There can hardly exist any doubt that in nature there occur not only disintegrations, but also (perhaps in the interior of the stars) building-up processes in which compound nuclei result from simple ones. It is therefore natural to suppose that by exerting on hydrogen exceptional conditions of temperature, pressure, electrical changes, etc., we could succeed by experiments here on earth in forming helium from it with the development of considerable energy. But at the same time it is very likely that even under favourable circumstances such a process would take place with very great slowness, because the formation of a helium nucleus might well be a very infrequent occurrence; it would probably be the result of a certain succession of collisions between hydrogen nuclei and electrons, a combination whose probability of occurrence in a certain number of collisions is infinitely less than the probability of winning the largest prize in a lottery with the same number of chances. Nature has time enough to wait for “wins,” while mankind unfortunately has not. We know concerning the disintegration of the radioactive substances that it is of the character here indicated; of the great number of atoms to be found in a very small mass of a radioactive substance, now one explodes and now another. But why fortune should pick out one particular atom is as difficult to understand as why in a lottery one particular number should prove to be the lucky one rather than any other. Our only understanding of the whole matter rests on the law of averages, or probability as we may call it. We know that of a billion radium atoms (10¹²) on the average thirteen explode every second; and even if in any single collection of a billion a few more or a few less may explode, the average of thirteen per second per billion will always be maintained in dealing with larger and larger numbers of atoms, as, for example, with a thousand billion or a million billion. For other radioactive substances we get wholly different averages for the number of atoms disintegrating per second; but in no case are we able to penetrate into the inner character of the process of disintegration itself. And what holds true of the radioactive substances will also hold true probably for elemental changes of all kinds; Rutherford with his hundreds of thousands of α-particle projectiles was able to make sure of but a few lucky “shots.” The whole matter must at this stage be looked upon as governed wholly by chance.
One interested in speculating on what would happen if it were possible to bring about artificially a transformation of elements propagating itself from atom to atom with the liberation of energy, would find food for serious thought in the fact that the quantities of energy which would be liberated in this way would be many, many times greater than those which we now know of in connection with chemical processes. There is then offered the possibility of explosions more extensive and more violent than any which the mind can now conceive. The idea has been suggested that the world catastrophes represented in the heavens by the sudden appearance of very bright stars may be the result of such a release of sub-atomic energy, brought about perhaps by the “super-wisdom” of the unlucky inhabitants themselves. But this is, of course, mere fanciful conjecture.
It seems clear, however, that we need have no fear that in investigating the problem of atomic energy we are releasing forces which we cannot control, because we can at present see no way to liberate the energy of atomic nuclei beyond that which Nature herself provides, to say nothing of a practical solution of the energy problem. The time has certainly not yet come for the technician to follow in the theoretical investigator’s footsteps in this branch of science. One hesitates, however, to predict what the future may bring forth.
Interesting and significant as is the insight which Rutherford and others have opened up into the inner workings of the nucleus, the study of the electron system of the atom bears more intimately upon the various branches of physical and chemical science, and hence presents greater possibilities of attaining, in a less remote future, to discoveries of practical significance.
CHAPTER V
THE BOHR THEORY OF THE
HYDROGEN SPECTRUM
The Nuclear Atom and Electrodynamics.
Even if Rutherford had not yet succeeded in giving a complete answer to the first of the questions propounded in the [previous chapter], namely, that concerning the positions of the positive and negative particles of the atom, one might at any rate hope that his general explanation of the structure of the atom—that is, the division into the nucleus and surrounding electrons, and the determination of the number of electrons in the atoms of the various elements—would furnish a good foundation for the answer to the second question about the connection between the atomic processes and the physical and chemical properties of matter. But in the beginning this seemed so far from being true that it appeared almost hopeless to find a solution of the problem of the atom in this way.
We shall best understand the meaning of this if we consider the simplest of the elemental atoms, namely, the atom of hydrogen with its positive nucleus and its one electron revolving about the nucleus. How could it be possible to explain from such a simple structure the many sharp spectral lines given by the Balmer-Ritz formula ([p. 57])? As has previously been mentioned, the classical electron theory seemed to demand a very complicated atomic structure for the explanation of these lines. According to the electron theory, the atoms may be likened to stringed instruments which are capable of emitting a great number of tones, and in these atoms the electrons are naturally supposed to correspond to the “strings.” But the hydrogen atom has only one electron, and it hardly seems credible that in a mass of hydrogen the individual atoms would be tuned for different “tones,” with definite frequencies of vibration.
Now, it certainly cannot be concluded from the analogy with the stringed instrument that a single electron can emit light of only a single frequency at one time, corresponding to a single spectral line. For a plucked string will, as we know, give rise to a simple tone only if it vibrates in a very definite and particularly simple way; in general it will emit a compound sound which may be conceived as made up of a “fundamental” and its so-called “overtones,” or “harmonies” whose frequencies are 2, 3, ... times that of the fundamental (i.e. integral multiples of the latter). These overtones may arise even separately because the string, instead of vibrating as a whole, may be divided into 2, 3, ... equally long vibrating parts, giving respectively 2, 3, ... times as great frequencies of vibration. We call such vibrations “harmonic oscillations.” The simultaneous existence of these different modes of oscillation of the string may be thought of in the same way as the simultaneous existence of wave systems of different wave-lengths on the surface of water. Corresponding to the possibility of resolving the motion of the string into its “harmonic components,” the compound sound waves produced by the string can be resolved by resonators ([cf. p. 44]) into tones possessing the frequencies of these components.
According to the laws of electrodynamics the situation with the electron revolving about the hydrogen nucleus might be expected to be somewhat similar to that described above in connection with the vibrating string. If the orbit of the electron were a circle, it should emit into the ether electromagnetic waves of a single definite wave-length and corresponding frequency, ν, equal to ω, the frequency of rotation of the electron in its orbit; that is, the number of revolutions per second. But just as a planet under the attraction of the sun, varying inversely as the square of the distance, moves in an ellipse with the sun at one focus, so the electron, under the attraction of the positive nucleus, which also follows the inverse square law, will in general be able to move in an ellipse with the nucleus at one focus. The electromagnetic waves which are emitted from such a moving electron may on the electron theory be considered as composed of light waves corresponding to a series of harmonic oscillations with the frequencies: