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So the photoelectric effect causes metals to emit electrons in contact with light. I have two questions...

1) Does this keep happening until no more electrons are being emitted? 2) Can't this effect the charge of the metal? (Losing electrons while keeping protons)?

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A metal exposed to light, with energy higher than the work function of the metal, will emit photoelectrons. If the metal is not grounded or connected to any other electron source, there will be excess positive charge accumulated on the surface which will stop further photoemission. Otherwise the metal will always replenish the lost electrons and keep emitting "new" photoelectrons.

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Yes and yes. If you form a circuit as with a solar cell you can generate electricity http://www.electronics-tutorials.ws/articles/solar2.gif?81223b

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If you shine high energy light on a piece of metal floating in space, electrons will continue to be ejected. However once a certain number of electrons have flown away, leaving the metal positive charged, the subsequent ejected electrons will simply fall back towards the metal as they are attracted to the positive charge.

So indeed for an isolated piece of metal it is a self-limiting process.

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