Theme E · Nuclear and Quantum Physics · SL 7h + HL 5h
E.3 Radioactive Decay
Why are some nuclei stable and others not, and what is released when they decay?
Nuclear stability is a balance: the strong nuclear force holds nucleons together (short range, very strong), while electromagnetic repulsion pushes protons apart (longer range). When a nucleus has too many or too few neutrons, or is simply too large, it becomes unstable and decays by emitting radiation. The type of decay depends on the nature of the instability.
Mass-energy equivalence (E = mc²) is essential for understanding nuclear energetics. A nucleus is lighter than the sum of its individual nucleons — the "missing mass" is the binding energy, converted to energy when the nucleus was assembled. The binding energy per nucleon peaks near iron-56; this is why nuclei lighter than iron release energy by fusion, and nuclei heavier than iron release energy by fission. Radioactive decay is always random and spontaneous — you cannot predict when any individual nucleus will decay, only the statistical half-life of a large sample.
A sample of iodine-131 (half-life 8 days) has initial activity 4.0 × 10⁸ Bq. What is its activity after 24 days? Write the decay equation for iodine-131 (it undergoes β⁻ decay), and state what changes in the nucleus.
Key equations and facts
Mass-energy equivalence: E = mc² (c = 3.0 × 10⁸ m s⁻¹)
Mass defect: Δm = Zmp + Nmn − mnucleus
Binding energy: EB = Δm × c²
Half-life and activity: A = A₀ × (½)^(t/t½)
HL Exponential decay: N = N₀ e^(−λt); A = A₀ e^(−λt); t½ = ln2/λ
What students must understand
Isotopes: same proton number, different nucleon number
Nuclear binding energy and mass defect; E = mc²
Binding energy per nucleon curve: peak at Fe-56; fusion and fission release energy on either side
Strong nuclear force: short-range, attractive, acts between nucleons
Radioactive decay: random, spontaneous; individual nuclei cannot be predicted
Alpha decay (α = ²₄He): A−4, Z−2; stopped by paper