Photoelectric Effect Threshold Calculator
Find whether light ejects electrons and their maximum kinetic energy, from the work function and wavelength.
💡 What is the Photoelectric Effect Threshold Calculator?
The photoelectric effect threshold calculator works out what happens when light strikes a metal: whether electrons are ejected, and if so, how energetic they are. You give it the metal's work function and the wavelength of the light, and it returns the photon energy, the maximum kinetic energy of the ejected electrons, the stopping voltage, and the threshold wavelength below which emission begins.
The photoelectric effect is a cornerstone of quantum physics and a staple of physics courses. Students use this tool to check homework and to build intuition for why the effect depends on colour, not brightness. It models the classic experiment behind Einstein's 1905 explanation, where the surprising result, that electron energy tracks wavelength rather than intensity, forced physics to accept that light comes in discrete photons of energy hf.
The key rule is a simple energy balance. Each photon carries energy E = hc divided by wavelength. To free an electron, that energy must exceed the work function W, the binding energy of electrons in the metal. Whatever is left over becomes the electron's kinetic energy: KE = E minus W. If the photon energy is below the work function, nothing is emitted no matter how intense the light, a fact classical wave theory could not explain. The longest wavelength that still works is the threshold wavelength, hc divided by W.
This calculator is useful because it does the unit gymnastics, converting between joules and electronvolts and between wavelength and frequency, and clearly flags the no-emission case. Choose a metal or type a work function, enter a wavelength, and read every quantity the experiment measures, with the working shown.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Caesium under violet light
Example 2 - Zinc under ultraviolet light
Example 3 - Copper under violet light (no emission)
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the photoelectric effect?
Find the photon energy from E = hc / wavelength, then subtract the work function W: maximum kinetic energy = E - W. If E is less than W, no electrons are emitted. For caesium (W = 2.1 eV) lit by 400 nm light (E = 3.1 eV), the max kinetic energy is 3.1 - 2.1 = 1.0 eV.
What is the work function?
The work function is the minimum energy needed to remove an electron from a metal's surface, measured in electronvolts. It varies by metal: caesium is about 2.1 eV, zinc about 4.3 eV, and copper about 4.7 eV. A photon must carry at least this much energy to eject an electron.
What is the threshold wavelength?
The threshold wavelength is the longest wavelength of light that can still eject electrons, given by lambda-nought = hc / W. Light with a longer wavelength has too little energy per photon. For caesium (2.1 eV) the threshold is about 590 nm, so red light and shorter can eject electrons.
Why does brighter light not always cause emission?
Because the photoelectric effect depends on the energy of each photon, not the total intensity. If each photon's energy is below the work function, no electrons are emitted no matter how bright the light. Brighter light of a sufficient wavelength ejects more electrons, but the wavelength must be short enough first.
What is the stopping voltage?
The stopping voltage is the reverse voltage needed to stop the most energetic ejected electrons, and it numerically equals the maximum kinetic energy in electronvolts. If the max kinetic energy is 1.0 eV, the stopping voltage is 1.0 volt. It is how experiments measure the electrons' energy.
How is photon energy related to wavelength?
Photon energy is E = hc / wavelength, so shorter wavelengths carry more energy. A convenient shortcut is E in electronvolts equals 1240 divided by the wavelength in nanometres. So 400 nm light has an energy of about 1240 / 400 = 3.1 eV per photon.
Does the photoelectric effect prove light is made of photons?
Yes, it was key evidence. Classical wave theory predicted that brighter light should eject more energetic electrons, but experiments showed the electron energy depends only on wavelength, not intensity. Einstein explained this in 1905 by treating light as photons of energy hf, work that earned him the 1921 Nobel Prize.
What happens if the photon energy exactly equals the work function?
The electron is just barely freed with essentially zero kinetic energy, and the wavelength equals the threshold wavelength. Any shorter wavelength gives the electron leftover energy as kinetic energy; any longer wavelength fails to eject it. This calculator flags the no-emission case when the photon energy falls below the work function.