U3.12 · Photoelectric EffectPractice · 光电效应

Photon energy E = hc/λ = $6.626 \times 10^{-34} \times 3.0 \times 10^{8}$ ÷ ($4.50 \times 10^{-7}$) = $4.417 \times 10^{-19}$ J. Work function Φ = 1.95 × $1.602 \times 10^{-19}$ = $3.124 \times 10^{-19}$ J. Maximum kinetic energy = E − Φ = $1.29 \times 10^{-19}$ J. Part of the photon’s energy frees the electron; only the rest becomes its kinetic energy.

A 500 nm photon carries hc/λ ≈ 2.48 eV, so only metals with a smaller work function eject electrons. Equivalently, compare the threshold wavelengths λ₀ = hc/Φ: Cs 636 nm, K 542 nm, Na 451 nm, Ca 432 nm, Mg 339 nm. Only light shorter than λ₀ (more energetic) works, so just Cs and K.

Each photon can eject at most one electron, so the same number of photons ejects about the same number of electrons. Each photon’s energy, E = hν, rises with frequency, and after subtracting the unchanged work function, more is left as the electron’s kinetic energy.

Φ = 2.75 × $1.602 \times 10^{-19}$ = $4.406 \times 10^{-19}$ J. At the threshold, a photon’s energy just equals the work function: hν₀ = Φ, so ν₀ = Φ/h = $4.406 \times 10^{-19}$ ÷ ($6.626 \times 10^{-34}$) = $6.65 \times 10^{14}$ Hz, a wavelength of about 451 nm (blue light).

In the wave model, light’s energy depends on intensity, so bright enough light, shone long enough, should always eject electrons. Instead there is a threshold frequency: an electron absorbs one photon at a time, and if hν is less than the work function, no intensity helps. That is strong evidence for photons. Diffraction and the constant speed of light fit the wave model.