Wave nature of light and modern physics
This domain links light interference and diffraction to photons, the photoelectric effect, matter waves, atomic models and basic relativity. PAU questions often ask you to interpret a graph or explain why a classical wave model fails.
Core rules
- Young's double slit: bright fringes at d sinθ = mλ; fringe spacing on a distant screen is Δy = λL/d. Diffraction by a single slit has minima at a sinθ = mλ.
- Photon energy: E = hf = hc/λ. The photoelectric equation is K_max = hf - W, where W is the work function. Stopping potential satisfies eV_s = K_max.
- Threshold frequency f₀ = W/h; below it no emission occurs regardless of intensity. Intensity changes the number of photons, not the maximum kinetic energy.
- de Broglie wavelength: λ = h/p = h/(mv). Bohr model: E_n = -13.6/n² eV for hydrogen; spectral lines arise from transitions between levels.
- Relativity basics: time dilation t = γt₀, length contraction L = L₀/γ, with γ = 1/sqrt(1 - v²/c²). Rest energy E₀ = mc².
Worked example
Light of wavelength 400 nm falls on a metal with work function 2.0 eV. Using hc = 1240 eV·nm, the photon energy is 1240/400 = 3.10 eV. Thus K_max = 3.10 - 2.0 = 1.10 eV. The stopping potential is 1.10 V. The maximum speed follows from K_max = ½mv²: v = sqrt(2K/m) = sqrt(2(1.10×1.6×10⁻¹⁹)/(9.11×10⁻³¹)) ≈ 6.2×10⁵ m/s. If the wavelength were longer than the threshold wavelength, no electrons would be emitted.
Traps
Do not use K_max = hf; subtract the work function. Increasing intensity does not increase K_max. Convert electron-volts and joules carefully. In double-slit problems, d is slit separation, not slit width. Diffraction and interference both require coherence. For de Broglie waves, use momentum, not kinetic energy directly, unless you convert. Relativistic formulas are needed when v is a significant fraction of c; do not apply γ blindly to low-speed problems.