Question

The Lennard-Jones potential experienced by two non-polar, non-covalently bonded atoms can be described by the equation V(r)=\frac{A}{r^{12}}-\frac{B}{r^{6}} where V(r) is the energy of the interaction, A and B are constants and r is the internuclear distance between the atoms. (a) Describe the interactions that give rise to the two terms in the Lennard-Jones potential and explain why they have such different distance dependencies. (b) Find the values of r and V(r) at which V(r) is a minimum. (c) Sketch a graph of V(r) versus r, indicating the equilibrium internuclear distance and the hard core radius. \text { For a pair of neon atoms, } A=4 \times 10^{-28} \mathrm{~J} \mathrm{~nm}^{12} \text { and } B=1 \times 10^{-24} \mathrm{~J} \mathrm{~nm}^{6} Calculate the value of r at equilibrium and the energy of equilibrium at that distance for a pair of neon atoms. (e) Calculate the hard core radius and the internuclear energy when r = 2.9 Å for a pair of neon atoms.

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