pchem question in thermodynamics law

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In the presence of a magnetic field, a nucleus with a spin of 3/2 (like sodium-23) is split into four non-degenerate energy levels whose energies (relative to the energy of the atom in the absence of a magnetic field) are : -3/2hγB, -1/2hγB, +1/2hγB, +3/2hγB. The gyromagnetic ratio for Na-23 is 11.25 MHz/Tesla.

a) What is the average energy of a Na-23 atom at 4K in the absence of a magnetic field? You can assume that the partition function for a monoatomic ideal gas is applicable here.

b) Assuming that the number you determined in part A gives a reasonable measure of the zero field energy of the Na-23 atom, calculate a numerical value for the partition function at 4K and a magnetic field strength of 100.0 Tesla.

c) Make a plot to show how the fraction of nuclei occupying the 2nd lowest energy level changes as a function of magnetic field strength (between 0 Tesla and 10000 Telsa) at a constant temperature of 4K.

d) Explain in words why your graph looks the way it looks. I me something about the underlying “why” based

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