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It's basically saying that one photon must have enough energy to remove one electron and if it doesn't than it cannot remove that electron. However, if it does have enough energy or more energy then it can remove the electron and the rest of the energy will become kinetic energy.
I think Dr. Lavelle explained this using an example of hurdles. If someone doesn't have enough energy, then they will not be able to successfully jump over the hurdle. Similarly, if a photon does not have enough energy, then we say it does not meet the threshold energy, and therefore cannot remove an electron.
Essentially each photon needs to have more energy than than the energy to remove an electron from the metal (aka the threshold energy). So if 1000 photons hit the metal surface and each individual photon has enough energy, then 1000 electrons will be released.
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