Failure of Wave Theory to Explain the Observations from Experiments on Photoelectric Effect

Nearly every one of the nine observations of the previous section is flatly contradicted by the predictions of classical (wave) theory. The most damning failure concerns TIME. According to the wave picture, the energy of the incident radiation is spread continuously and uniformly over the whole illuminated area of the metal surface, and every electron near the surface absorbs some of this energy continuously. To be ejected, an electron needs to accumulate a certain minimum amount of energy -- called the WORK FUNCTION of the metal, $\phi_0$ -- the least energy needed to pull a free electron out through the metal's surface (exactly analogous to the ionization energy needed to remove an electron from a single atom, except here applied to a metal, which is effectively a huge collection of atoms sharing a common sea of free electrons).

If the incident intensity is very low, the energy arriving per unit area per unit time is small, so on the wave picture an electron should take a correspondingly LONG time -- Example 14.1 works out an estimate of about half a day for a very weak beam on potassium -- to accumulate enough energy to escape. But experimentally, emission is essentially INSTANTANEOUS (within $10^{-9}$ s) even at very low intensity. This single contradiction -- a predicted delay of hours versus an observed delay of nanoseconds -- is already fatal for the wave picture.

The wave picture also predicts that a LARGER incident intensity should deliver MORE energy to each electron, and hence should produce photoelectrons with HIGHER kinetic energy. But observation 6 says the opposite: $KE_{max}$ does not depend on intensity at all, only on frequency. …