Transition Probabilities: Their Relation to Thermionic Emission and the Photo-Electric Effect

Assuming (a) Wien's formula for black body radiation, (b) that electrons ejected thermally from a hot body have the experimentally known Maxwell distribution of velocities, and (c) that photo-electric emission from a solid surface is independent of the temperature of the solid, a theory is developed which leads directly to Richardson's thermionic current equation without importing into the argument circumstances not realized in experiment or assumptions and approximations that can be questioned. Detailed consideration of the mechanism of emission and absorption along the lines of Einstein's derivation of Planck's radiation formula leads to the same expression for the ratio of absorption to emission $\frac{B_{\nu }}{q_{\nu }}$ obtained in other theories based on application of the principle of detailed balancing of processes occurring in systems in equilibrium. It is thus shown that observed photo-electric and thermionic phenomena from solid surfaces may be regarded as experimental confirmations of expressions $\frac{B_{\nu }}{q_{\nu }}$ deduced in such theories.