Theory of the Energy Distribution of Photoelectrons

Because of the thermal energies of the electrons in a metal there can be no sharply defined maximum emission energy of photoelectrons, as was once supposed. On the basis of the Sommerfeld theory and the Fermi-Dirac statistics, expressions are derived for the form of the energy distribution and current voltage curves in the vicinity of the apparent maximum energy. The method used is similar to that used by Fowler in computing the total emission current. In Part I the energies normal to the emitting surface are considered. At 0^ the theoretical current-voltage curve is a parabola tangent to the energy axis at V₌₀ₗ, while for higher temperatures it approaches the axis asymptotically. In Part II the treatment is extended to the total energy of emission and in this case the current-voltage curve at 0^ is a parabola concave toward the voltage axis and cutting it at a large angle. At higher temperatures there is an asymptotic approach. Even at room temperature there is an uncertainty of several hundredths of a volt in V₌₀ₗ, though the theory yields a method of determining the maximum energy which would be observed at 0^. Both parts of the theory are found to be in agreement with new experiments on molybdenum. The bearing of the theory on the photoelectric determination of h is discussed.