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Photoelectric Effect Calculator

Find the kinetic energy of photoelectrons.

How it is calculated

Light arrives as photons whose energy is E = hc / λ. With wavelength λ in nanometres and energy in electron volts, hc = 1239.842 eV·nm. An electron leaves the metal only if the photon energy exceeds the work function φ (in eV), and the fastest electrons carry KEmax = E − φ. The threshold wavelength is λ0 = hc / φ: longer wavelengths cannot free any electron, however bright the light. If E is not above φ, the tool reports that no electrons are emitted. Wavelength must be above zero and φ cannot be negative. If φ is 0 there is no threshold, and the tool shows "—" for it. Light intensity changes the number of electrons, not their energy.

Worked example

Ultraviolet light of 250 nm on a metal with work function 4.3 eV. Photon energy = 1239.842 / 250 = 4.959 eV. KEmax = 4.959 − 4.3 = 0.659 eV. The threshold wavelength is 1239.842 / 4.3 ≈ 288.34 nm, so any light shorter than 288.34 nm frees electrons from this metal and anything longer does not.

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Common mistakes

  • Entering the wavelength in metres or micrometres; the field is in nanometres.
  • Using the work function in joules instead of electron volts.
  • Expecting brighter light to free electrons at wavelengths above the threshold; only the photon energy decides that.
  • Confusing the threshold wavelength with a threshold frequency: shorter wavelength means higher frequency.
  • Reading the kinetic energy as the speed; convert it with KE = ½mv² separately.

About this calculator

This calculator applies Einstein's photoelectric equation, KE_max = hf − φ (or equivalently hc/λ − φ), to find the maximum kinetic energy of electrons ejected from a metal surface when struck by light. Here h is Planck's constant, f is the photon frequency (c/λ for wavelength λ), and φ is the material's work function — the minimum energy needed to free an electron from the metal. If the photon energy is below the work function, no electrons are emitted regardless of light intensity, which is the key evidence for light's particle nature.

Physics students and instructors use it to work through Einstein's 1905 Nobel-winning explanation of the photoelectric effect, verifying threshold frequency and stopping potential problems from textbooks.

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Comments (1)

  • Editorial team

    For a feel of the numbers, cesium has a work function of roughly 2.1 eV, which puts its threshold near 590 nm. Green 532 nm light, at 2.331 eV, frees electrons with up to about 0.231 eV, while 700 nm red light, at 1.771 eV, frees none however bright it is. Work function values differ between sources and surface conditions. Which metal and wavelength are you working with?

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