Theory of the Work Functions of Monovalent Metals

Abstract

The factors which determine the work function of a metal are described in a qualitative way. The work function is defined as the difference in energy between a lattice with an equal number of ions and electrons, and the lattice with the same number of ions, but with one electron removed. The work function is then found by first calculating the energy of a lattice with $n_i$ ions and $n_e$ electrons. The final formula gives the work functions of monovalent metals in terms of the heats of sublimation. This formula is approximate, and can claim validity only in a qualitative way, as one of the important factors, the electric double layer on the surface, is omitted entirely, and it is assumed that the Fermi energy is as great as if the electrons were entirely free. The values obtained from this formula check very closely with the experimental values for the alkalis, so that it can be concluded that the double layer is probably small for these metals. Finally, the deviations to be expected for other than monovalent metals are considered. A more exact calculation of the work function of one substance (Na) will be given by one of us in an ensuing paper.