The Photoelectric Effect

The photoelectric effect — the emission of electrons from a metal surface when electromagnetic radiation above a certain frequency is shone on it.

Work function (φ) — the minimum energy required to release an electron from the surface of the metal. Different metals have different work functions.

Threshold frequency (f₀) — the minimum frequency of radiation that can cause emission:

f₀ = φ / h

Below it, no electrons are emitted however intense the radiation or however long you wait.

Einstein's photoelectric equation —

hf = φ + KEmax

The photon's energy is used to free the electron, and whatever remains becomes the electron's kinetic energy. Electrons deeper in the metal need more energy to escape, so they emerge with less — which is why the equation gives the maximum kinetic energy.

Example: a metal of work function 2.0 eV illuminated with 3.5 eV photons emits electrons with KEmax = 3.5 − 2.0 = 1.5 eV. Working in electronvolts avoids converting to joules and back.

The four observations the wave model cannot explain

A threshold frequency exists. A wave model says energy arrives continuously, so any frequency should eventually free an electron. In fact nothing at all happens below f₀, however bright the source.

Emission is instantaneous. A wave model predicts a delay while enough energy accumulates. Emission actually begins immediately, within nanoseconds.

Intensity affects the number, not the energy. Brighter light of the same frequency releases more electrons per second but does not increase their maximum kinetic energy.

KEmax depends on frequency alone. Raising the frequency raises KEmax linearly; raising the intensity does not change it.

The photon explanation — one photon interacts with one electron, transferring all its energy or none. If hf is less than φ the electron cannot escape, and the photons do not pool their energy, so intensity cannot compensate. Brighter light means more photons per second, so more electrons per second, each with the same maximum energy as before.

Why this mattered — the photoelectric effect could not be reconciled with light as a wave, and required light to be treated as particles. It is the experimental foundation of the photon model.