When the frequency of light falling on a metal is increased while keeping the intensity constant, the photoelectric current does increase. This phenomenon is known as the photoelectric effect.
The photoelectric effect refers to the emission of electrons from a material's surface when it is exposed to light. The energy of the incident light is transferred to the electrons in the material, allowing them to overcome the binding forces of the material and be emitted.
In the photoelectric effect, the energy of a photon (a particle of light) is given by the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the light. When a photon interacts with an electron in the material, it transfers its energy to the electron. For the photoelectric effect to occur, the energy of the incident photon must be greater than or equal to the work function of the material.
The work function is the minimum energy required to remove an electron from the material. It represents the strength of the binding forces holding the electrons in the material. If the energy of the incident photon is less than the work function, no electrons will be emitted.
Now, when the frequency of the light is increased while the intensity (number of photons per unit time) remains constant, the energy of each photon increases. This means that more photons will have energy greater than the work function of the material, enabling them to eject electrons from the surface.
As a result, increasing the frequency of light leads to an increase in the number of photoelectrons emitted per unit time, thereby increasing the photoelectric current. This phenomenon demonstrates the particle-like nature of light, where the energy is quantized into discrete packets (photons) that can transfer their energy to electrons, liberating them from the material.
It's worth noting that the intensity of the light, which is the total energy per unit time per unit area, does not directly affect the photoelectric current in this scenario. Instead, it is the energy per photon (determined by the frequency) that influences the emission of electrons.