Atoms of an element, E, are being adsorbed on the surface of a material, M. Materials M has N adsorption sites available per square centimeter of surface. (a) Derive an expression for the entropy of NE atoms of the element E adsorbed on M (per square centimeter) assuming that the adsorbing atoms have zero interaction energy with each other. They do, of course, have an interaction energy with the surface atoms of M; (b). At what ratio of E atoms to adsorption sites (NE/N) will this entropy be a maximum?