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(rij) = 4ε((σ/rij)12 - (σ/rij)6).
with rij 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.