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 Kelvin46. 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. Thomson47 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.
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