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[1]. 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[2] 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:—
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| Number of electrons | 60 | 55 | 50 | 45 | 40 | 35 |
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| 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 | | | |
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