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 ($\frac{1}{n^{2}_{f}}$ – $\frac{1}{n^{2}_{i}}$)

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

ΔE = -13.6 ($\frac{1}{n^{2}_{f}}$ – 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?

ie

4$\rightarrow$3 = 0.66 ev
4$\rightarrow$2 = 2.55 ev
4$\rightarrow$1 = 12.75 ev

3$\rightarrow$2 = 1.89 ev
3$\rightarrow$1 = 12.09 ev

2$\rightarrow$1 = 10.2 ev

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