and the radiation would be more intense by day than by night. This is found not to be the case, so that the radiation cannot come from the stars, and so must originate in nebulae or cosmic masses other than stars. Millikan is confident that its sources lie outside the galactic system.

_The Mechanical Effects of Radiation_

+------------+-----------+----------------+-------------+-----------+
|Wave-lengths| Nature of | Effect on Atom | Temperature | Where |
| (cms.) | Radiation | | (deg. abs.) | found |
+------------+-----------+----------------+-------------+-----------+
|7500 × 10⁻⁸ | Visible | Disturbs | 3,850°| Stellar |
| to | light | outermost | to |atmospheres|
|3750 × 10⁻⁸ | | electrons | 7,700°| |
| | | | | |
| 250 × 10⁻⁸ | X-rays | Disturbs inner | 115,000°| Stellar |
| to | | electrons | to | interiors |
| 10⁻⁸ | | | 29,000,000°| |
| | | | | |
| 5 × 10⁻⁹ | Soft | Strip off all | 58,000,000°| Central |
| to | γ-rays | or nearly all | to |regions of |
| 10⁻⁹ | | electrons | 290,000,000°|dense stars|
| | | | | |
| 4 × 10⁻¹⁰| γ-rays of |Disturbs nuclear| 720,000,000°| ? |
| | radium-B | arrangement | | |
| | | | | |
| 5 × 10⁻¹¹| Shortest | —— | 5.8 × 10⁹ °| |
| | γ-rays | | | |
| | | | | |
| 1·3 × 10⁻¹²| Highly |Annihilation or | 2.2 × 10¹² °| |
| |penetrating| creation of | | |
| | radiation | proton and | | |
| | (?) | accompanying | | |
| | | electron | | |
+------------+-----------+----------------+-------------+-----------+

The amount of the radiation is very great. Even at sea-level, where it is least, Millikan and Cameron find that it breaks up about 1·4 atoms in every cubic centimetre of air each second. It must break up millions of atoms in each of our bodies every second—and we do not know what its physiological effects may be. The total energy of the radiation received on earth is just about a tenth of that of the total radiation, light and heat together, received from all the stars. This does not mean that light and heat are ten times as abundant as this radiation in the universe as a whole. For if the radiation originates in extra-galactic regions, then the stars which send us light and heat are comparatively near, while the sources of the highly penetrating radiation are far more remote. On taking an average through the whole of space, including the vast stretches of internebular space, it seems likely that the highly penetrating radiation is far more plentiful than stellar light and heat, and so is the most abundant form of radiation in the whole universe.

It is the most penetrating form of radiation known. Ordinary light will hardly pass through metals or solid substances at all; only a tiny fraction emerges through the thinnest of gold-leaf. On account of their shorter wave-length, and so of their more energetic quanta, X-rays will pass through foils of a few millimetres thickness of gold or of lead. The most highly penetrating γ-rays from radium-B will pass through inches of lead. The radiation we have just been discussing varies in penetrating power; the most penetrating part of it will pass through 16 feet of lead.

It is not altogether clear whether the radiation is of the nature of very short γ-radiation or is of a corpuscular nature, like β-radiation; it may even be a mixture of both. Its penetrating power far exceeds that of any known β-radiation, so that if it is corpuscular, the corpuscles must be moving with very nearly the velocity of light.

If, as seems far more likely, the radiation is, in part at least, of the nature of γ-radiation, then it ought to be possible to determine its wave-length from its penetrating power. Until quite recently different theories on the relation between the two have been in the field. The latest theory of all, that of Klein and Nishina, which is more perfect and more complete than any of the earlier theories, assigns to the most penetrating part of the radiation the amazingly short wave-length of 1·3 × 10⁻¹³ cms., as indicated in the table on p. 144.

We perhaps get the clearest conception of what this means if we apply the 860-rule; this shews that the radiation would break up an electric structure whose dimensions are only about 10⁻¹⁶ cms. No structure formed of electrons and protons can possibly be as small as this, for the radius of a single electron is about 2 × 10⁻¹³ cms. The radiation is of about the wave-length needed to break up the proton itself, the smallest and most compact structure known to science.

Approaching the problem from another angle, the numerical relations already given shew that a quantum of radiation of this wave-length must have energy equal to 0·0015 erg, and so must have a weight of about 1·66 × 10⁻²⁴ grammes. Every physicist recognises this weight at once, for the best determinations give the weight of the hydrogen atom as 1·662 × 10⁻²⁴ grammes. The quantum of highly penetrating radiation has, then, just about the weight, and just about the energy, that would result from a complete hydrogen atom suddenly being annihilated and having all its energy set free as radiation.

It can hardly be supposed that all the highly penetrating radiation received on earth has its origin in the annihilation of hydrogen atoms. If for no other reason, there are probably not enough hydrogen atoms in the universe for such a hypothesis to be tenable. The hydrogen atom consists of a proton and an electron, and its weight is roughly the same as the combined weight of a proton and an electron selected from any atom in the universe, so that, to a near enough approximation, the quantum of highly penetrating radiation has the wave-length and energy which would result from a proton and electron in any atom whatever coalescing and annihilating one another. We have seen how the weights of the different known types of atoms approximate to integral multiples of the weight of the hydrogen atom, or to be more precise, differ by almost exactly equal steps, each of which is about equal to the weight of the hydrogen atom. The weight of the quantum of highly penetrating radiation is equal to the change of weight represented by a single step, so that the quantum could be produced by any transformation which degraded the weight of an atom by a single step. In the most general case possible, this degradation of weight must, so far as we can see, arise from the coalescence of a proton and electron, with the resulting annihilation of both.

While this seems far and away the most probable source of this radiation, it is not the only conceivable source. For instance, the most abundant isotope of xenon, of atomic number 54 and atomic weight 129, is built up of 129 protons, 75 nuclear electrons and 54 orbital electrons. The sudden building up of such an atom out of 129 protons and 129 electrons would involve a loss of weight just about equal to the weight of the hydrogen atom. If the building took place absolutely simultaneously, so that the whole of the liberated energy was emitted catastrophically as a single quantum, this quantum would have about the same wave-length and penetrating power as the observed highly penetrating radiation. Some time ago Millikan suggested the formation of other complex atoms out of simpler constituents as a possible source of the radiation, but it now appears that the schemes he propounded would not result in radiation of sufficiently short wave-length, at any rate if the modern Klein-Nishina theory is correct.

On the physical evidence alone, such schemes cannot be dismissed as impossible, but they must be treated as suspect on account of their high improbability. The xenon atom with its 258 constituent parts is a highly complicated structure, and it is exceedingly hard to believe that all these 258 parts could be hammered into a fully-formed atom by a single instantaneous act, accompanied by the catastrophic emission of only one quantum of radiation. If atoms ever are built up out of simpler constituents—and there is no evidence whatever that this process ever occurs in nature—it seems so much more likely that the aggregation would take place by distinct stages, and that the radiation would be emitted in a number of small quanta rather than in one large quantum. Moreover, any such hypothesis has to explain the numerical agreement of the calculated weight of the observed quanta of radiation with the known weight of the hydrogen atom as a pure coincidence. Not only so, but also we have to suppose that atoms of xenon, and possibly others of approximately the same atomic weight, are formed far more frequently than atoms of other atomic weights. Indeed the amount of the highly penetrating radiation received on earth is so great that if it were evidence of the creation of xenon, a large part of the universe ought already to consist of xenon, mixed perhaps with elements of nearly equal atomic weight. So far is this from being the case, that xenon and its neighbours in the atomic weight table are among the rarest of elements. For these reasons, and on the general principle that the simpler and more natural hypothesis is always to be given preference in science, we may say that the annihilation of electrons and protons forms a more probable and more acceptable origin for the observed highly penetrating radiation.

We may leave the problem in this state of uncertainty for the present, because it will appear later that astronomy has some evidence to give on the question.