The Photoelectric Effect

The photoelectric effect gives $K_{\text{max}} = hf - \phi$, where the frequency describes the light and the work function describes the metal, and intensity appears nowhere. Emission therefore requires a minimum frequency, below which no electron leaves however bright the beam, because each electron interacts with one photon at a time. Above threshold, frequency sets the maximum kinetic energy and the stopping voltage while intensity sets how many electrons come off per second. On a plot of stopping voltage against frequency the slope is $h/e$, the vertical intercept is $-\phi/e$ and the horizontal intercept is the threshold frequency.

Four errors dominate. Treating the emission threshold as a brightness threshold, so a strong enough beam of any colour is expected to eject electrons. Treating the work function as a property of the incident beam rather than of the plate, so switching to ultraviolet is said to raise it. Letting beam intensity control the maximum kinetic energy instead of the number of electrons per second, which predicts a stopping voltage that moves with brightness. And reading the stopping-voltage graph backwards, taking the slope as the work function or the intercept as Planck's constant.