(sorry to hijack thread)
but any ideas on how to do this one?
Well the electrons in the atom are being bombarded with energy. I presume it's not that different from being bombarded with photons.
This means we follow "Bohr's Postulates" and that any of the possible energies must be discrete. My approach to finding out the discrete energies is inefficient, it involves guessing at what a number will be and then punching it into the calculator (and then repeating until I find one that matches). This usually works on the simpler questions where you don't need to find out much.
So, elimination:
It cannot be 10.2 eV (E), so it cannot be (F). A few quick calculations show that it can't be 1.4eV (B) - (the smallest I found was 1.6). This also allows us to eliminate (A).
We are left with (C) and (D) to check.
My method seems a bit inefficient, I might be missing a few numbers.
A better way might be to systematically punch in numbers (e.g. 10.4 - 8.8, then 10.4 - 6.7 etc. and when you do all the 10.4 calculations, drop down to 8.8 - 6.7 (you won't need to do 8.8 - 10.4, since you've already done it at the start - only difference is the answer will be negative).
I don't know why I wasn't doing that before. I went through all the possible discrete energies in about 1 minute. Which raises a problem, none of the energies matched the energies in the list. I'm confused, is there anything I'm forgetting?
Oh of course.
Emerging electrons. The energies listed are the energy after the electron has been emitted. The electrons are left with a bit of extra kinetic energy. I should have realised this earlier, it would have made calculations quicker.
To quickly show you all the possible calculations, I just used excel:

So we can get B - 1.4, C - 3.5, D - 5.3
Sorry for the almost stream of consciousness style, I can't be bothered editing the post to just focus on the correct working out.