The Photoelectric Effect
Shine light on a metal surface and, under the right conditions, it will fling out electrons — a stubbornly strange result once classical physics tried to explain it. Nineteenth-century wave theory predicted that dimmer light should still eject electrons, just more slowly, given enough time to build up energy. Real experiments showed the opposite: below a sharp cutoff frequency, no amount of intensity or waiting produces a single electron, while even the faintest light above that frequency ejects electrons instantly. Einstein's 1905 explanation — that light itself arrives in discrete packets of energy, later called photons — resolved the puzzle and became one of the founding results of quantum mechanics, for which he won the 1921 Nobel Prize in Physics.
Light doesn't hit a metal as a smooth wave — it arrives in tiny bursts called photons, each carrying a fixed amount of energy. An electron escapes only if a single photon's energy is at least as big as the metal's work function, the energy that normally holds the electron in place. Whatever energy is left over becomes the kinetic energy of the electron as it flies off.
The formula
KEₘₐₓ = h · f − φ
- KEₘₐₓ — maximum kinetic energy (eV): the greatest energy an ejected electron carries away
- h — Planck's constant (eV·s): tiny constant linking a photon's frequency to its energy
- f — frequency (Hz): how many light waves arrive each second
- φ — work function (eV): minimum energy needed to pull an electron free from the metal
Worked example
A photon striking a sodium surface carries 3.1 eV of energy. Sodium's work function is 2.1 eV. What is the maximum kinetic energy of an ejected electron?
- hf = 3.1 eV
- φ = 2.1 eV
- KEₘₐₓ = h · f − φ
- KEₘₐₓ = 3.1 eV − 2.1 eV
KEₘₐₓ = 1.0 eV
Test yourself
Now the light source is swapped for one with a higher frequency, delivering photons with 3.6 eV of energy to the same sodium surface (work function still 2.1 eV). What is the new maximum kinetic energy?
- 5.7 eV
- Correct answer: 1.5 eV
- 1.0 eV
Yes! KEₘₐₓ = 3.6 eV − 2.1 eV = 1.5 eV.
Suppose the photon's energy hf is smaller than the metal's work function φ. What happens?
- The electron is ejected but slower
- The electron is ejected with negative kinetic energy
- Correct answer: No electron escapes at all
Right — below the work function, a single photon can't supply enough energy, so no electron escapes no matter how bright the light is.
Where you see this
A solar panel on a roof is this effect working for a living: sunlight's photons strike the silicon, each one knocking loose at most one electron, and those freed electrons flow out as current. Dusk-sensing streetlights and old photocell doors run on the same photon-per-electron trade.
Common mistakes
The classic error is that brighter light should fling electrons out harder — intensity only produces MORE electrons; each one's energy depends on the photon's frequency alone, through KEₘₐₓ = h · f − φ. And below the threshold nothing happens, no matter how bright the beam: kinetic energy cannot be negative, so if hf is less than the work function φ, no electron leaves at all. Above threshold, subtract: photons of 3.6 eV on sodium (φ = 2.1 eV) eject electrons with 1.5 eV.
How it connects
This is the founding crack in classical physics — light behaving as particles — and the door to the whole modern-physics module: Compton scattering, next, shows those photons carry momentum like billiard balls, and the wave-particle duality that ends in matter waves starts right here.