Question: Electronic Spectroscopy
1. (a) Which ?? → ??+1 transition(s) in the hydrogen atom occur in the visible range of the spectrum?
(b) Given your answer to (a), why would a (hypothetical) gas of hydrogen atoms not appear colored?
2. Electronic spectroscopy makes transitions between electronic states, as well as vibrational (and rotational) states. Explain why no general vibrational-state selection rule exists for electronic transitions.
3. (a) Which "part" of a molecule (whole molecule, vibrations, electrons, nuclei, etc.) does UV/Vis spectroscopy affect?
(b) Given your answer to part (a), write the transition dipole operator for UV/Vis spectroscopy.
(c) Of what coordinates is your operator in part (b) a function?
(d) When your operator in (b) acts on a general nuclear-electronic wavefunction Ψ(??,??), what happens? (Hint: For something like the benzene molecule, in how many dimensions is this integral defined?)
(e) When your operator in (b) instead acts on a Born-Oppenheimer-like nuclear-electronic wavefunction Ψ(??,??) = ??(??;??)??(??), what happens?
(f) Write the general form of the transition-dipole matrix element ∫???????? Ψ????^Ψi using the approximation from part (e).