Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 40

40 The potential energy of a diatomic molecule (a two-atom system like \( H_2 \) or \( O_2 \)) is given by \[ U = \frac{A}{r^{12}} - \frac{B}{r^6} \] where \( r \) is the separation of the two atoms of the molecule and \( A \) and \( B \) are positive constants. This potential energy is associated with the force that binds the two atoms together. (a) Find the equilibrium separation—that is, the distance between the atoms at which the force on each atom is zero. Is the force repulsive (the atoms are pushed apart) or attractive (they are pulled together) if their separation is (b) smaller and (c) larger than the equilibrium separation?