7. (15 pts) The potential energy function for either one of the two atoms in a diatomic molecule can be approximated by \(U(r) = a / r^{12} - b / r^{6}\) , where \(a\) and \(b\) are constants and \(r\) is the distance between the atoms. (a) Derive an expression for the force on an atom as a function of \(r\) , \(a\) , and \(b\) . (b) At what distance \(r\) does the potential energy have a local minimum (not at \(r = \infty\) )? (c) What is the force on the atom for this value of \(r\) ? 讲题 解题