The nuclei of atoms in a certain crystalline solid haw spin one. According to quantum theory, each nucleus can therefore be in any one of three quantum states labeled by the quantum number m. where m = -1, 0, or +1. This quantum number measures the projection of the nuclear spin along a crystal axis of the solid. Since the electric charge distribution in the nucleus is not spherically symmetrical, but ellipsoidal, the energy of a nucleus depends on its spin orientation with respect to the internal electric field existing at its location. Thus a nucleus has the same energy E = elementof in the state m = 1 and the state m = -1, compared with an energy E = 0 in the state m - 0.

(a) Find an expression, as a function of absolute temperature T, of the nuclear contribution to the molar internal energy of the solid.

(b) Find an expression, as a function of T, of the nuclear contribution to the molar entropy of the solid.

(c) By directly counting the total number of accessible states, calculate the nuclear contribution to the molar entropy of the solid at wry low temperatures. Calculate it also at wry high temperatures. Show that the expression in part (b) reduces properly to these values as T rightarrow 0 and T rightarrow infinity.

(d) Make a qualitative graph showing the temperature dependence of the nuclear contribution to the molar heat capacity of the solid. Calculate its temperature dependence explicitly. What is the temperature dependence for large values of T?