Nuclear and Quantum Physics: Radioactivity, Nuclear Reactions, Photoelectric Effect, Energy Levels and Tunnelling
Nuclear and quantum physics covers radioactivity, nuclear reactions, the photoelectric effect, atomic energy levels and quantum tunnelling. The exam tests exponential decay, conservation in nuclear equations, mass defect and binding energy, the photoelectric equation, de Broglie wavelength and discrete spectra. HL questions often compare classical and quantum predictions.
Core rules
- Decay: N = N₀(1/2)^(t/T½); activity A = λN, with λ = ln2/T½.
- Nuclear equations conserve nucleon number A and charge Z.
- Mass defect: ΔE = Δmc²; binding energy per nucleon peaks near iron-56.
- Photoelectric effect: hf = Φ + E_k(max); threshold frequency f₀ = Φ/h.
- de Broglie: λ = h/p; energy levels: hf = E₂ − E₁.
- Tunnelling probability falls rapidly as barrier height or width increases.
Worked example
Light of wavelength 400 nm strikes a metal with work function 2.0 eV. Photon energy is E = hc/λ = (6.63 × 10⁻³⁴)(3.00 × 10⁸)/(4.00 × 10⁻⁷) = 4.97 × 10⁻¹⁹ J = 3.11 eV. Thus E_k(max) = 3.11 − 2.0 = 1.11 eV, or 1.78 × 10⁻¹⁹ J. The stopping voltage would be 1.11 V. Increasing intensity increases current, not maximum kinetic energy.
Traps
Convert electronvolts to joules before using SI equations, or keep every term in eV. Intensity does not change E_k(max); frequency does. Half-life is probabilistic, so not exactly half the nuclei decay in one half-life. In nuclear equations, check both A and Z. Do not confuse binding energy with mass defect.