Answers to spectroscopy/quantum mechanics problems from the practice final.

21. Electronic transitions are the highest energy and correspond to transitions between electronic orbitals of an atom or molecule. The next highest energy transitions are vibrational transitions. These correspond to transitions between the vibrational states of molecules. The lowest energy transition of the three are rotational. These correspond to transitions between different frequencies of rotation within a molecule.

22. The energy of a transition is the energy required to go from one orbital to another. Thus, transitions energies are energy differences between orbitals.

23. No, in most large molecule spectra the vibrational bands are substantially broadened by the fact that large molecules can exist in many conformations giving rise to inhomogeneous broadening.

24. Uncertainty Broadening. There is always an uncertainty in the energy (and therefore a spread in the wavelengths) of a transition which is related to the fact that it is only in the upper (excited) state for a short period of time (the uncertainty in time and energy, like the uncertainty in position and momentum, are governed by an uncertainty relationship).

25.

26. 1cal = 4.184 J therefore 30 kcals/mole = 125520 J/mole. The energy to make one ATP under standard conditions is 125520/6.0221x10²³ = 2.084x10^-19 J. A 700 nm photon has 2.8378x10^-19 J. Thus, it would only take one.

27. A couple of things can happen. First, the lower the temperature, the larger the number of molecules or atoms that exist in the lowest vibrational state in the ground electronic state. Thus all the molecules start in the same state. Also, it is frequently the case that the slowly interconverting forms of the molecule (which each have different spectral characteristics) also tend to convert to the lowest energy for upon cooling.

28. k_obs = k_NR + k_f where k_NR is the nonradiative rate constant and k_f is the radiative rate constant. k_NR = k_obs - k_f = 1 ns^-1 - 0.1 ns^-1 = 0.9 ns^-1.