8.2 Exercise 9

The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by $U \left(x\right) = a / x^{12} - b / x^{6}$ where x is the distance between the atoms. (a) At what distance of separation does the potential energy have a local minimum (not at $x = \infty \left.\right) ?$ (b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance?