Chapter 14, Problem 84GP

In some diatomic molecules, the force each atom exerts on the other can be approximated by $F=-C/r^2+D/r^3$, where r is the atomic separation and C and D are positive constants, (a) Graph F vs. r from r = 0.8D/C to r = 4D/C. (b) Show that equilibrium occurs at r = r₀ = D/C. (c) Let Δr = r – r₀ be a small displacement from equilibrium, where $\Delta r\ll r_0$. Show that for such small displacements, the motion is approximately simple harmonic, and (d) determine the force constant. (e) What is the period of such motion? [Hint: Assume one atom is kept at rest.]