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Photoelectric Effect Calculator

Calculate a photoelectron's maximum kinetic energy and ejection speed from incident light's wavelength and a material's work function, KE_max = hc/λ − φ.

Photon energy
3.1 eV
Photoelectrons emitted?
Yes
Max photoelectron kinetic energy
0.8 eV
Threshold wavelength (longest that still ejects an electron)
539.1 nm
Max photoelectron speed
530.4 km/s

How it works

A single photon of light carries energy E = hc/λ, where h is the Planck constant, c is the speed of light, and λ is the wavelength. When that photon strikes a material and is absorbed by one electron, the electron is ejected only if the photon's energy exceeds the material's work function φ — the minimum energy needed to free an electron from the surface — with any leftover energy becoming the electron's kinetic energy: KE_max = hc/λ − φ (Einstein's photoelectric equation). Below that threshold, no electrons are emitted no matter how long you wait, which is the key observation 19th-century wave theory couldn't explain and the photon picture resolved.

The threshold wavelength, λ₀ = hc/φ, is the longest wavelength (lowest photon energy) that still exactly clears the work function with zero leftover kinetic energy — any longer and the photon simply doesn't carry enough energy regardless of how bright the light is. When emission does occur, the ejected electron's maximum speed follows from KE_max = ½m_ev², solved for v; this is accurate non-relativistically because KE_max stays far below the electron's 511 keV rest energy for ordinary visible and ultraviolet light.

FAQ

Why doesn't brighter light eject electrons below the threshold wavelength?

Because each electron is ejected by absorbing a single photon, and a photon's energy depends only on its wavelength (E = hc/λ), not on the light's intensity. Brighter light just means more photons per second, which increases how many electrons are ejected once above the threshold — it never gives any individual photon more energy, so below the threshold wavelength, no number of photons will do.

Where do I find a material's work function?

It's a property of the specific material's surface, typically published in electronvolts in physics or materials-science references (common metals range roughly from about 2 eV for alkali metals like sodium up to around 6 eV for platinum) — this calculator takes it as a direct input rather than guessing, since surface contamination, crystal face, and material purity can all shift the real value.

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