Photoelectric effect
The photoelectric effect is easiest to understand when light is treated as packets of energy. Each photon carries energy E = hf. An electron can escape a surface only if one photon supplies at least the work function of that material.
Threshold first, intensity second
hf = φ + Kmax
φ is the work function and Kmax is the maximum kinetic energy of emitted electrons.
Below the threshold frequency f₀ = φ/h, increasing intensity does not eject electrons. Above threshold, raising intensity mainly increases the number of photons arriving per second and therefore the emission rate; raising frequency increases the energy available to each emitted electron.
Stopping potential measures electron energy
A reverse voltage can be applied to stop even the fastest photoelectrons. At the stopping potential Vs, eVs = Kmax. Plotting Vs against frequency gives a straight line whose intercept reveals the threshold.
Threshold explorer
What the experiment established
The immediate emission and the existence of a threshold frequency are not explained by simply spreading wave energy continuously over the surface. The photon model accounts for both without requiring a time delay. The effect does not mean light has stopped behaving as a wave; interference and diffraction remain essential evidence for wave behaviour.
Reading the variables correctly
Do not confuse photon energy with beam power. A bright low-frequency beam can deliver lots of energy each second while every individual photon remains below threshold. Conversely, a weak high-frequency beam may eject relatively few electrons, but those electrons can have substantial kinetic energy.
Worked examples
1. Find the threshold wavelength
Solution
For φ = 2.5 eV, λ₀ = hc/φ ≈ 1240/2.5 = 496 nm.
2. Maximum kinetic energy
Solution
Photons of 4.2 eV strike a surface with φ = 2.0 eV. Kmax = 4.2 - 2.0 = 2.2 eV.
3. Stopping potential
Solution
If Kmax = 1.6 eV, an electron is stopped by about 1.6 V because eVs = Kmax.