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When you increase the intensity of light you increase the number of photons emitted. As intensity increase the amplitude increases. Yes, intensity is like brightness in that intensity is the amount of energy delivered in a certain time to a certain area.
In the photoelectric effect, intensity has little to do with the intensity of the light. Because the energy emitted in this experiment doesn't act like a wave, high intensity/amplitude does not eject electrons and produce kinetic energy from the metal surface unless the E(photon) is greater than or equal to the E(threshold of removing an electron). In the photoelectric effect, higher frequency is what will produce kinetic energy as electrons are removed and photons are emitted.
Regarding the photoelectric effect, increasing the intensity of light means that you are increasing the amount of photons present. However, increasing the intensity of light does not allow for the displacement of electrons as the threshold is not meant since only the amplitude of the waves are changing and not the frequency.
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