Modern Physics and Quantum Phenomena
Modern physics questions cover the photoelectric effect, photon energy, atomic energy levels, de Broglie wavelength, radioactive decay and mass–energy equivalence.
Core rules
- Photon energy E = hf = hc/λ, with h = 6.63×10⁻³⁴ J s. A useful value is hc ≈ 1240 eV nm.
- Photoelectric equation: K_max = hf − φ. Threshold frequency f₀ = φ/h; stopping potential satisfies eV_s = K_max.
- Bohr model for hydrogen: E_n = −13.6/n² eV. A transition emits or absorbs a photon with ΔE = hf.
- de Broglie wavelength λ = h/p = h/(mv).
- Radioactive decay: N = N₀e^(−λt); half-life T½ = ln2/λ; activity A = λN.
- Mass–energy: E = mc²; a mass defect appears as released energy.
Worked example
Light of wavelength 400 nm falls on a metal with work function 2.0 eV. Photon energy = 1240/400 = 3.1 eV. Hence K_max = 3.1 − 2.0 = 1.1 eV, and the stopping potential is 1.1 V. A more intense beam of the same wavelength gives more electrons but the same K_max.
Traps
Entering nanometres directly into hc/λ without matching units; mixing electronvolts and joules; thinking intensity changes maximum kinetic energy; treating the work function as negative; confusing half-life with mean lifetime.