Problem 7.9. Consider a solid surface to be a two-dimensional lattice with N, sites. Assume that N atoms (Na N,) are adsorbed on the surface, so that each lattice site has either zero or one adsorbed atom. An adsorbed atom has energy E = -e, where >0. Assume the atoms on the surface do not interact with one another.

(a) If the surface is at temperature T, compute the chemical potential of the adsorbed atoms as a function of T,

e, and Na/N, (use the canonical ensemble).

(b) If the surface is in equilibrium with an ideal gas of similar atoms at temperature T compute the ratio Na/N, as a function of pressure, P, of the gas. Assume the gas has number density n. (Hint: Equate the chemical potentials of the adsorbed surface atoms and the gas.)