The Photo-Electric Effect and Thermionic Emission: A Correction and an Extension

In this note the analysis which I recently gave connecting the photo-electric effect with thermionic emission is freed from the assumption that the photo-electric characteristic frequency is independent of temperature. The thermonic work function and the photo-electric work functions are found to differ by a universal constant, which must be zero in the light of the work of Warner and the recent work of DuBridge. Furthermore, it is found that the temperature derivative at 0° Abs of the photo-electric threshold differs by a universal constant, which is also probably zero, from ${(S_p-S_m)}_0$, the difference of entropy at 0° Abs of surface ions and neutral atoms. The quantity ${(S_p-S_m)}_0$ enters the constant of the thermionic emission formula, so that there is a connection between this constant and the temperature derivative of the photo-electric threshold. In spite of the known small value of this latter, experiment allows a sufficient range of numerical values to account for the extreme variation of the thermionic emission constant from the "universal" value. The connection found by DuBridge between the thermionic emission constant and the work function is shown to be reasonable from the point of view of this analysis.