# Photoelectric effect with electrons

Consider a beam of electrons (each electron with energy E0) incident on a metal surface kept in an evacuated chamber. Then,.
(a) no electrons will be emitted as only photons can emit electrons.
(b) electrons can be emitted but all with an energy, E0.
(c) electrons can be emitted with any energy, with a maximum of E0 – ɸ (ɸ is the work function).
(d) electron can be omitted with energy ,with a maximum of E0.
This question was in my textbook. I thought the answer would be option C but it was given the answer is option D. I can't understand why is this so. Why can't we extend Photoelectric effect here?

• Just think of what would happen if an electron “rebounded” from the surface. – Farcher Sep 5 '18 at 5:28

You fire an electron at the metal surface with some energy $E_0$. The work function $\phi$ is the energy an electron loses when it leaves the surface, and therefore it is also the energy an electron gains when it enters the surface. So when the electron you fire at the surface passes through the surface its energy increases to $E_0+\phi$.
Assuming the incident electron manages to put all its energy into ejecting some other electron that electron will start with an energy $E_0+\phi$, lose an energy $\phi$ leaving the surface and end up with a final energy $E_0$.