General Considerations on the Photo-Electric Effect

It is shown that the equality of the stopping potentials, which is expressed in the equation $V_{\mathrm{AB}}=\left(\frac{h}{\epsilon }\right)({\nu }_{\mathrm{oB}}-{\nu }_{\mathrm{oA}})$, is a consequence of the principle of detailed balancing, without any assumption about the mechanism of photo-electric emission. If the relation is not satisfied, the system cannot be in equilibrium, and there must be slow transformations taking place with evolution of energy. Differentiation of the equation above gives a hold on the numerical magnitude of the temperature coefficient of the Volta difference, and also on the magnitude of the surface heat. In potassium the latter must be much larger than the ordinary Peltier heat. In a cavity in any body the equilibrium electron density is the same whether the photo-electric or the thermionic mechanisms act separately or conjointly. This gives certain connections between the photo-electric threshold frequency and thermionic emission. It is shown that the difference between the photo-electric and the thermionic work functions must be a universal constant for all metals, as must also the difference between the specific heat of the metal and a surface charge, and the difference between the entropy of the metal and a surface charge at 0° Abs. Experiment makes it probable that these three universal constants are each zero. Applying this result to thermionic emission, it is probable that the abnormal emission from coated substances involves non-equilibrium conditions. Finally it is suggested that the considerations of this paper enable another significance to be attached to the argument of Lawrence that photoelectric and thermionic emission are identical.