Photoelectric Effect Calculator
Calculate photon energy, electron kinetic energy, threshold frequency, threshold wavelength, and emitted-electron speed.
About the photoelectric effect
The photoelectric effect occurs when electromagnetic radiation transfers enough energy to an electron at a material surface for that electron to escape. Its observed behavior helped establish that light arrives in discrete packets called photons. A photon has energy E = hf, where h is Planck's constant and f is frequency. Because frequency and wavelength obey c = λf, shorter-wavelength light carries more energy per photon. This calculator accepts frequency in hertz, wavelength in nanometres, or photon energy directly in electron volts. A material's work function is the minimum energy needed to release an electron from its surface. Einstein's photoelectric equation states that the maximum kinetic energy of an emitted electron is photon energy minus the work function. If the photon energy is equal to or below that work function, the calculated kinetic energy is zero and photoemission does not occur. Raising light intensity supplies more photons and may release more electrons, but it cannot make an individual sub-threshold photon eject an electron. The threshold frequency is the work function divided by Planck's constant. It is the lowest incident frequency capable of emission. The corresponding threshold wavelength is the longest wavelength capable of emission and equals the speed of light divided by threshold frequency. The calculator also converts positive electron kinetic energy from electron volts to joules and applies the classical relation KE = mv²/2 to estimate the fastest emitted electron's speed. That speed represents an ideal maximum; electrons originating deeper in a real material can lose energy before leaving the surface. Work functions depend on the material, crystal face, surface cleanliness, coatings, temperature, and measurement conditions. Published values are therefore representative rather than universal. Common classroom examples include cesium near 2.14 eV, sodium near 2.28 eV, zinc near 4.33 eV, and gold near 5.1 eV. Use a value appropriate to the actual sample whenever precision matters. Photoelectric calculations are useful in quantum-physics exercises, photocathode selection, vacuum phototubes, surface spectroscopy, and detector design. The simple model assumes one photon transfers its energy to one electron and ignores band structure, contact potentials, electron scattering, and relativistic corrections. It is best used to understand energy thresholds and ideal maximum values rather than to predict a complete measured emission spectrum.
Photoelectric effect examples
| Incident light and material | Ideal result |
|---|---|
| 400 nm light, work function 2.00 eV | Photon energy 3.10 eV; maximum KE 1.10 eV |
| 550 nm light, sodium work function 2.28 eV | Photon energy 2.25 eV; no emission |
| 250 nm light, zinc work function 4.33 eV | Photon energy 4.96 eV; maximum KE 0.63 eV |
| Photon energy 6.00 eV, gold work function 5.10 eV | Maximum KE 0.90 eV |
How to use the calculator
- Enter the incident light as frequency, wavelength, or photon energy.
- Enter the illuminated material's positive work function in electron volts.
- Select Calculate photoelectric effect.
- Compare photon energy with the threshold and review electron kinetic energy and speed.
Frequently asked questions
What is the photoelectric equation?
Einstein's equation is KEmax = hf - φ, where φ is the material work function. Emission occurs only when photon energy exceeds that work function.
Does brighter light give emitted electrons more energy?
Not when frequency stays fixed. Greater intensity increases the number of photons and potentially the number of emitted electrons, while each electron's maximum energy depends on photon frequency.
What is threshold frequency?
Threshold frequency is the lowest light frequency that can eject electrons from a particular surface. It equals the work function divided by Planck's constant.
Why can I enter wavelength or frequency?
They are equivalent descriptions of the incident light through c = λf. The calculator converts either measurement into photon energy before applying Einstein's equation.
Is the calculated electron velocity exact?
It is the ideal maximum classical speed for the calculated kinetic energy. Real emitted electrons can lose energy inside the material, producing a distribution of lower speeds.