[QUE/SM-03008] 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?

 MANDL