In a monatomic 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 an atom at a lattice site by an amount ε. Assume that the numberof 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 N atoms are at interstitial sites. What is the temperature of the crystal in this state, if the crystal is in thermal equilibrium? If ε = 1 eV and the temperature of the crystal is 300 K, what is the fraction of atoms at interstitial sites?
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