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My notes says "Increasing the voltage drives increasingly more energetic electrons back until finally none of them are able to leave the metal surface and the ammeter reads zero. The voltage at which this occurs is called the stopping voltage $V_s$ and is a measure of the maximum kinetic energy of the photoelectrons emitted."

The part I believe may be incorrect is where they say 'none of them are able to leave the metal surface and the ammeter reads zero'. Because other sources say stopping voltage is 'the voltage which just prevents electrons from arriving at the anode.'

Are my notes incorrect? Thanks for the clarification..

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Your notes are wrong!

It's wrong to say that stopping potential prevent electron from leaving the electron from the surface because it's clear that if photons of high enough energy bump to electrons it will eventually leave the metal surface. $$h\nu-h\nu_0=K>0\rightarrow \ e^- \text{will leave the surface.}$$

$$\text{If}\ \ K<eV_0\rightarrow I=0$$

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I suspect it's just a question of semantics. A rocket that leaves the atmosphere of Earth but doesn't achieve escape velocity will eventually "fall" back down. Can it be said that this rocket has truly "left" the Earth?

That said, it is not correct to say that the presence of a stopping voltage will keep electrons permanently trapped in their current energy states within the metal--"stuck to the surface", if you will. It is correct to say that they are prevented from reaching "escape velocity"--that is, they will eventually return to the metal without being detected.

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