Afternoon! Please help, I've been stuck on this question for quite some time, and I'd sincerely appreciate a detailed response from anyone soon. Thank you!

Canonical Probability Distribution The nucleus of the nitrogen isotope 14N acts, in some ways, like a spinning, oblate sphere of positive charge. The nucleus has a spin of 1 and an equatorial bulge; the latter produces an electric quadrupole moment. Consider such a nucleus to be spatially fixed, but free to take on various orientations relative to an external homogeneous electric field (whose direction at the nucleus we take to be the z-axis). The nucleus has three energy eigenstates, each with a definite value for the projection sz of the spin along the field direction. The spin orientations and the associated energies are the following: spin up (sz=1), energy =0; spin "sideways" (sz=0), energy =0; spin down (sz=1), energy =0 (again). Here energy 0 denotes a small positive energy. a. In thermal equilibrium at temperature T, what is the probability of finding the nucleus with spin up? In what limit would this be 1/3 ? b. Calculate the energy estimate in terms of energy =0,T, etc. Sketch as a function of T. c. Calculate the heat capacity and sketch as a function of T. d. What value does the estimate sz have? Give a qualitative reason for the numerical result