Dual Nature of Matter and Radiation
The unit establishes that light behaves as a stream of photons and that particles behave as waves. The examinable core is the photoelectric effect - Einstein's equation, threshold frequency, stopping potential and the intensity-versus-frequency distinction - together with the de Broglie relation and the Davisson–Germer experiment as its confirmation. A very common long answer asks you to derive or interpret the photoelectric equation and to explain why stopping potential depends on frequency but not on intensity.
Core rules
- Photon energy E = hν = hc/λ; a convenient working form is E(eV) = 1240/λ(nm).
- Einstein's photoelectric equation: hν = φ₀ + eV₀, where φ₀ = hν₀ is the work function and V₀ the stopping potential.
- Below threshold frequency ν₀ no emission occurs, however intense the light; above it, saturation current is proportional to intensity while stopping potential depends only on frequency.
- Emission is instantaneous (≈10⁻⁹ s) because energy is absorbed one photon at a time.
- de Broglie wavelength λ = h/p = h/mv = h/√(2mK); for an electron accelerated through V volts, λ ≈ 12.27/√V Å.
- Photon momentum p = h/λ; photons have zero rest mass but carry energy and momentum.
Worked example
Light of wavelength 400 nm falls on a metal of work function 2.0 eV. Find the maximum kinetic energy and the stopping potential. Photon energy = 1240/400 = 3.1 eV. K(max) = hν − φ₀ = 3.1 − 2.0 = 1.1 eV. Therefore the stopping potential is V₀ = 1.1 V, since eV₀ = K(max). Note that doubling the intensity would double the photocurrent but leave K(max) and V₀ at 1.1 eV; using 500 nm light would instead give 2.48 − 2.0 = 0.48 eV.
Traps that cost marks
- Saying brighter light gives faster photoelectrons; intensity controls number, frequency controls energy.
- Forgetting to convert nm to metres, or mixing eV and joule in the same line.
- Writing λ = h/mv with the velocity of a photon - the formula applies to particles with mass.
- Omitting the threshold condition in graph questions (V₀ versus ν is a straight line with slope h/e and intercept −φ₀/e).