Calculate maximum kinetic energy, stopping voltage, and threshold wavelength for the photoelectric effect across 12 metals with multiple input modes.
The photoelectric effect — the emission of electrons from a metal surface when illuminated by light — was one of the key experiments that launched quantum physics. Albert Einstein's 1905 explanation, which earned him the Nobel Prize, proposed that light consists of discrete energy packets (photons) with energy E = hf. When a photon strikes a metal surface, it can eject an electron only if its energy exceeds the metal's work function φ, the minimum energy needed to free an electron from the surface. Any excess energy becomes the kinetic energy of the emitted photoelectron.
The maximum kinetic energy of photoelectrons is KE_max = hf − φ, independent of light intensity — a result that classical wave theory could not explain. The stopping voltage V₀ = KE_max/e is the reverse voltage needed to halt all photoelectrons, providing a direct measurement of KE_max. Below a threshold frequency f₀ = φ/h (or above a threshold wavelength λ₀ = hc/φ), no electrons are emitted regardless of how intense the light is.
This calculator supports four input modes — wavelength, frequency, photon energy, or stopping voltage — and includes work function data for 12 common metals. Use it to predict photoelectric emission, compare metals at a given photon energy, or explore how wavelength affects electron kinetic energy.
The photoelectric effect is a core topic in modern physics courses and standardized tests. This calculator lets students instantly verify homework problems, explore how different metals respond to various photon energies, and build intuition through the metal comparison and wavelength scan tables. Researchers can use it to quickly estimate photocathode performance or select metals for specific UV detection applications.
Photoelectric Effect Equations: • Photon energy: E = hf = hc/λ • Einstein equation: KE_max = hf − φ (if hf > φ) • Stopping voltage: V₀ = KE_max / e • Threshold frequency: f₀ = φ / h • Threshold wavelength: λ₀ = hc / φ • Max electron speed: v = √(2·KE_max / mₑ)
Result: KE_max = 1.00 eV, V₀ = 1.00 V
A 400 nm photon has energy 3.10 eV. Cesium has φ = 2.1 eV, so KE_max = 3.10 − 2.1 = 1.00 eV, and the stopping voltage is 1.00 V.
When Max Planck quantized the energy of oscillators in 1900 to explain blackbody radiation, he viewed it as a mathematical trick. Einstein went further in 1905, proposing that light itself is quantized into photons with energy E = hf. This radical idea explained three puzzling features of the photoelectric effect: (1) the existence of a threshold frequency, (2) the instantaneous emission of electrons, and (3) the linear dependence of KE_max on frequency. The photoelectric effect paper, not relativity, was cited when Einstein received the 1921 Nobel Prize in Physics.
The work function depends on the crystal face, surface cleanliness, and adsorbed molecules. Typical values range from ~2 eV (alkali metals) to ~5.5 eV (platinum). In surface science, photoemission spectroscopy (PES and XPS) uses the photoelectric effect with precisely known photon energies to map electronic band structures and chemical compositions of surfaces — one of the most powerful analytical techniques in materials science.
The internal photoelectric effect — where absorbed photons create electron-hole pairs within a semiconductor — is the basis of all modern photodetectors, solar cells, and image sensors. Advances in thin-film photocathodes and negative electron affinity (NEA) surfaces have pushed single-photon detection down to visible and near-infrared wavelengths, enabling quantum key distribution and low-light astronomical imaging.
It is the emission of electrons from a material (usually a metal) when light of sufficient frequency shines on it. Einstein explained it by proposing that light energy comes in quantized packets called photons.
The work function φ is the minimum energy required to remove an electron from a metal surface. It depends on the metal and its surface conditions. Cesium has one of the lowest work functions (~2.1 eV), making it useful in photocathodes.
Each photon interacts with one electron. Increasing intensity means more photons (more electrons emitted) but each photon still has the same energy hf. Only frequency determines the maximum kinetic energy per electron.
No electrons are emitted, regardless of light intensity or exposure time. The photon energy is simply insufficient to overcome the work function.
The stopping voltage V₀ is the minimum reverse voltage applied between the metal and a collector electrode that stops all photoelectrons. It equals KE_max/e and provides a direct way to measure the maximum kinetic energy.
It is the basis for photomultiplier tubes, solar cells (internal photoelectric effect), CCD/CMOS image sensors, and photocathodes in night-vision devices and particle detectors. Use this as a practical reminder before finalizing the result.