The experiment. Light shines on a clean metal plate in a vacuum. The electrons that come out (the photoelectrons) cross to a collector, and an ammeter measures the current. A voltage between the plate and the collector can hold the electrons back. The smallest retarding voltage that stops all of the electrons is the stopping voltage V₀, and it tells us the greatest kinetic energy that any electron has: K_max = eV₀.

What was seen (1887 to 1902, Hertz and Lenard). (1) Below a threshold frequency f₀ there is no photocurrent at all, however bright the light, and however long you wait. (2) Above f₀ making the light brighter gives more electrons (a bigger current), but the same K_max. (3) K_max goes up with the frequency, in a straight line. (4) The electrons come out at once, even when the light is very dim.

The wave model fails. If light is a wave, its energy comes in at a rate that depends on the intensity. A brighter wave should shake the electrons harder, so K_max should rise with the intensity and not depend on the frequency; light of any frequency should work if it is bright enough; and a dim wave should need a long time to deliver the energy to one electron (the energy falls on an area much bigger than the electron, so a dim light would take seconds, minutes or hours: try an intensity of 0.001 W/m² in the second tab). All four observations disagree with it.

The photon model (Einstein, 1905). Light comes in packets, photons, and each photon has energy E = hf. One photon gives all of its energy to one electron, or none. The electron must use up an energy φ (the work function) to get out of the metal. What is left is its kinetic energy:

K_max = hf − φ, threshold frequency f₀ = φ / h

If hf is less than φ, no electron can get out, whatever the number of photons. A brighter light has more photons a second, so more electrons come out (a bigger current), but each has the same K_max. A photon is absorbed at once, so there is no delay. All four observations follow. Einstein won the Nobel Prize in 1921 for this.

Measuring h. The graph of K_max against f is a straight line, K_max = hf − φ. The gradient is Planck’s constant (h = 4.14 × 10⁻¹⁵ eV s = 6.63 × 10⁻³⁴ J s), the intercept on the frequency axis is the threshold frequency and the intercept on the energy axis is −φ. Different metals give parallel lines with the same gradient, because h is a constant of nature. Millikan measured the lines very carefully in 1916 and found h, even though he had expected to prove Einstein wrong.

What the model leaves out. The photoelectrons have a spread of energies from 0 to K_max, which I show as an even spread (in a real metal the electrons come from different depths, and the spread is not even). The numbers of electrons per photon (1 in 1000) and the area of an atom (10⁻²⁰ m²) are typical values. The work functions are typical values for clean surfaces. The measurements in the third tab are made up, with a small random error.

Things to try. (1) With sodium, find the lowest frequency that gives a current. Is it where you expect (f₀ = φ/h)? (2) At a frequency just above that, raise the intensity. What changes, and what does not? (3) Find the stopping voltage in the first tab for violet light. Does it match (hf − φ)/e? (4) In the second tab, set the intensity very low. Which model predicts a delay? (5) Measure h from the graph for two different metals.