Photoelectric Effect Calculator
Einstein’s photoelectric equation: the energy of a photon at a wavelength, the maximum kinetic energy of the electrons it knocks out of a metal, the stopping voltage, and the threshold wavelength below which nothing is emitted.
Light arrives in photons of energy hc ÷ λ.
How the photoelectric effect calculator works
Light arrives in photons of energy hc ÷ λ. An electron needs the metal’s work function φ to escape; whatever is left becomes its kinetic energy, KE = hc/λ − φ. Below the threshold frequency no electrons come out however bright the light — the observation that won Einstein his Nobel Prize. The stopping voltage is simply KE in electronvolts.
Formula: E = hc ÷ λ = 1239.84 eV·nm ÷ λ; KE_max = E − φ; λ₀ = hc ÷ φ
Worked examples
| Inputs | Maximum electron kinetic energy (eV) | Note |
|---|---|---|
| 400 nm violet on sodium (2.28 eV) | 0.82 | 0.82 eV |
| 600 nm orange on sodium | 0 | no emission (2.07 eV < 2.28) |
| 200 nm UV on copper (4.7 eV) | 1.499 | 1.50 eV |
FAQFrequently asked questions
Why does brighter light not give faster electrons?
Brightness means more photons, not more energetic ones; each electron absorbs a single photon. More light gives more electrons per second at the same maximum energy — the result classical physics could not explain.
What is the work function?
The minimum energy to pull an electron out of a metal’s surface — a few electronvolts, lowest for the alkali metals (caesium 2.1 eV), which is why they are used in photocathodes.
What is the stopping voltage?
The reverse voltage that just stops the fastest electrons reaching the collector. Measured in volts, it equals the maximum kinetic energy in electronvolts, which is how Millikan measured Planck’s constant.
Why 1239.84?
It is hc expressed in eV·nm: Planck’s constant times the speed of light, divided by the charge of the electron. Dividing it by a wavelength in nanometres gives photon energy in electronvolts directly.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.