On the Influence of Temperature upon the Photo-electric Effect

Photo-electric threshold frequency for metals.—Free electron theory. A discussion is given of the suggestion by Millikan that in the photo-electric effect the energy of the light is transferred to the free electrons of the metals as well as to the bound electrons, and the threshold frequency ${\nu }_0$ is interpreted by the equation $h{\nu }_0={\varphi }_p-E_k$ where ${\varphi }_p$ is the work necessary to remove a free electron from the metal. In cases where $E_k$ is not small compared with ${\varphi }_p$ the theory leads to a lack of sharpness in the definition of ${\nu }_0$. Neglecting variations of kinetic energy, the difference of stopping potentials comes out equal to the Peltier coefficient; hence the uniformity of stopping potentials for different metals observed by Millikan is due, according to the theory, to the smallness of the Peltier effect. The variation of the long wave-length limit with temperature comes out $\frac{\partial {\lambda }_0}{\partial T}=\left(\frac{\lambda _0^{}{}_{}{}^2}{\mathrm{hc}}\right)e\sigma$, $\sigma$ being the Thomson coefficient. In most cases ${\lambda }_0$ should be practically independent of temperature. In the case of aluminum, after prolonged heating, the photo-electric current due to $\lambda 2537$ was found to remain constant within 1/2 per cent as the target was cooled from 400° to 100°C and this constancy is interpreted as evidence that the shift of the long wavelength limit with change of temperature is less than 1A. The limit was found to be at about 2700A. Similar observations with a nickel target and 2412A gave inconclusive results, as in spite of heating to 1300°C and reduction of the oxide on the surface by heating in hydrogen, reproducible results were not obtained.