Radioactivity — Half-life & Decay (Years 10–11) — Science

Alpha, beta and gamma radiation, nuclear decay equations, half-life calculations, uses and safety, and fission versus fusion.

Deep inside some atoms the nucleus is unstable — sooner or later it will break apart, firing out radiation. We cannot predict when any single nucleus will decay, yet across billions of atoms the process is astonishingly regular, ticking away like a clock. That clock, the half-life, lets us date ancient bones, power spacecraft and treat cancer.

Why this matters Radioactivity powers nuclear stations, sterilises medical equipment, dates archaeological finds by carbon-14 and treats tumours. Understanding half-life and the radiation types is essential both for using them and for staying safe.

Three types of radiation

Unstable nuclei emit one of three kinds of radiation, with very different penetrating powers:

Type	What it is	Stopped by
Alpha (α)	helium nucleus (2p + 2n)	paper / skin
Beta (β)	fast electron	a few mm of aluminium
Gamma (γ)	electromagnetic wave	thick lead / concrete

Each half-life the activity falls to half its previous value.

Decay equations

Nuclei are written as ^A_ZX, where A is the nucleon (mass) number and Z the proton number. Radiation changes these numbers:

Alpha decay: the nucleus loses 2 protons and 2 neutrons, so A decreases by 4 and Z decreases by 2. Example: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂α.
Beta decay: a neutron turns into a proton and emits an electron, so A is unchanged and Z increases by 1. Example: ¹⁴₆C → ¹⁴₇N + ⁰_-1β.
Gamma emission carries away energy only, so A and Z are unchanged.

Half-life

The half-life is the time taken for half the undecayed nuclei in a sample (or for its activity) to decay. It is fixed for a given isotope. To solve half-life problems, count how many times the quantity halves:

Alpha decay of radium-226: nucleon and proton numbers balance on both sides.

Uses, safety, and fission vs fusion

Uses: carbon-14 dating, medical tracers and cancer treatment, sterilising equipment, thickness gauges, smoke detectors.
Safety: keep sources far away, handle with tongs, store in lead-lined boxes, and limit exposure time. Gamma is the most penetrating; alpha is very dangerous if swallowed or inhaled.
Nuclear fission splits a large nucleus (e.g. uranium-235) into smaller ones, releasing energy — this powers today's nuclear stations. Nuclear fusion joins small nuclei (e.g. hydrogen) into a larger one, releasing even more energy — this powers the Sun.

Worked example (3 marks). A source has an activity of 480 counts/s and a half-life of 6 hours. How long until the activity falls to 60 counts/s? Halve repeatedly: 480 → 240 → 120 → 60, which is 3 half-lives [1]. Each half-life is 6 hours [1], so time = 3 × 6 = 18 hours [1].

Common exam mistake: in beta decay, thinking the mass number changes. It does not — a neutron becomes a proton, so A stays the same and only Z rises by 1. Also, always check both the top and bottom numbers balance in a decay equation.

Memory hook: penetration order "alpha-paper, beta-aluminium, gamma-lead." For half-life questions, keep halving and count the halvings — that count times the half-life is your answer.