E.3 Radioactive decayIB Physics SL: Revision notes

Isotopes are nuclides of the same element (same Z) with different numbers of neutrons.

The mass of a nucleus is less than the total mass of its separate nucleons. The difference is the mass defect Δm. The binding energy is the energy needed to separate a nucleus completely into its nucleons, and equals the energy equivalent of the mass defect: E = Δmc². With masses in u, use 1 u = 931.5 MeV c⁻², so E (in MeV) = Δm (in u) × 931.5.

Binding energy per nucleon measures stability. It rises steeply for light nuclei, peaks at about 8.8 MeV near iron-56 / nickel-62, then falls slowly for heavy nuclei (about 7.6 MeV for uranium). Helium-4 is unusually high for its size.

Any nuclear reaction whose products have more total binding energy releases energy: fusion of light nuclei and fission of heavy nuclei both move towards the peak. The energy released equals the mass lost × c².

Protons in a nucleus repel electrostatically, yet nuclei hold together. The strong nuclear force acts between all nucleons (proton–proton, proton–neutron, neutron–neutron). It is attractive, much stronger than the electrostatic force at nuclear distances, and short-range (about 10⁻¹⁵ m); at very small separations it becomes repulsive, preventing collapse.

Decay is random (you cannot predict which nucleus decays next) and spontaneous (unaffected by temperature, pressure or chemistry).

• Alpha: A falls by 4, Z by 2. $^{A}_{Z}\mathrm{X} \rightarrow\ ^{A-4}_{Z-2}\mathrm{Y} + ^{4}_{2}\alpha$
• β⁻: a neutron becomes a proton; Z rises by 1, A unchanged; an electron and an antineutrino are emitted.
• β⁺: a proton becomes a neutron; Z falls by 1; a positron and a neutrino are emitted.
• Gamma: a nucleus drops from an excited state; A and Z unchanged.

Neutrinos and antineutrinos are uncharged, almost massless and interact very weakly with matter.

• Alpha (+2e, heavy): most ionising, stopped by paper or a few cm of air.
• Beta (±e, light, fast): moderately ionising, stopped by a few mm of aluminium.
• Gamma (uncharged photon): weakly ionising, most penetrating; intensity reduced by several cm of lead.

The more a radiation ionises, the faster it loses energy and the shorter its range.

Activity is the number of decays per second (unit: becquerel, Bq). A detector measures a count rate, which is only a fraction of the activity. Half-life is the time for the number of undecayed nuclei, or the activity, to halve. After n whole half-lives, the fraction remaining is (1/2)ⁿ.

Background radiation (rocks, cosmic rays, medical sources) is always present. Measure it with the source removed and subtract it from every reading before finding a half-life.