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1. Consider a three level system in which the energies are equally spaced (by energy ε);...

1. Consider a three level system in which the energies are equally spaced (by energy ε); each of the levels has certain (nonzero) degeneracy g .

A. Write down the general expression for the average energy and the partition function of the system.

B. Compute the occupations for ε = kT, when (i) all the states are singly degenerate and (ii) when the degeneracies are g0 = 1, g1 = 1, g2 = 3. Here gj represents the degeneracy of the jth state.

C. Suppose that ε = 2kcal·mol−1 and the degeneracies are g0 = 1, g1 = 1, g2 = 1000. At what temperature T will the occupation probability for finding the system in energy state 0 and 2 be the same? What will be the occupation of state 1 at this temperature?

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