Reference no: EM131550473

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).