E.3 · IB Physics
Half-life with dice
Throw a set of dice repeatedly; any die landing on a decay face is removed. Compare the random results with the exponential model and read off the half-life.
p = k / s (decay chance per throw)
N = N₀(1 − p)ⁿ
λ = −ln(1 − p) per throw
n½ = ln 2 / λ ≈ 0.693 / p
N = N₀(1 − p)ⁿ
λ = −ln(1 − p) per throw
n½ = ln 2 / λ ≈ 0.693 / p
Try this
- With N₀ = 1000, 6 faces and k = 1, run one trial and read where the curve crosses N₀/2. Compare it with the model half-life of 3.80 throws.
- Set N₀ = 20 and run five trials. How much do the measured half-lives vary? Repeat with N₀ = 1000 and compare the spread.
- Change to 12 faces with k = 2: predict the half-life before running, then check. What about 20 faces with k = 1?
Exam tip: read the half-life from more than one pair of points on a decay graph (N₀ to N₀/2, then N₀/2 to N₀/4) and average them, since each interval should take the same time.