Chemistry 3730 Practice Problems

1. In intense laser fields, two-photon processes sometimes occur. In a two-photon process, two photons are simultaneously absorbed by a molecule (hence the name). Derive the selection rule for the change in the rotational angular momentum quantum number J during a two-photon process.
2. Describe a spectroscopic method for measuring the equilibrium bond length of a molecule.
3. 1. Give the Hamiltonian and boundary conditions for the particle-in-a-box problem.
   2. Apply the variational method to the particle-in-a-box problem using a sine function as your trial wavefunction. Do you get all of the particle-in-a-box solutions by this method? Discuss.
4. Describe in detail two different methods for solving the quantum mechanical problem consisting of a pair of particles bound by the potential

   

   where , R is the bond length, and is the equilibrium bond length.

5. 1. Write down the Born-Oppenheimer electronic Hamiltonian for LiH. If you use summation symbols in your Hamiltonian (a practice which I recommend), make sure to write down the summation limits explicitly.
   2. Explain how you would go about determining approximate formulas for the LiH molecular orbitals at a particular internuclear separation R.
   3. Explain why I specified ``at a particular internuclear separation'' in the previous question in relation to Born-Oppenheimer theory.
6. Describe in detail a method for obtaining an accurate ground-state energy for the helium atom. Show all relevant equations and discuss any difficulties which you anticipate in their solution. Also briefly describe how excited state energies might be obtained.
7. Describe one flaw of standard Hückel molecular orbital theory. Explain how the flaw in question can be corrected.
8. If there were no Pauli exclusion principle, could be synthesized? Explain.
9. 1. Describe (in simple terms) the design of a Raman spectrometer. Explain (again, in simple terms) the operating principles involved.
   2. Name the frequency range in which the spectrometer should operate to study pure rotational transitions.
10. What information would you need to calculate the delocalization energy of ethanal ( )?
11. Describe Einstein's contribution to the development of quantum mechanics.
12. 1. Sketch the MO diagram necessary to treat second-row homonuclear diatomics. You may need to guess at the order of some of the MOs. The objective is to draw a reasonable MO diagram, not necessarily to get the ``correct'' MO diagram which must be determined experimentally.
    2. Use your MO diagram to predict the bond order of . Draw a Lewis diagram corresponding to your predicted electronic configuration.
13. Describe the effect of the following NMR pulse sequence on the magnetization vector:

    

14. Give a complete MO treatment of bonding in the gas-phase molecule LiF. Explain how you would decide, on a quantum mechanical basis, whether the bond in this molecule is mostly ionic or mostly covalent.
15. Calculate the approximate de Broglie wavelength of a hockey puck during a hockey game. Based on your calculation, would quantum mechanical effects be important for hockey pucks? Explain.
16. 1. Phenylalanine is a fluorescent amino acid. Its fluorescence lifetime in water is 6.4ns and the quantum yield for fluorescence is 0.004. Calculate the rate constants for fluorescence and thermal deactivation.
    2. In your opinion, would phenylalanine be a good pigment for fluorescent paints? Why or why not?