Chapter 11, Problem 14P

(a)

To determine

Show that $R_0$ is the equilibrium separation and that the potential energy far from equilibrium approaches $U_0$.

(b)

To determine

Show that for near equilibrium, $r\approx R_0$, the Morse potential is harmonic with the force constant $K=m{\omega }^2=2U_0{\beta }^2$.

(c)

To determine

The expression for the dissociation energy of the molecule using lowest vibrational energy for the Morse oscillator.

(d)

To determine

The Morse parameters $U_0$ and $\beta$ for the hydrogen molecule.