Half-life: a constant chance per nucleus, not a countdown

Year 12 Physics · every undecayed nucleus has the same chance of decaying in the next instant, no matter how many have already gone · N(t) = N₀ e^−λt with λ = ln 2 / t_½ · the dashed line is that law, the solid line is this sample

Set up the sample

Same isotope, different sample sizes — watch what changes and what does not

Half-life t_½ 5.0 days

Starting nuclei N₀ 800

seed 20260831 · run 0

Fraction remaining against time

this sample (solid) the law (dashed)

Each dashed vertical line is one more half-life. Equal fractions disappear over equal times — that is what makes the curve a half-life curve rather than a countdown.

The nuclei themselves

Each square is one nucleus. They flip at random, independently.

Time elapsed

0.0 d

0.00 half-lives

Still undecayed

800

of 800

Fraction remaining

1.0000

this sample

The law predicts

1.0000

difference 0.0000

Predict first

A sample of 800 nuclei has a half-life of 5 days. After the first 5 days, 400 have decayed. How much of the original sample is still undecayed after 10 days, that is after two half-lives?