why in Photoelectric effect the number of photoelectrons emitted is proportional to intensity of incident beam
Answers
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The frequency of the light is proportional to the energy of the light (through E=hf) and therefore only affects the kinetic energy of the photoelectrons coming out from the surface not their numbers.
For example, if you use light with low energy (that is low frequency) than the work function of the metal then you can increase the intensity as much as you want; no photoelectrons would be emitted. On the other hand, if you have light with energy higher than the work function of the metal even a very dim light source would emit photoelectrons.
So, the number of electrons emitted is only proportional to the intensity of the light not the energy (or frequency) as long as the energy of the photons is higher then the work function of the metal.