E.3 · IB Physics
Radioactive decay
Decay is random for any one nucleus but predictable in bulk. Watch the sample of nuclei, the smooth exponential curve and the real, jagged count of what remains.
Predict first
Start from the default settings (t½ = 3 s). If you change the half-life to 6 s, what happens to the decay constant λ?
λ = ln 2 ÷ t½, so doubling the half-life halves λ (0.231 s⁻¹ becomes 0.116 s⁻¹).
Check it in the model: Move the Half-life, t½ slider from 3 to 6 s and compare the Decay constant λ readout.
expected N = N₀e^(−λt) this sample (random) · gold dots are undecayed nuclei
N = N₀ e^(−λt) = N₀ (½)^(t ÷ t½)
λ = ln 2 ÷ t½
A = λN
λ = ln 2 ÷ t½
A = λN
Try this
- With N₀ = 100 and t½ = 3 s, restart several times and note N after exactly one half-life. Then repeat with N₀ = 400 and compare the scatter.
- Tick the logarithmic axis. What shape does the expected curve take, and what does its gradient equal?
- Change t½ from 3 s to 6 s. Compare the decay constant λ and the activity at the start of the run.
Exam tip: decay is exponential, N = N₀e^(−λt) with λ = ln 2 ÷ t½: after each half-life the remaining number halves, and a straight ln N against t graph has gradient −λ.