Molecules have additional degrees of freedom that atoms don't possess, namely, rotation and vibration. The energies associated with molecular rotation and vibration are quantized and photons can be emitted or absorbed by molecules making transitions from one rotational or vibrational state to another.
a. Show that the rotational energy of a system can be written as E(rot)=(L^2)/(2I) where L=angular momentum and I=moment of inertia
b. Suppose that angular momentum is quantized according to Bohr's hypothesis: L=jh with j being a positive integer. Consider the case of the diatomic molecule where the two atoms have equal mass M (for instance H2, N2 or O2) Derive an expression for the rotaional energy in terms of j, h, M, and r(0), the seperation between the two atomic nuclei in the molecule.
c. In the case of molecular hydrogen which has r(0)~ 1 Angstrom estimate the wavelength produced by the j=2 to 1 rotaional transition. Is this longer or shorter than the wavelength of visible light?