A hydrogen iodide molecule, HI, has a force constant of 314 N/m and a bond length of 160 ppm. Due to the large difference in mass between the H-atom and the I-atom, the mass to use in the expression for the vibrational frequency can in good approximation, be taken as the mass of the H-atom. For the same reason, the rotation of the molecule can be pictures as an orbital motion of the H-atom around a stationary I-atom.
A) Calculate the zero-point energy associated with its rotation in three-dimensional space. Also calculate the zero-point energy associated with its vibration.
B) What is the smallest quantum of energy that can be absorbed by this molecule in a rotational excitation? What is the smallest quantum of energy that can be absorbed in a vibrational excitation? In what regions of the electromagnetic spectrum do the transitions lie?
Note: This is a 3D problem, so particle in a sphere should be used.