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It is important to consider light as photon packets of energy where a single photon interacts with a single electron. Therefore, each individual photon must have enough energy to remove each electron. Increasing the intensity only increased the number of photons that are hitting the surface of the metal, not the energy of each photon. However, it is true that if the energy per photon is greater or equal to the energy needed to remove an electron, then increasing the light's intensity would eject more electrons (since there are more photon-to-electron interactions).
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