Chem 455 Spring 2015 Homework 7 due Mon May 18 5:00pm (in box 71 on 3rd floor)

1. Vibration/rotation. For 1H2H, the equilibrium bond length is pm, and the force constant is

   575.0 N m-1. (A) Use the rigid rotator-harmonic oscillator approximation to calculate the energies (in

   cm-1) of the first five rotational levels in the two lowest vibrational states. (B) Draw the corresponding

   energy level diagram to scale. (C) Indicate the allowed transitions in an infrared absorption

   experiment. (D) Calculate the frequencies of the first line in the P and R branches of the rotation-

   vibration spectrum.

2. Spherical coordinates. Confirm explicitly the following three differential operators are identical:

                   1  2                     1 2    ...