Observations
When light of suitable frequency falls on a metal surface, electrons are emitted. Hertz noticed that ultraviolet light helped sparks jump across a gap; Hallwachs and Lenard studied the effect in detail. The main experimental results are:
- Photocurrent is proportional to the intensity of light (number of electrons emitted per second).
- For each metal there is a threshold frequency ν₀; below it no electrons are emitted, however intense the light.
- The stopping potential V₀ (and so the maximum kinetic energy of photoelectrons) depends on frequency, not on intensity; it increases linearly with frequency.
- Emission is practically instantaneous (within about 10⁻⁹ s), even for weak light.
Wave theory cannot explain the threshold frequency, the independence of Kmax from intensity, or the absence of delay.
Einstein's photoelectric equation
Einstein proposed that light consists of photons, each of energy E = hν. One photon gives all its energy to one electron. Part of it, the work function φ₀, is used to free the electron; the rest appears as kinetic energy: Kmax = hν – φ₀ = eV₀ with φ₀ = hν₀. A graph of V₀ against ν is a straight line of slope h/e that cuts the frequency axis at ν₀.
Photons
A photon has energy hν, momentum p = h/λ = hν/c and zero rest mass. Increasing intensity at fixed frequency means more photons, not more energetic ones.
Worked example
A useful shortcut: E (in eV) ≈ 1240/λ (in nm). Light of 310 nm has photon energy about 4.0 eV. On a metal with φ₀ = 2.5 eV, Kmax ≈ 1.5 eV and the stopping potential is about 1.5 V.
Key points
- Kmax = hν – φ₀ = eV₀; φ₀ = hν₀.
- Intensity changes current, not stopping potential.
- No emission below ν₀.
- Slope of V₀–ν graph = h/e.
Common mistakes
- Thinking brighter light gives faster electrons.
- Mixing joules and electronvolts in one equation (1 eV = 1.6 × 10⁻¹⁹ J).