5. (a) Calculate the rate for spontaneous transitions between the n = 1 and n = 0 states of a simple harmonic oscillator, carrying charge e. Take the mass of the oscillator to be equal to the mass of an atom of some typical ionic molecule, and the restoring force constant C to be 103 joules/m2, which is typical for such a molecule. (Hint: Normalized eigenfunctions must be used.) (b) From the transition rate, estimate the average time required to complete the transition. This is the lifetime of the n = l Vibrational state of the molecule