Photoelectric effect calculator
Enter the wavelength or frequency of the light and the work function of the metal. The calculator applies Einstein's photoelectric equation and gives the photon energy, the maximum kinetic energy and speed of the electrons, the stopping voltage and the threshold below which no electrons come out. Switch to the work function mode to work backwards from a measured stopping voltage.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose whether to find the electron energy or the work function.
- Give the light as a wavelength in nm or a frequency in THz.
- Enter the work function of the metal in eV, or the stopping voltage you measured.
- Read the kinetic energy and stopping voltage (or the work function), the photon energy and the threshold.
- Photon energy: E = h f = h c ÷ λ; in eV, E = 1239.84 ÷ λ(nm)
- Einstein’s equation: K_max = E − φ
- Stopping voltage: V₀ = K_max ÷ e (numerically the same as K in eV)
- Threshold: λ₀ = h c ÷ φ, f₀ = φ ÷ h
- Fastest electron: v = √(2 K ÷ mₑ)
- h = 6.62607015 × 10⁻³⁴ J·s, e = 1.602176634 × 10⁻¹⁹ C, c = 299,792,458 m/s
Worked example
400 nm light on a metal with φ = 2.3 eV:
- E = 1239.84 ÷ 400 = 3.0996 eV
- K_max = 3.0996 − 2.3 = 0.7996 eV, so the stopping voltage is 0.7996 V
- The fastest electrons move at 530,351 m/s
- Threshold: λ₀ = 1239.84 ÷ 2.3 = 539.06 nm (556.14 THz)
The same metal under 650 nm red light: 1.9074 eV is less than 2.3 eV, so no electrons leave.
Working back: 1000 THz light (4.1357 eV) and a stopping voltage of 1.5 V give φ = 4.1357 − 1.5 = 2.6357 eV.
Tips
- Threshold is about energy per photon. Light longer than λ₀ never frees electrons.
- The stopping voltage measures the fastest electrons only; most come out slower because they lose energy inside the metal.
- eV and volts match. An electron with 0.8 eV is stopped by 0.8 V.
Frequently asked questions
What is Einstein's photoelectric equation?
K_max = h f − φ. A photon of energy h f frees an electron; the work function φ is spent getting it out of the metal and the rest is kinetic energy. The stopping voltage is V₀ = K_max ÷ e.
How do I convert wavelength to photon energy?
E (eV) = 1239.84 ÷ λ (nm). 400 nm violet light carries 3.0996 eV, 650 nm red light 1.9074 eV.
Why does brighter light not give faster electrons?
Brightness is the number of photons, not their energy. More photons free more electrons, but each electron's energy depends only on the frequency. Below the threshold frequency no electrons come out at all, however bright the light.
Where do I find the work function of a metal?
In physics tables or your textbook – values depend on the metal and the state of its surface. Or measure it – shine light of known wavelength, find the stopping voltage and use the work function mode.