The photoelectric effect

Shine light on a clean metal and electrons can jump out: the photoelectric effect. The experiments gave results that the wave picture of light could not explain:

• Below a certain threshold frequency ν₀, no electrons come out at all, however bright the light.
• Above ν₀, the fastest electrons' energy depends only on the frequency, not on the brightness.
• Brighter light gives more electrons (a bigger current), not faster ones.
• Emission is instant: no waiting, even in dim light.

Einstein's explanation: light arrives as photons, and one photon gives all its energy to one electron. The electron needs a minimum energy to escape the metal, the work function φ₀. Whatever is left over becomes kinetic energy:

K_max = hν – φ₀

This explains everything at once. If hν < φ₀, no single photon can free an electron, however many arrive: hence the threshold, with φ₀ = hν₀. More photons free more electrons, but each still gets only hν.

Stopping potential V₀: a reverse voltage that just stops even the fastest electrons. Then eV₀ = K_max, so eV₀ = hν – φ₀.

Example: a metal with φ₀ = 2 eV under 400 nm light. Photon energy = 1240/400 = 3.1 eV. K_max = 3.1 – 2 = 1.1 eV, so V₀ = 1.1 V. Its threshold wavelength is 1240/2 = 620 nm: red light beyond that frees nothing.

A graph of V₀ against ν is a straight line. Its slope is h/e, the same for every metal, and it cuts the ν-axis at ν₀. Millikan used this to measure h.

Uses: photocells in automatic doors, light meters and solar cells.