Work functions of elements expressed in terms of the Fermi energy and the density of free electrons

On the basis of Brodie's definition of the work function and the length of spontaneous polarization of plasma, the following new formula for calculation of the work functions of elements has been derived: phi/eV = 43.46 alpha r(s)(-3/2) (E-F/eV)(-1/2), where r(s) is the electron density parameter expressed in units of the Bohr radius, EF is the Fermi energy and alpha is an empirical constant (alpha = 0.86 for the alkali metals, Ca, Sr, Pa Ra and Tl, whereas alpha = 1.00 for the remaining elements). The density parameter was calculated from the atomic mass, the bulk density of the element and the assessed number of free electrons per atom which is equal to the nominal valence of the element or, in the case of transition metals, close to this number (within +/-0.5). The values obtained by using the above formula are in excellent agreement with experimental data for pure-metal polycrystalline surfaces, within 5% in most cases. A table with the work functions and with complete input data for most of the elements is presented.