513.001 Molecular and Solid State Physics

van der Waals crystal

In weakly interacting systems, the interaction between two atoms i and j is often described by the Lennard-Jones potential.

U(r_ij) = 4ε((σ/r_ij)¹² - (σ/r_ij)⁶).

with r_ij being the interatomic distance. Near T = 0 K, krypton is an fcc crystal with σ = 0.365 nm and ε = 2.25 10^-21 J. Calculate the lattice constant and the binding energy per atom assuming that only interactions between nearest neighbor atoms have to be considered.