Starting from a set of rate equations for the bound-state occupation functions for gas-solid systems in which the surface potential has many physisorbed bound states, we derive a master equation; its kernel is explicitly calculated for phonon-mediated adsorption and desorption in a Morse potential. We give the equivalent Smoluchowski-Chapman-Kolmogorov equation for which we find the Kramers-Moyal expansion. Identifying van Kampen's large parameter $\Omega$ for such gas-solid systems, we establish explicit criteria for the validity of a Fokker-Planck equation.

• Received 14 January 1981

DOI:https://doi.org/10.1103/PhysRevB.24.4456