Quantum physics: photon model, photoelectric effect, wave-particle duality, Bohr model, quantum phenomena
What this domain tests
Quantum physics covers the photon model, the photoelectric effect, wave–particle duality, the Bohr model and the qualitative features of quantum phenomena. The exam expects energy balances in electronvolts, the interpretation of graphs, and an argument for why a classical wave model fails.
Photon model and photoelectric effect
- Light of frequency f consists of photons with E = h·f = h·c/λ; h = 6.63·10⁻³⁴ J·s and h·c = 1.24·10⁻⁶ eV·m, so E ≈ 1240 eV·nm / λ in nm.
- Einstein equation: E_kin,max = h·f − W_A, where W_A is the work function of the material.
- Threshold frequency f_G = W_A/h; below it no electrons are emitted, whatever the intensity.
- Stopping voltage: e·U_G = E_kin,max.
- Intensity sets the number of photons per second, hence the photocurrent, not the maximum energy.
Wave–particle duality
- de Broglie wavelength λ = h/p = h/(mv); electrons accelerated through U have λ = h/√(2meU).
- Electron diffraction on graphite shows interference - a wave property of particles.
Bohr model and spectra
- Stationary states with quantised energy; for hydrogen E_n = −13.6 eV/n².
- A spectral line appears when h·f = E_m − E_n; line spectra are direct evidence for discrete levels.
- The Franck–Hertz experiment confirms discrete excitation energies.
Worked example
Light of λ = 400 nm falls on caesium, W_A = 1.94 eV. Photon energy E = 1240/400 eV = 3.10 eV. Hence E_kin,max = 3.10 − 1.94 = 1.16 eV and the stopping voltage is 1.16 V. Doubling the intensity leaves 1.16 eV unchanged but doubles the saturation current - a standard exam argument that must be stated, not implied.
Traps
- Explaining the maximum energy with intensity instead of frequency.
- Mixing J and eV, or forgetting to convert before subtracting.
- Using the work function of the wrong metal, or treating it as a property of the light.
- Confusing the wavelength of the light with the de Broglie wavelength of the electron.
- Claiming the Bohr model explains all atoms - it fails for multi-electron atoms.