The maximum kinetic energy of photoelectrons depends on the frequency of the light incident on the material, not on its intensity or wavelength. This is known as the photoelectric effect, which is the phenomenon where electrons are emitted from a material when it absorbs photons of sufficient energy. The energy of a photon is directly proportional to its frequency (E = hf), where E is the energy, h is Planck's constant, and f is the frequency.
According to the photoelectric effect, electrons can only be emitted from a material if the energy of the incident photons is greater than the work function of the material. The work function is the minimum energy required to remove an electron from the material. If the energy of the incident photons is greater than the work function, the excess energy appears as the kinetic energy of the emitted electrons.
The intensity of light, which refers to the brightness or the number of photons per unit area, does not affect the maximum kinetic energy of photoelectrons. It determines the number of photoelectrons emitted but not their energy. Similarly, the wavelength of light does not directly affect the maximum kinetic energy of photoelectrons. It is the frequency of the light that determines the energy of the photons, which in turn determines the maximum kinetic energy of the emitted photoelectrons.
Therefore, the correct answer is B. Frequency.