Quantum Physics: Photoelectric Effect, Photon Model, Wave-Particle Duality, Bohr Model
Quantum physics tasks in the Abitur are almost always quantitative: a stopping potential, an h-determination from a straight-line graph, or a de Broglie wavelength compared with an atomic spacing.
Photon model
E = h·f = h·c/λ with h = 6.63×10⁻³⁴ J·s. A convenient shortcut is h·c = 1240 eV·nm. Photon momentum p = h/λ. Intensity sets the number of photons per second; frequency sets the energy per photon.
Photoelectric effect
E_kin,max = h·f − W_A; threshold frequency f_G = W_A/h; the stopping potential satisfies e·U_G = E_kin,max. Raising the intensity increases only the saturation current; the maximum kinetic energy depends on the frequency and the cathode material.
Wave–particle duality
de Broglie: λ = h/p, and for an electron accelerated through U, λ = h/√(2·m·e·U). Electron diffraction on graphite gives rings; single photons build up the interference pattern statistically.
Bohr model
E_n = −13.6 eV/n² for hydrogen; a transition emits or absorbs h·f = |E_n − E_m|, which reproduces the line spectrum including the series limits. The model fails for multi-electron atoms and for fine structure.
Worked example
Light of 450 nm strikes caesium (W_A = 2.14 eV). Photon energy = 1240/450 eV = 2.76 eV. So E_kin,max = 2.76 − 2.14 = 0.62 eV and U_G = 0.62 V. At 500 nm the photon energy is 2.48 eV, giving E_kin,max = 0.34 eV - the stopping potential falls although the light may be more intense.
Traps
- Mixing eV and joule in one equation.
- Believing brighter light gives faster electrons.
- Reading the slope of U_G(f) as h instead of h/e (the intercept is −W_A/e).
- Using λ = h/p with a classical p for fast electrons without checking the energy.
- Confusing the work function (a material property) with the photon energy (a property of the light).