The effective force constant of the molecular "spring" in HCl is 480 N/m, and the...

The effective force constant of the molecular "spring" in HCl is 480 N/m, and the bond length is 0.13 nm.

(a) Determine the energies of the two lowest-energy vibrational states.

(b) For these energies, determine the amplitude of vibration if the atoms could be treated as oscillating classical particle

(c) For these energies, by what percentage does the atomic separation fluctuate?

(d) Calculate the classical vibrational frequency  and the rotational frequency ωrot=L/l. For the rotational frequency, assume that L is its lowest nonzero value,  and that the moment of inertia I is μa2.

(e) Is it valid to treat the atomic separation as fixed for rotational motion while changing for vibrational?