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A solid surface is in diffusive and thermal equilibrium with a monatomic ideal gas at temperature...

A solid surface is in diffusive and thermal equilibrium with a monatomic ideal gas at temperature t and chemical potential μ. An adsorption site on the solid surface can be either empty (energy ε0 = 0), singly occupied (ε1 = ε), or doubly occupied (ε2 = 2ε) by an atom from the gas. If two atoms adsorb onto the same site, they also interact by a vibrational mode of frequency w. Thus, the energy of a doubly occupied site can take on the values ε2 + n!w, where n = 0, 1, 2,….

a) What are the limiting probability ratios when the vibrational frequency is large

such that ℏ? ≫ ??

b) Prove that when the vibrational frequency is very small (ℏ? ≪ ?), double

occupancy becomes strongly favored.

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genius_generous answered 2 years ago
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