Quantization/hydrogen atom problem

[zl1corvette]

I have a homework problem that goes like this.
A beam of electrons is incident upon a gas of hydrogen atoms. What minimum speed must the electrons have to cause the emission of 656 nm light from the 3 -> 2 transition of hydrogen?
So I had a couple of thoughts
1) It was the velocity needed to have state 3 orbit, but that's not right.
2) It was the velocity needed to have n=2 orbit, but that's not right either.
3) It was the velocity such that an electron had KE equal to the difference in E of states 3 and 2 but that's not it either.
I suppose the wavelength of the light has something to do with this but it's just the wavelength of hydrogen emission 3->2 so I don't know what that tells you.

 

[jtbell]

In order to produce transitions from n=3 to n=2 , you have to get the atoms into the n=3 state to begin with. Atoms are normally in their ground state (n=1).

 

[zl1corvette]

So if the incoming electrons had KE greater than the ionization energy it could remove an electron from the n=1 orbit and the atom completely. So a KE equal to the difference of the n=1 E and n=3 E would move it to the n=3 orbit? Then the orbiting electron simply falls back to the n=2 level?
*goes to try it*

edit:
It works!
Danke sehr
Does it just go back to n=2 because it's attacted to the nucleus or?