Q.It is observed in an experiment on photoelectric effect that an increase in the intensity of the incident radiation does not change the maximum kinetic energy of the electrons. Where does the extra energy of the incident radiation go? Is it lost? State your answer with explanatory reasoning.

[!TLDR] The extra energy is not lost -- it goes into producing MORE photoelectrons per second (a larger photocurrent), since each additional photon still only carries the same fixed energy $h\nu$ and can only eject one electron with that same $KE_{max}=h\nu-\phi_0$; more intensity means more photons, not more energetic ones. [!ANSWER] The extra energy is not lost; it produces MORE photoelectrons (a larger photocurrent), not more energetic ones.

In Einstein's photon picture, each photon of a given frequency $\nu$ carries a FIXED energy $h\nu$, entirely independent of the beam's intensity. Increasing the intensity of the incident radiation, at a fixed frequency, does not make each individual photon any more energetic -- it only increases the NUMBER of photons arriving per unit area per unit time.\n\nWhen a photon collides with an electron, it can only transfer its own fixed energy $h\nu$ to that one electron; this energy splits into the work function $\phi_0$ needed to escape the surface, plus whatever is left over as kinetic energy, so the maximum possible kinetic energy $KE_{max}=h\nu-\phi_0$ is fixed by frequency alone, with no way for a 'more intense' photon to somehow give an electron extra energy -- there simply is no such thing as a more energetic photon at the same frequency.\n\nThe genuinely EXTRA energy carried by a more intense beam (compared to a less intense one at the same frequency) is therefore not lost at all: it goes into producing MORE electron-photon collisions per second -- that is, MORE photoelectrons ejected per second, each still with the same $KE_{max}$ as before. This directly produces a LARGER photocurrent (more charge flowing per second), which is exactly what observations 3 and 5 in section 14.2.2 record: photocurrent (and saturation current) increases proportionally with intensity, while the maximum kinetic energy of each individual electron stays completely unchanged. So nothing is 'wasted' -- the additional incident energy is fully accounted for by the additional number of electrons emitted, not by making any single electron more energetic. [!ANSWER] The extra energy is not lost; it produces MORE photoelectrons (a larger photocurrent), not more energetic ones.

Apply Einstein's photon picture: intensity controls the NUMBER of photons (hence number of electrons emitted, i.e. photocurrent), while frequency alone controls each photon's (and hence each electron's) energy.

Assuming that 'more energy in' must somehow mean 'more energy per electron out' -- this conflates the total energy of the beam (which does scale with intensity) with the energy of a SINGLE photon (which does not), missing that intensity and photon count, not photon energy, are what scale together.