Upper secondary · 12 min

Radioactive decay: reading the half-life

Follow the surviving fraction N/N₀ for four medical isotopes and check that it halves after every half-life.

Goal

Read a decay curve, verify N/N₀ = (1/2)^(t/T½), and link each isotope’s half-life to its medical use.

Apparatus and reagents

Simulation only — real sources are sealed and handled by licensed staff; a Geiger–Müller counter is used in demonstrations.

Procedure

Select iodine-131 and hover at t = 8.02 days: the red parent curve should read about 0.50.
Check t = 2T½ and t = 3T½: expect N/N₀ ≈ 0.25 and 0.125, while the blue daughter curve reaches 0.75 and 0.875.
Switch to phosphorus-32 (T½ = 14.3 d) and gold-198 (T½ = 2.70 d): compare how fast each curve falls.
Confirm that parent and daughter fractions always add to 1: nuclei are transformed, not destroyed.

What to observe

The two curves cross exactly at T½, where half the nuclei remain and half have decayed.
Shorter T½ gives a steeper fall: gold-198 nearly vanishes in two weeks while phosphorus-32 persists for months.

Explanation

Each nucleus decays independently with constant probability per unit time, so the ensemble follows N = N₀ e^(−λt) = N₀ (1/2)^(t/T½) with λ = ln 2 / T½. These β⁻ emitters all give stable daughters: ¹³¹I → ¹³¹Xe, ³²P → ³²S, ¹⁹⁸Au → ¹⁹⁸Hg, ¹³³Xe → ¹³³Cs; half-lives are chosen so medical doses fade quickly.

History of the experiment

Becquerel discovered uranium's penetrating rays in 1896; Marie Curie coined 'radioactivity' and, with Pierre, isolated polonium and radium from tonnes of pitchblende. Rutherford and Soddy then argued that atoms literally transmute — α emission changes the element by two units of charge — and Rutherford's statistical measurements gave the constant half-life this simulation reproduces.

Chemists behind it

Marie Curie Ernest Rutherford Frederick Soddy