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I believe the electron can still be ejected. I have in my notes from lecture that as long as the energy of the photon is greater than or equal to the work function, then the electron will be emitted.
I think maybe the electron wouldn't really move from the surface, but it would still be physically separated from the other atoms/electrons (it wouldn't be bound). Then again, that's a pretty rare scenario, for the energy of the photon to match the threshold energy exactly haha :DD
That's a good question and I believe the answer is revealed in your question: you say that the energy of the photon would be exactly the same as the energy needed to remove the electron, so wouldn't this imply that the electron is ejected because it received the EXACT amount NEEDED to REMOVE it from the surface. Based on this logic, I would assume that the electron is ejected, but I am not completely sure.
I believe in an experiment, there is a machine that has a positive charge that will attract that electron to it. However, in real life, if the electron doesn't have any excess kinetic energy, it would be removed from the atom temporarily and then reabsorbed as it is pulled by the positive charge of the nucleus.
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