7 · IGCSE Physics
Half-life and decay graphs
Watch a sample of unstable nuclei decay at random, see the activity–time graph build up, and read the half-life straight from the curve. Drag across the graph to read off values.
Drag on the graph (or focus it and use ← →) to read the activity at any time. Esc hides the cursor.
A = A₀ × (½)^(t / T½)
N = N₀ × (½)^n after n half-lives
λ = ln 2 / T½ , A = λN
N = N₀ × (½)^n after n half-lives
λ = ln 2 / T½ , A = λN
Try this
- Run the decay with T½ = 8 s, then drag the cursor to find when the activity falls from A₀ to A₀/2, and again from A₀/2 to A₀/4. Are the two times equal?
- Set n = 3 and predict the fraction left before reading it. Then compare the sample's undecayed count at t = 3T½ with N₀/8.
- Repeat with N₀ = 100 and then N₀ = 800. Which gives measured points that sit closer to the smooth curve, and why?
Exam tip: read the half-life from the graph at least twice from different starting values (for example A₀ to A₀/2 and A₀/2 to A₀/4) and quote the average — and remember that background count must be subtracted before you halve.