Photoelectric Effect Calculator (electron energy, stopping voltage, cut-off wavelength)

Understanding the photoelectric effect calculator — concept and principle

This calculator applies Einstein's photoelectric equation. From the light's wavelength, frequency or photon energy and the metal's work function, it gives the maximum kinetic energy of the emitted electrons, whether any are emitted, the stopping potential, the cut-off wavelength and frequency, and the electrons' top speed. It is a standard tool for modern-physics courses.

How it is calculated

Photon energy E = h f = h c ÷ λ, with hc = 1,239.84 eV·nm

K_max = E − φ

Stopping potential V_s = K_max ÷ e (in volts, equal to K_max in eV)

Cut-off wavelength λ_c = hc ÷ φ; cut-off frequency f_c = φ ÷ h

Maximum speed v = √(2 K_max ÷ mₑ)

The principle

Light delivers energy in packets, photons, each of energy hf. An electron absorbs one photon and must use part of that energy, the work function φ, to escape the metal; the rest is kinetic energy. If a photon has less energy than φ, no electron escapes, however bright the light. Brighter light means more photons and more electrons, but not faster ones. This result, unexplained by wave theory, was key evidence for the quantum nature of light.

Worked example

Default inputs: wavelength 400 nm, work function 2.3 eV.

1. E = 1,239.84 ÷ 400 = 3.1 eV.
2. K_max = 3.1 − 2.3 = 0.8 eV; electrons are emitted: yes — above the work function.
3. Stopping potential = 0.8 V.
4. λ_c = 1,239.84 ÷ 2.3 = 539.1 nm; f_c = 556.1 THz.
5. v = √(2 × 0.8 eV ÷ mₑ) = 530 km/s.

How to read the result

Light with a wavelength shorter than 539 nm, that is green to violet, will eject electrons from this metal; red light will not. Metals with lower work functions, such as caesium, respond to longer wavelengths, which is why they are used in photocathodes.

Common mistakes

• Thinking brighter light gives faster electrons.
• Mixing joules and electronvolts.
• Using a work function for a different surface condition; oxides and contamination change it.

Frequently asked questions

Why does red light not eject electrons from some metals?

Each red photon has less energy than the work function.

What is the stopping potential?

The reverse voltage that just stops the fastest electrons.

Does intensity matter?

It changes how many electrons are emitted, not their maximum energy.

What is hc in handy units?

About 1,239.84 eV·nm.

Sources: OpenStax, University Physics Volume 3 (2016), section 6.2 "Photoelectric Effect"