In a vacuum, if electrons are accelerated by a certain voltage, giving the electrons a specific de Broglie wavelength and were incident on a piece of metal, providing the wavelength was roughly the diameter/distance between two of the atoms in the metal, would the electrons interact with the metal as a wave due to diffraction of the elections taking place?
If so, would this mean that the delocalised electrons further in the metal would receive the energy carried by the accelerated electrons in the form of a wave and as a result electrons in the metal would gain energy over a period of time as appose to instantaneous electron emission due to the transfer of energy from electron-electron collisions, as particles?
This is all theoretical, assuming perfect 'conditions'.
I apologise if this makes no sense what so ever. I was just looking at the photoelectric effect and wave particle duality and this question just arose out of curiosity.