When the frequency of light falling on a metal is increased, while keeping the intensity constant, the photoelectric current does increase. This phenomenon is described by the photoelectric effect, which states that the emission of electrons from a metal surface occurs when photons of sufficient energy (corresponding to the frequency of light) interact with the metal.
The photoelectric effect can be summarized as follows: When photons of light strike the surface of a metal, they can transfer their energy to the electrons in the metal. If the energy of the photons is greater than the work function of the metal (the minimum energy required to remove an electron from the metal), then electrons are emitted from the surface. These emitted electrons can then be collected as a photoelectric current.
When the frequency of light is increased, the energy of the individual photons increases as well. If the increased frequency corresponds to photon energies that are above the work function of the metal, more electrons can be ejected from the metal surface. This leads to an increased photoelectric current.
The intensity of light, which refers to the number of photons striking the metal surface per unit time, does not directly affect the photoelectric current for a fixed frequency. The number of photons reaching the surface increases with increasing intensity, but each photon will still only eject one electron, provided it has enough energy (frequency) to do so. Therefore, while the number of emitted electrons per second may increase with higher light intensity, the photoelectric current per ejected electron remains the same.
To summarize, increasing the frequency of light falling on a metal surface, while keeping the intensity constant, increases the energy of the photons reaching the metal. If the increased frequency corresponds to energies above the work function of the metal, more electrons are ejected, resulting in an increased photoelectric current.