Now consider a Rigid Rotor-Harmonic oscillator model for the HD molecule at temperature T=3 K. a) Where is each nuclei located relative to the center of mass in nm? b) What is the fraction of molecules in the first 5 rotational states in the vibrational ground state? c) Assuming that transition probabilities are independent of the rotational quantum number J, i.e., it only depends on the fraction/number of molecules in each J level, plot the rotational-vibrational spectrum as a function of wavelength for the n=0 to the n=1 vibrational transition, showing the rotational P and R branches for J=0 to 4 in the vibrational ground state? d) What is the average rotational energy assuming that only J=0 to 4 levels are populated in the vibrational ground state n=0?