[QUE/SM-03002] SM-PROBLEM

In a monoatomic crystalline solid each atom can occupy either
a regular lattice site or an interstitial site. The energy of an atom at an
interstitial site exceeds the energy of a atom at a lattice site by an amount
\(\epsilon\). Assume that the number interstitial sites equals the number of
lattice sites, and also equals the number of atoms \(N\). Calculate the entropy
of the crystal in the state where exactly \(n\) of the atoms are at the
interstitial sites. What is the temperature of the crystal in this state,if the
crystal is in thermal equilibrium? If \(\epsilon=1 \text{ev}\) and the
temperature of the crystal is 300K, what is the fraction of the atoms at the
interstitial sites?