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

  1. Consider the cyclobutadiene (C4H4) 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.
  2. 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.
  3. Problem 4-6 from text. Discuss why <E2> - <E>2 is not zero for this problem.
  4. If the vibrational frequency of H2 is 4401 cm-1, what is the frequency of HD? Of D2? Sketch on the same graph the vibrational wavefunctions of H2 and HD, taking care to show the qualitative differences.
  5. Problem 5-26 from text. (Use the results given in problem 5-24.)
  6. Evaluate L2f where L2 is the angular momentum operator and f = 1, cosq , and (sinq )eif .