Xenon crystallises into an fcc lattice in its solid state. Xe atoms interact via a Lennard-Jones pair potential 12 ¹² [(-)¹² - ()] Upair (r) = 4€ (a) Derive an expression for the lattice energy per atom in solid fcc Xe considering only the first nearest neighbours. (b) Give expressions, in terms of o, for (i) the equilibrium spacing of nearest neighbours r₁, (ii) the lattice parameter a, and (iii) the density p of solid Xe denoting the mass of the Xe atom as mxe.

Xenon crystallises into an fcc lattice in its solid state. Xe atoms interact via a Lennard-Jones pair potential 12 ¹² [(-)¹² - ()] Upair (r) = 4€ (a) Derive an expression for the lattice energy per atom in solid fcc Xe considering only the first nearest neighbours. (b) Give expressions, in terms of o, for (i) the equilibrium spacing of nearest neighbours r₁, (ii) the lattice parameter a, and (iii) the density p of solid Xe denoting the mass of the Xe atom as mxe.