Consider the rotational and vibrational spectra of H2 molecule (neglect the effect of nuclear spins!). A (10 pts) What is the rotational quantum number J of a hydrogen molecule (the interatomic distance is 0.75˚A ), if you know that the molecule has rotational energy EJ = 4.24 × 103 J · mol−1 . B (10 pts) Calculate the vibrational quantum number n of the hydrogen molecule if you know that the molecule is in a particular vibrational state with energy En = 4.13 × 10−20 J. The force constant describing the bond between the two H atoms is k = 5.1 × 105 g·s −2 . C (10 pts) Calculate the relative occupation of the rotational and vibrational states N(J) N(J=0) and N(n) N(n=0) of H2 for all the rotational/vibrational states characterized by J and n between 1 and 3. (Note: do not consider coupling between rotations and vibrations).