A 5d electron emits a photon, what are the possible quantum n,l, quantum numbers of the final s tate electron? What would the quantum num bers be a fter a photon with the smallest allowed (non-zero) energy is emitted?

Answer 1

Sketch the energy level diagram for atomic orbitals from 1s to 2s etc up to 5d. Then delta l can be +/-1 ONLY. Is 4f the next energy level down. If so then delta l (where l is 2 with a 5d) can go to 4f where the delta l is +1 or from 5d to 4p where delta l is -1. The series then could be 5d to 4p, 5d to 3p, 5d to 2p. The other selection rule is that ml can be 0,+/-1. This should get you started with the hard part. Then fill in the other quantum numbers given the transitions I've shown. It appears to me that the 5d to 4f is the transition with the smallest energy emitted.