Homework # 3, Chem 1410, assigned Jan 25. Due. Jan 31.

- Consider the cyclobutadiene (C
_{4}H_{4}) molecule, which has a square-shaped structure. Using a two-dimensional particle-in-the-box model for the p electrons, estimate the energy in eV for exciting the lowest electronically excited state. - For the one-dimensional particle-in-the-box problem, calculate the probability of finding the particle between x = a/3 and x=2a/3, where is the length of the box, and the particle is an electron.
- Problem 4-6 from text. Discuss why <E
^{2}> - <E>^{2}is not zero for this problem. - If the vibrational frequency of H
_{2}is 4401 cm^{-1}, what is the frequency of HD? Of D_{2}? Sketch on the same graph the vibrational wavefunctions of H_{2}and HD, taking care to show the qualitative differences. - Problem 5-26 from text. (Use the results given in problem 5-24.)
- Evaluate L
^{2}f where L^{2}is the angular momentum operator and f = 1, cosq , and (sinq )e^{if }.