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Photoelectric Effect Calculator

The photoelectric effect calculator computes the kinetic energy of electrons ejected from material by incident light.

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Maximum kinetic energy0.819605 eVhf − φ: a 3.0996 eV photon minus the 2.28 eV work function of Sodium
Stopping voltage0.819605 Vnumerically equal to the kinetic energy in eV, because that is exactly what an electron-volt means
Photon energy3.099605 eV4.966e-19 J
Work function2.28 eVSodium
Threshold wavelength543.7903 nmhc/φ — light LONGER than this ejects nothing, however intense. That threshold is what classical wave theory could not explain
Threshold frequency551.3015 THz
Maximum electron speed536943 m/s0.001791 of the speed of light — non-relativistic, since a few eV is nothing against the electron's 511 keV rest energy
Fraction of the photon energy kept26.442%the rest goes into freeing the electron from the metal
Photon arrival rate2.014e+18 per m² per secondat 1 W/m²
What intensity changesthe CURRENT, not the energydoubling the brightness doubles the number of electrons ejected per second and leaves the maximum kinetic energy of each one exactly unchanged. This is the observation that forced the photon
Why this needed a quantumno delay, and a sharp thresholda classical wave would pour energy in gradually, so dim light should eject electrons after a measurable wait and any colour should work eventually. Neither happens: emission is instant, and below the threshold frequency nothing is emitted at all

The formula

K_max = hf − φ; eV₀ = K_max; λ₀ = hc/φ

Intensity and frequency do different things

Making the light brighter ejects more electrons per second but does not give any one of them more energy. Making it bluer gives each electron more energy but does not eject more of them. Classical wave theory predicts the opposite on both counts, and that is the whole reason the photoelectric effect forced the photon into existence.

Two observations do the damage. There is a sharp threshold frequency below which nothing at all is emitted, however intense and however long you wait. And above it emission is immediate, with no delay while energy accumulates. Both follow at once if light arrives in lumps of energy hf, and neither can be reconciled with a continuous wave depositing energy gradually.

The stopping voltage is the answer in disguise

The stopping voltage in volts is numerically equal to the maximum kinetic energy in electron-volts, because an electron-volt is defined as exactly the energy one electron gains across one volt. Measuring the stopping voltage against frequency gives a straight line whose slope is h/e and whose intercept is the work function — which is how Millikan measured Planck's constant while trying to disprove Einstein.