Could the saturation current last forever? (Photoelectric effect)

Question

It is understood that the saturation current is achieved when the potential difference across the emitting and collecting plate allow for the rate of photoelectric emissions to equal the rate of photoelectric collection.

However, given that the photoelectric effect ultimately is the ‘removal’ of electrons- wouldn’t electrons in the metal eventually run out? Or at least, as more and more electrons are removed, the net attractive force towards nuclei grow stronger such that a work function energy becomes greater than the energy of incident photons?

To me, such a scenario seems logical. If the emitter plate is unearthed/without any infinite supply of electrons, there should be a limit to the number of electrons that can be emitted from it, which could be dependent on factors such as the energy of incident photons. As the total number of photoelectric emissions reaches this limit, the ‘saturation’ current should slowly die out to zero.

I couldn’t find any answer to this question so it would be good to have any input/references! Thanks in advance :)

Answer 1

If the emitter plate is isolated, every electron removed gives it some positive potential. If the collector plate potential is fixed, that increases the retarding potential. Eventually, the retarding potential exceeds the cutoff and no more current flows.

The usual form of the experiment involves fixing the potential between the two electrodes using an external voltage source, which moves electrons as needed to maintain the potential.