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In the textbook I refer to,and various places online, it is given that saturation current is independent of the frequency of light used and only depends on the intensity .

But, let intensity= I ,here,can we define I=nhf/A? ( Since intensity is energy per unit area per unit time, where f is the frequency) here A is the area of cross section of the plate, and n is the number of photons incident per unit time.

For the sake of simplicity, let us assume that each photon emits an electron. This means, photocurrent=i=ne. Putting n from the first equation, we get, i=IAe/hf. This expression certainly depends on frequency and intensity both. For reference, see this graph-

enter image description here

Even here , why is the saturation current the same for the 3 frequencies?

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Accurately - The saturation current depends on the number of photons striking the metal surface. Since , Intensity is proportional to number of photons per cross section hence you'll find a lot of books stating that Intensity decides the saturation current. If you keep intensity fixed , and change the frequency then the Saturation current will in fact decrease. This is because Intensity = nhf/A ; for intensity to remain constant with increasing frequency the number of photons striking the metal surface must decrease.


The graph you are referring to has different frequency but same current , which implies than the number of photons are equal in all the cases , however intensity may not be.

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