A Quantum Theory of the Impulse Radiation

Abstract

A quantum theory of the impulse radiation.---Evidence is presented which indicates that the quantum ejects the photo-electron by a sideways impulsive action in the direction of the electric force. It is therefore assumed that a similar sideways reaction perpendicular to the direction of emission of the quantum acts on the cathode electron during the creation of the quantum. From this it follows that the frequency of the radiation emitted at an angle $\ensuremath{\varphi}$ with the cathode beam cannot exceed the value ${v}_{0}=\frac{m{\ensuremath{\beta}}^{2}{c}^{2}{sin}^{2}\ensuremath{\varphi}}{[2h\sqrt{1\ensuremath{-}{\ensuremath{\beta}}^{2}}(1\ensuremath{-}\ensuremath{\beta}cos\ensuremath{\varphi})]}$ where $\ensuremath{\beta}c$ is the velocity of the cathode electron; hence the forward radiation exceeds the backward in hardness, in agreement with observation. Assuming the electric force of the quantum is determined by the sideways impulse acting in the creation of the quantum, results for polarization are obtained which agree with those of the wave theory and hence with observation. The problem of intensity distribution of the radiation from a target is a statistical one which will be treated later; but it is shown that the results of Stark and Loebe are in accord with this theory. The quantum is supposed to be a tiny corpuscle which undergoes a sideways cyclic vibration as it proceeds. This theory is seen to include a momentum relation as well as the Einstein photoelectric relation. It agrees in most formal results with Sommerfeld's wave theory.