Shine light on a metal and electrons can fly off. But only if the frequency is high enough, no matter how bright the beam. That single fact forces us to treat light as a stream of energy packets.
One photon frees at most one electron, and only if the photon's energy exceeds the work function Φ. Below the threshold frequency f₀ = Φ/h there is no emission at any intensity. Above it, Einstein's equation gives the maximum kinetic energy: hf = Φ + KE_max. Intensity sets the rate of emission; frequency sets the maximum energy.
Pick a metal, then lower the wavelength until electrons just begin to escape. Cross the threshold and raise the intensity: more electrons leave each second, but their maximum speed does not change. Drop below the threshold and the brightest beam does nothing.
The photoelectric effect is mostly about telling intensity and frequency apart.
Wave theory predicts that any frequency should eventually free electrons if you wait or brighten the light. The experiment shows the opposite: there is a sharp threshold, emission is instantaneous, and KE_max rises with frequency, not intensity. These are the points that "explain why the photoelectric effect is evidence for the particle nature of light".
Four quick checks on the photoelectric effect. Each correct answer earns XP and lights this skill on your star map.
When light below the threshold frequency shines on a metal, increasing the intensity:
The maximum kinetic energy of the photoelectrons depends on:
Einstein's photoelectric equation is:
For light above the threshold frequency, increasing the intensity increases:
A graph of KE_max against frequency is a straight line of gradient h, crossing the frequency axis at f₀ and the energy axis at −Φ. Be ready to read the work function and the Planck constant straight off such a graph.
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