A system of a particle in a magnetic field has a simple energy-level diagram that looks li...

A system of a particle in a magnetic field has a simple energy-level diagram that looks like this:

a. Write an expression for the partition function Q for the system. Your answer should be given in terms of D, T, and universal constants.

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b. Write an expression for the average energy of the system. Your answer should be given in terms of D, T, and universal constants.

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c. Calculate the average energy in the high-temperature limit.

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d. Calculate the average energy in the low-temperature limit.

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e. Write an expression for the ratio of the probabilities of finding the particle in the two states. Your answer should be given in terms of D, T, and universal constants.

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f. Calculate the entropy of the particle in the high-temperature limit.