A nitrogen nucleus spin can adopt any of three orientations in a magnetic field, and its energies

Question:

A nitrogen nucleus spin can adopt any of three orientations in a magnetic field, and its energies are 0, ±YNn'13, where YN is the magnetogyricrati ratio of the nucleus. Deduce an expression for the partition function and mean energy of the nucleus and sketch the variation of the functions with 13. Calculate the relative populations of the spin states at
(a) 1.0 K,
(b) 298 K when13=20.0 T.