Question

Is the energy of the photon coming in greater than or less than the energy of the electronic transition?

Answer 1

Neither. It has the energy given by the difference in energy, `E_f - E_i`.

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When photons are absorbed to excite an electron from initial energy `E_i` to final energy `E_f`, they must account for the difference in energy, `DeltaE = E_f - E_i` in order for the electron to transition upwards by that energy.

Suppose you wanted to go from `E_1` to `E_2` in the hydrogen atom. Then,

`E_"photon" = DeltaE = -"13.6 eV"(1/2^2 - 1/1^2)`

would be the energy that the one absorbed photon needs to be in order to get the electron from `n = 1` (where `E_1 = -"13.6 eV"`) to `n = 2` (where `E_2 = -"3.4 eV"`).

If you had `"13.6 eV"` for that photon, you wouldn't be going from `E_1` to `E_2`; you'd be going way past that, since the difference is only `+"10.2 eV"`. And since the difference is that, you can't have `"3.4 eV"` available and bridge that gap.