Modern physics
Radioactive decay
Random decay, predictable statisticsN = N₀ · 2^(−t/T½)λ = ln2/T½ | A = λN
Decay curve N–t
Blue dot: theory N₀·2^(−t/T½) — Red dot: your random sample. They agree better with larger N₀.
Parameters
Initial nuclei N₀400
Larger samples follow the theory curve more closely
Half-life T½5 s
Calculated
Decay constant λ0.1386 s⁻¹
Initial activity55.5 Bq
N after 1 T½200
N after 2 T½100
N after 3 T½50
Curriculum
WAECNECOIGCSESATJUPEB
📋 Teacher notes
- •Decay is RANDOM for one nucleus but statistically predictable for many — the red measured dot scatters around the smooth blue theory curve, and the scatter shrinks as N₀ grows.
- •After each half-life exactly half of what remains decays: N₀ → N₀/2 → N₀/4 → N₀/8 … the dashed gridlines mark 1T½, 2T½, 3T½.
- •The decay constant λ = ln2/T½ is the probability per second that any one nucleus decays. Activity A = λN falls with the same half-life as N.
- •Nothing changes the half-life — not temperature, pressure, or chemistry. It is a nuclear property.
- •Carbon-14 dating: living things maintain constant C-14; after death it halves every 5730 years. Measuring the remaining fraction gives the age.
✏️ Exercises