Q.Explain why the maximum kinetic energy of the emitted photoelectrons depends only on the frequency of the incident light and the nature of the metal, and does not depend on the intensity of the light.

The governing equation. Einstein's photoelectric equation, $K_{max}=h\nu-\phi_0$, contains only two physical quantities on the right-hand side: $\nu$, the frequency of the light (which fixes the energy $h\nu$ of a SINGLE absorbed photon), and $\phi_0$, the work function of the metal (a fixed property of the material). Intensity does not appear in this equation at all.

Why intensity is absent. In the one-photon-one-electron picture (Section 11.7), each photoelectron's kinetic energy comes from exactly ONE photon's energy, minus the fixed 'entry cost' $\phi_0$ of escaping the metal -- it has no way of 'knowing' how many OTHER photons are also arriving at the surface each second. Increasing the intensity of light of the SAME frequency increases only the NUMBER of photons striking the surface per second, and so increases the number of successful photon-electron events ( …

Point to Einstein's equation and note intensity does not appear in it, then explain physically why: $K_{max}$ comes from one photon's energy, and intensity onl …

• Confusing $K_{max}$ (the energy of ONE electron) with the photocurrent (which DOES depend on intensity, since it counts electrons per second) -- these are two different quantities, and only the current is intensity-dependent. …