Chapter 42, Problem 47CP

As an alternative to Equation 42.1, another useful model for the potential energy of a diatomic molecule is the Morse potential

$U(r)=B{[e^{-a(r-r_0)}-1]}^2$

where B, a, and r₀ are parameters used to adjust the shape of the potential and its depth. (a) What is the equilibrium separation of the nuclei? (b) What is the depth of the potential well, defined as the difference in energy between the potential’s minimum value and its asymptote as r approaches infinity? (c) If μ is the reduced mass of the system of two nuclei and assuming the potential is nearly parabolic about the well minimum, what is the vibrational frequency of the diatomic molecule in its ground state? (d) What amount of energy needs to be supplied to the ground-state molecule to separate the two nuclei to infinity?