Photoelectric Effect Calculator

Find the energy of the photoelectrons, the threshold frequency and the cut-off wavelength for any metal and any light source.

What it does

Shine light on a metal and electrons jump off the surface. That is the photoelectric effect, and it is the experiment that split physics in two, because nothing in the wave theory of light can explain it. OpenStax lists the three facts that upset the old picture: the effect happens the instant the light arrives, it needs a threshold frequency rather than simply enough intensity, and the energy of the emitted electrons does not depend on how bright the light is.

Einstein explained all three in one move. Light is made of packets, and each packet carries an energy set only by its frequency, E equals h f. A photon hands its whole energy to a single electron, and if that energy is enough to cover the binding energy of the metal, called the work function, the electron escapes with whatever is left over. That leftover is the maximum kinetic energy, so the equation reads K maximum equals h f minus phi. If the photon is too weak, nothing happens at all, however bright the lamp.

Each metal has its own work function, and OpenStax tabulates the usual values: sodium at 2.46 eV, aluminium at 4.08 eV, lead at 4.14 eV, zinc at 4.31 eV, iron at 4.50 eV, copper at 4.70 eV, silver at 4.73 eV and platinum at 6.35 eV. Those numbers fix two thresholds for each metal. The threshold frequency follows from phi divided by h, and the cut-off wavelength follows from h c divided by phi, since light below that wavelength simply does not carry enough energy per photon.

This page puts those pieces together. Pick a metal or type in a work function, give the wavelength of the light, and it returns the energy of a photon, the maximum energy of the photoelectrons, the threshold frequency, the cut-off wavelength and how many photons per second arrive on each square metre at the intensity you entered. If the light is too weak, it says so instead of giving a negative number.

The constants come from NIST. Planck's constant is 4.135667696 x 10 to the power of minus 15 eV s and the product h c is 1239.841984 eV nm, so the arithmetic matches the reference values rather than a rounded classroom number. The stopping potential is worth noting too, because it is the easiest thing to measure: it is the reverse voltage that just stops the photocurrent, and it equals the maximum kinetic energy in volts.

How to use

1. Choose the units for the light intensity, metric or imperial.
2. Pick the metal from the list, or choose to enter your own work function in electron volts.
3. Enter the wavelength of the light in nanometres. Visible light runs from about 380 nm at the violet end to 700 nm at the red end.
4. Enter the light intensity, which sets how many photons arrive each second.
5. Read the photon energy, the maximum photoelectron energy and the two thresholds for the metal.
6. If the result says no photoelectrons, either use shorter wavelength light or pick a metal with a lower work function.

Formula

E

Energy carried by one photon, in electron volts.

h

Planck's constant, 4.135667696 x 10 to the power of minus 15 eV s.

c

Speed of light in a vacuum, 299792458 m per second.

phi

Work function of the metal, the energy needed to release an electron.

K maximum

Largest kinetic energy an emitted photoelectron can carry.

The product h c is 1239.841984 eV nm, which is the number used for every wavelength on this page. Work functions are surface properties, so a clean metal in a vacuum and a worn plate in air do not give the same number. The photoelectric effect needs light in a vacuum or a narrow gap, because the electrons are easy to lose to air molecules before they reach a collector.

Worked example

Reference table

Limits

• The model covers a clean metal surface in a vacuum. A film of oxide, a scratched surface or gas in the apparatus all shift the measured numbers.
• Only the maximum energy is calculated. The full energy spread of the emitted electrons, which comes from electrons deeper inside the metal, is not modelled.
• The work function list covers the common metals in the textbook table. Other materials, and semiconductors with their own band structure, need their own value.
• Photon flux assumes the light arrives at a right angle and spreads evenly, so a focused beam gives a higher local flux.

Common mistakes

• Raising the intensity and expecting the electron energy to rise. Brighter light gives more electrons, not faster ones.
• Using the photon energy without subtracting the work function. The work function is the energy lost on the way out.
• Working in hertz while the wavelength is in nanometres without converting. Either use f = c / lambda or E = h c / lambda, not a mix of the two.
• Expecting photoelectrons from light that is too long. Above the cut-off wavelength nothing is emitted, whatever the intensity.
• Reading the stopping potential as volts per electron rather than as the number of volts that cancels the kinetic energy.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• OpenStax University Physics Volume 3, 6.2: the photoelectric effect and work functions
• NIST: Planck's constant from the CODATA recommended values
• OpenStax University Physics Volume 3, chapter 6 key equations

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