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In photoelectric effect, when the photon gives energy to the electron, then what happens to itself? Where does it go?

For me the photon must take the place of electron after the electron escapes the atom. And now the photon acts as electron for the atom and that's the atomic spectra must be different for atoms in excited state

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The photon is absorbed by the electron. In other words: The photon just disappears.

Remember, the number of photons is not conserved in nature, unlike for example the number of electrons (more precisely: the number of electrons minus the number of positrons).

Photons can be created by charged particles ("emission"), and they can be destroyed by charged particles ("absorption").

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The photon is not converted into an electron in the photoelectric effect. Photons do not have charge and cannot fill the void of an electron. In bulk conductors such as metals, the charge imbalance is restored by current.

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