Einstein's idea
Einstein explained the photoelectric effect using the photon model. When light hits a metal, one photon gives all its energy (hf) to one electron. Part of this energy is used to free the electron from the metal (the work function W₀) and the rest becomes the electron's maximum kinetic energy (KEmax).
Key formula / 关键公式
Einstein's photoelectric equation:
hf = W₀ + KEmax
so KEmax = hf − W₀ and W₀ = hf₀.
Electrons are emitted only when hf ≥ W₀, i.e. f ≥ f₀.
What the equation explains
- If f < f₀, then hf < W₀, so KEmax would be negative — impossible — and no electrons are emitted.
- Increasing frequency increases hf, so KEmax increases.
- Increasing intensity sends more photons, freeing more electrons per second but not changing KEmax.
Worked example / 例题
Light of frequency 8.0 × 10¹⁴ Hz falls on a metal of work function 3.0 × 10⁻¹⁹ J. Find KEmax.
hf = (6.63 × 10⁻³⁴)(8.0 × 10¹⁴) = 5.3 × 10⁻¹⁹ J.
KEmax = hf − W₀ = 5.3 × 10⁻¹⁹ − 3.0 × 10⁻¹⁹ = 2.3 × 10⁻¹⁹ J.
Einstein received the Nobel Prize in 1921 largely for this explanation, which confirmed the quantum (photon) nature of light.
Remember / 记住
- hf = W₀ + KEmax (energy is conserved for one photon and one electron).
- KEmax = hf − W₀; emission needs hf ≥ W₀.
- Frequency controls KEmax; intensity controls the number of electrons.