Light ejects electrons from a metal when photon energy hν exceeds the work function φ. Einstein's equation: hν = φ + K_max. Maximum kinetic energy K_max = e V₀ (V₀ = stopping potential). Work function φ = hν₀ = hc/λ₀. Cut-off wavelength λ₀ (Å) = 12400/φ (eV). de Broglie wavelength of photoelectron: λ = h/√(2m K_max).
Photoelectric calculators
K_max, V₀, work function, photon energy, λ₀, de Broglie
☀️ Photoelectric energy diagram
| Concept | Formula | Notes / Units |
|---|---|---|
| Einstein's photoelectric equation | hν = φ + K_max | ν = frequency, φ = work function |
| Maximum kinetic energy | K_max = e V₀ = hν − φ | V₀ = stopping potential |
| Work function | φ = h ν₀ = hc / λ₀ | ν₀ = threshold frequency, λ₀ = threshold wavelength |
| Energy of photon | E = hν = hc / λ | h = 6.626×10⁻³⁴ J·s |
| Cut-off wavelength (φ in eV) | λ₀ (Å) = 12400 / φ (eV) | Useful numerical relation |
| de Broglie wavelength (photoelectron) | λ = h / √(2m K_max) | m = electron mass |
About the photoelectric effect
When light of frequency ν strikes a metal surface, electrons can be ejected if the photon energy hν exceeds the work function φ. Einstein's equation hν = φ + K_max states that photon energy goes into overcoming the work function plus the maximum kinetic energy of the ejected electron. The stopping potential V₀ is the voltage that stops the most energetic electrons: K_max = e V₀.
Work function and threshold
The work function φ = hν₀ = hc/λ₀, where ν₀ is the threshold frequency and λ₀ the threshold (cut-off) wavelength. For φ in eV, λ₀ (in Ångströms) = 12400 / φ (eV). Light with wavelength longer than λ₀ cannot eject electrons.
de Broglie wavelength
The ejected electron has a matter wavelength given by λ = h / √(2m K_max), where m is the electron mass. This is the de Broglie wavelength of the photoelectron.