The various arrangements of electrons can be classified into families, in which the groupings of the electrons have certain features in common. Thus the group of 60 electrons consists of the same arrangement of electrons as the group of 40 with the addition of an outer ring of 20 electrons; the group of 40 is the same as the group of 24 with an additional ring outside; and the group of 24 in turn is the same as the group of 11 with an extra ring. A series of model atoms may be formed in this way, in which each atom is derived from the preceding member by an additional ring of electrons. Such atoms would be expected to possess many properties in common, and would correspond to the elements in the same vertical column of the periodic table of Mendeléef.
Different arrangements of electrons vary widely in stability. Some may acquire an extra electron or two and yet remain stable, others readily lose an electron without disturbing their stability. The former would correspond to an electro-negative atom, the latter to an electro-positive.
Certain arrangements of electrons are stable if the electrons move with an angular velocity greater than a certain value, but become unstable when the velocity falls below this value. Four electrons in motion, for example, are stable in one plane, but when the velocity falls below a certain critical value, the system is unstable, and the electrons tend to arrange themselves at the corners of a regular tetrahedron. J. J. Thomson (loc. cit.) applies this property to explain why an atom of radio-active matter breaks up, as follows:—
“Consider now the properties of an atom containing a system of corpuscles (electrons) of this kind. Suppose the corpuscles were originally moving with velocities far exceeding the critical velocity; in consequence of the radiation from the moving corpuscles, their velocity will slowly—very slowly—diminish; when, after a long interval, the velocity reaches the critical velocity, there will be what is equivalent to an explosion of the corpuscles, the corpuscles will move far away from their original position, their potential energy will decrease, while their kinetic energy will increase. The kinetic energy gained in this way might be sufficient to carry the system out of the atom, and we should have, as in the case of radium, a part of the atom shot off. In consequence of the very slow dissipation of energy by radiation the life of the atom would be very long. We have taken the case of the four corpuscles as the type of a system which, like a top, requires for its stability a certain amount of rotation. Any system possessing this property would, in consequence of the gradual dissipation of energy by radiation, give to the atom containing it radio-active properties similar to those conferred by the four corpuscles.”
271. Heat of the sun and earth. It was pointed out by Rutherford and Soddy[[380]] that the maintenance of the sun’s heat for long intervals of time did not present any fundamental difficulty if a process of disintegration, such as occurs in the radio-elements, were supposed to be taking place in the sun. In a letter to Nature (July 9, 1903) W. E. Wilson showed that the presence of 3·6 grams of radium in each cubic metre of the sun’s mass was sufficient to account for the present rate of emission of energy by the sun. This calculation was based on the estimate of Curie and Laborde that 1 gram of radium emits 100 gram-calories per hour, and on the observation of Langley that each square centimetre of the sun’s surface emits 8·28 × 106 gram-calories per hour. Since the average density of the sun is 1·44, the presence of radium in the sun, to the extent of 2·5 parts by weight in a million, would account for its present rate of emission of energy.
An examination of the spectrum of the sun has not so far revealed any of the radium lines. It is known, however, from spectroscopic evidence that helium is present, and this indirectly suggests the existence of radio-active matter also. It can readily be shown[[381]] that the absence of penetrating rays from the sun at the surface of the earth does not imply that the radio-elements are not present in the sun. Even if the sun were composed of pure radium, it would hardly be expected that the γ rays emitted would be appreciable at the surface of the earth, since the rays would be almost completely absorbed in passing through the atmosphere, which corresponds to a thickness of 76 centimetres of mercury.
In the Appendix E of Thomson and Tait’s Natural Philosophy, Lord Kelvin has calculated the energy lost in the concentration of the sun from a condition of infinite dispersion, and concludes that it seems “on the whole probable that the sun has not illuminated the earth for 100,000,000 years and almost certain that he has not done so for 500,000,000 years. As for the future we may say, with equal certainty, that inhabitants of the earth cannot continue to enjoy the light and heat essential to their life for many million years longer, unless sources now unknown to us are prepared in the great storehouses of creation.”
The discovery that a small mass of a substance like radium can emit spontaneously an enormous quantity of heat renders it possible that this estimate of the age of the sun’s heat may be much increased. In a letter to Nature (Sept. 24, 1903) G. H. Darwin drew attention to this probability, and at the same time pointed out that, on Kelvin’s hypotheses, his estimate of the duration of the sun’s heat was probably much too high, and stated that, “The lost energy of the sun, supposed to be a homogeneous sphere of mass M and radius a, is (⅗)μM2/a where μ is the constant of gravitation. On introducing numerical values for the symbols in this formula, I find the lost energy to be 2·7 × 107 M calories where M is expressed in grams. If we adopt Langley’s value of the solar constant, this heat suffices to give a supply for 12 million years. Lord Kelvin used Pouillet’s value for that constant, but if he had been able to use Langley’s, his 100 million would have been reduced to 60 million. The discrepancy between my results of 12 million and his of 60 million is explained by a conjectural augmentation of the lost energy to allow for the concentration of the solar mass towards its central parts.” Now it has been shown ([section 266]) that one gram of radium emits during its life an amount of heat corresponding to 1·6 × 109 gram-calories. It has also been pointed out that there is every reason to suppose that a similar amount of energy is resident in the chemical atoms of the inactive elements. It is not improbable that, at the enormous temperature of the sun, the breaking up of the elements into simpler forms may be taking place at a more rapid rate than on the earth. If the energy resident in the atoms of the elements is thus available, the time during which the sun may continue to emit heat at the present rate may be at least 50 times longer than the value computed from dynamical data.
Similar considerations apply to the question of the age of the earth. A full discussion of the probable age of the earth, computed from its secular cooling from a molten mass, is given by Lord Kelvin in Appendix D of Thomson and Tait’s Natural Philosophy. He has there shown that about 100 million years after the earth was a molten mass, the gradual cooling due to radiation from its surface would account for the average temperature gradient of ¹⁄₅₀° F. per foot, observed to-day near the earth’s surface.
Some considerations will now be discussed which point to the probability that the present temperature gradient observed in the earth cannot be used as a guide to estimate the length of time that has elapsed since the earth has been at a temperature capable of supporting animal and vegetable life; for it will be shown that probably there is sufficient radio-active matter on the earth to supply as much heat to the earth as is lost by radiation from its surface. Taking the average conductivity K of the materials of the earth as ·004 (C.G.S. units) and the temperature gradient T near the surface as ·00037° C. per cm., the heat Q in gram-calories conducted to the surface of the earth per second is given by