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2 Photons & the photoelectric effect

Photon energy E=hf=\frac{hc}{\lambda} h = 6.63×10⁻³⁴ J s. Light comes in quanta (photons). Photoelectric equation h f = W + E<sub>k(max)</sub> W = work function (minimum energy to release an electron). Threshold frequency W = h f₀ Below f₀ no electrons are emitted, however bright the light. Stopping voltage e V<sub>s</sub> = E<sub>k(max)</sub> The p.d. that just stops the fastest photoelectrons.

Why it needed photons

  • Emission depends on frequency, not intensity. Below f₀, nothing happens.
  • Emission is instant above f₀, a wave model predicts a delay while energy builds up.
  • Increasing intensity increases the number of electrons, not their maximum energy.
  • These facts only make sense if light delivers energy in discrete photons (E = hf).
Worked example Max kinetic energy Light of λ = 400 nm hits a metal with work function W = 2.0 eV. Find E_k(max) in eV. (hc = 1240 eV·nm) Photon energy: E = hc/λ = 1240/400 = 3.1 eV. E_k(max) = E − W = 3.1 − 2.0 = 1.1 eV. ✓ E_k(max) = 1.1 eV.

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