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: , where is the electron density parameter expressed in units of the Bohr radius, is the Fermi energy and is an empirical constant ( for the alkali metals, Ca, Sr, Ba, Ra and Tl, whereas 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 ).