A particle can be one of the 3 allowed microscopic quantum mechanical states and

Question

A particle can be one of the 3 allowed microscopic quantum mechanical states and it is in thermal equilibrium with its surroundings at absolute temperature T. The energies of these 3 states are: E1 = -, E2 = 0, and E3 = + where is a positive constant microscopic energy value. Find a) the canonical partition function Z, b) the average energy of this particle, and c) the contribution to the constant volume heat capactity of this particle all in temrs of the paramters T, , and Boltzmann's Constant k. Suppose that the absolute temperature T is given by kT = /ln(2). In this case, find d) the probabilities for the particle being in each of its three microscopic states and evaluate the answers to parts a)-c) for this case.

Explanation / Answer

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