Why does one electron gain energy when another drops in helium?

[aaaa202]

I have an exercise with the following text:

Suppose you put both electrons in a helium atom into the n=2 state. What would the energy of the emitted electron be?

I have attached the solution to the problem, but I am not sure I understand it. I understand the first part about the total initial energy. But I don't understand what follows. If the energy of each electron is E1 and one electron drops to a state below then shouldn't it only lose a portion of energy while leaving the other electrons energy unchanged?
Maybe I am thinking too clasically and should think of it as a total quantum system. But it is just weird for me that the electron can gain energy through the other jumping down - how is this energy transferred? (maybe too classical again) - and most importantly, why are we not considering the fact that the energy jump will cause a photon to be emitted like in the hydrogen case?

 

[TSny]

When one electron jumps to the ground state it must give up energy in some way. One way is the emission of a photon. But in this problem it is assumed that the energy is given directly to the other electron causing it to be ejected. This is called the Auger Effect . I agree that the process is hard to imagine classically. (But so is the emission of a photon, to me anyway. )