It seems probable that the primary cause of the disintegration of the atom must be looked for in the loss of energy of the atomic system due to electromagnetic radiation ([section 52]). Larmor[[376]] has shown that the condition to be fulfilled in order that a system of rapidly moving electrons may persist without loss of energy is that the vector sum of the accelerations towards the centre should be permanently zero. While a single electron moving in a circular orbit is a powerful radiator of energy, it is remarkable how rapidly the radiation of energy diminishes if several electrons are revolving in a ring. This has recently been shown by J. J. Thomson[[377]], who examined mathematically the case of a system of negatively electrified corpuscles, situated at equal intervals round the circumference of a circle, and rotating in one plane with uniform velocity round its centre. For example, he found that the radiation from a group of six particles moving with a velocity of ⅒ of the velocity of light is less than one-millionth part of the radiation from a single particle describing the same orbit with the same velocity. When the velocity is ¹⁄₁₀₀ of that of light the amount of radiation is only 10-16 that of a single particle moving with the same velocity in the same orbit.
Results of this kind indicate that an atom consisting of a large number of revolving electrons may radiate energy extremely slowly, and yet, finally, this minute but continuous drain of energy from the atom must result either in a rearrangement of its component parts into a new system, or of an expulsion of electrons or groups of electrons from the atom.
Simple models of atoms to imitate the behaviour of polonium in shooting out α particles, and of radium in shooting out β particles have been discussed by Lord Kelvin[[378]]. It is possible to devise certain stable arrangements of the positively and negatively electrified particles, supposed to constitute an atom, which, on the application of some disturbing force, break up with the expulsion of a part of the system with great velocity.
J. J. Thomson[[379]] has mathematically investigated the possible stable arrangements of a number of electrons moving about in a sphere of uniform positive electrification. The properties of such a model atom are very striking, and indirectly suggest a possible explanation of the periodic law in chemistry. He has shown that the electrons, if in one plane, arrange themselves in a number of concentric rings; and generally, if they are not constrained to move in one plane, in a number of concentric shells like the coats of an onion.
The mathematical problem is much simplified if the electrons are supposed to rotate in rings in one plane, the electrons in each ring being arranged at equal angular intervals. The ways in which the number of electrons group themselves, for numbers ranging from 60 to 5 at intervals of 5, are shown in the following table:—
| Number of electrons | 60 | 55 | 50 | 45 | 40 | 35 |
|---|---|---|---|---|---|---|
| Number in successive rings | 20 | 19 | 18 | 17 | 16 | 16 |
| 16 | 16 | 15 | 14 | 13 | 12 | |
| 13 | 12 | 11 | 10 | 8 | 6 | |
| 8 | 7 | 5 | 4 | 3 | 1 | |
| 3 | 1 | 1 |
| Number of electrons | 30 | 25 | 20 | 15 | 10 | 5 |
|---|---|---|---|---|---|---|
| Number in successive rings | 15 | 13 | 12 | 10 | 8 | 5 |
| 10 | 9 | 7 | 5 | 2 | ||
| 5 | 3 | 1 | ||||
In the next table is given the possible series of arrangements of electrons which can have an outer ring of 20:—
| Number of electrons | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 |
|---|---|---|---|---|---|---|---|---|---|
| Number in successive rings | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |
| 16 | 16 | 16 | 17 | 17 | 17 | 17 | 17 | 17 | |
| 13 | 13 | 13 | 13 | 13 | 13 | 14 | 14 | 15 | |
| 8 | 8 | 9 | 9 | 10 | 10 | 10 | 10 | 10 | |
| 2 | 3 | 3 | 3 | 3 | 4 | 4 | 5 | 5 |
The smallest number of electrons which can have an outer ring of 20 is 59, while 67 is the greatest.