Electrons bombard gaseous hydrogen – photon energies emitted?

1. The problem statement, all variables and given/known data

A beam of 13.0 eV electrons is used to bombard gaseous hydrogen in ground state.
What photon energies will be emitted?

2. Relevant equations

ΔE = -13.6 ([itex]\frac{1}{n^{2}_{f}}[/itex] – [itex]\frac{1}{n^{2}_{i}}[/itex])

However hydrogen is in the ground state therefore n_i= 1:

ΔE = -13.6 ([itex]\frac{1}{n^{2}_{f}}[/itex] – 1)

3. The attempt at a solution

Rearranging the above equation I got n_f = 4.76.

Am I correct in saying "the photon can be emitted from a maximum energy state of n=4"?
I’m unsure how to word it.

WRT the initial question, it asks what photon energies will be emitted so would I have to write them all down?


4[itex]\rightarrow[/itex]3 = 0.66 ev
4[itex]\rightarrow[/itex]2 = 2.55 ev
4[itex]\rightarrow[/itex]1 = 12.75 ev

3[itex]\rightarrow[/itex]2 = 1.89 ev
3[itex]\rightarrow[/itex]1 = 12.09 ev

2[itex]\rightarrow[/itex]1 = 10.2 ev


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