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Concerning the photoelectric effect: When the intensity and applied voltage are both constant, then the current is inversely proportional to frequency $f$ (above threshold frequency). If we increase $f$ then the current decreases and vice-versa, because the number of photons from a source is inversely proportional to the incident photon's frequency at constant Intensity. So the current vs. frequency graph will be hyperbolic. Am I right?

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The number of photons from a light source is not necessarily inversely proportional to the frequency of the light emitted. It appears that this consideration followed from an artificial requirement of fixed power emitted by the source (perhaps this is what you meant by "constant intensity") across all frequencies, which is not necessarily true for a real light source. If this is the case, then the photoelectric current will indeed be inversely proportional to the frequency of light, when the latter is above the threshold frequency.

In the general (steady) case, the photoelectric current is as such directly proportional to the rate of photon incidence and independent of the frequency of incident light, with the assumption that one can independently control these two parameters. This is the case that one normally considers, and here, the current vs frequency graph (at constant rate of photon incidence) steps up to a constant value from zero when the frequency increases beyond the threshold frequency.

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