The Balmer Law as an Equation of Motion

Abstract

Dynamics of intra-atomic charges.---The attempt is provide an atom in which the radiating electrons have a unifrequentic motion. Modification of the classical conceptions of the electron and of kinetic reaction seem required. (1) Differentiation of "active" from "passive" charge of the electron. The passive charge (that acted upon by an external field) is supposed to consist of a dipole each element of which describes one of the two orbits involved in a transition and is acted on by the nucleus according to an inverse first power law. The active charge (that which produces an electromagnetic field) is assumed to lie on the line joining the two elements of the dipole and to pass gradually from one to the other during a transition. (2) Definition of kinetic reaction as a space change of velocity. The classical dynamics is replaced by a new dynamics in which the kinetic reaction is made proportional to the vector difference of the velocities at the same time of two points on the tangent to the path of the particle equal distnaces in front of and behind it. Since the active charge is a dipole, the force is proportional to the difference of the potentials at two points on the radius vector a finite distance apart. Under certain conditions the new dynamics reduces to the classical dynamics. (3) Application of the new dynamics to an atom containing only one electron leads to unifrequentic motion in an elliptical orbit with the nucleus at the focus, and when the quantum conditions are imposed an orbital frequency is obtained identical with the optical frequency deduced on the Bohr theory. The energy of the orbit agrees exactly with that obtained on the classical theory. The theory is applied to the case where the mass of the nucleus is finite (two body problem) and to linear simple harmonic motion, and leads to results identical with those of the Bohr theory. This theory accounts for the emission of series of the Balmer type and also for the absence of radiation in a stationary state.