Upper secondary · 15 min

Measuring half-life and dating a sample

Follow the decay of four real nuclides on one chart, read their half-lives off the curves, and choose which isotope could date a mummy, a wine cellar or nuclear fallout.

Goal

Extract the half-life from a decay curve and pick the right isotope for a dating problem at a given timescale.

Apparatus and reagents

Four nuclides spanning days to millennia: $\ce{^{131}I}$ , $\ce{^{60}Co}$ , $\ce{^{137}Cs}$ and $\ce{^{14}C}$ , each with its own time axis.

Procedure

Select $\ce{^{131}I}$ and hover the red curve at the first marker: check it crosses exactly 0.5 at T½ = 8.02 days.
Check the second and third markers: the curve should read 0.25 and 0.125 — halving is multiplicative, not additive.
Switch to $\ce{^{14}C}$ and read off how much carbon-14 remains after about 5730 and 11460 years — the working range of radiocarbon dating.
For each nuclide write down T½ and decide which sample it could date: a medical dose (days), a fallout field (decades) or a mummy (millennia).

What to observe

Every curve crosses 50 % exactly at its labelled T½, then 25 % and 12.5 % at two and three half-lives — the exponential law $N = N_0\,(1/2)^{t/T_{1/2}}$ .
The blue (decayed) curve is the mirror image of the red one: parent and daughter fractions always sum to 1.
After about ten half-lives less than 0.1 % remains — the practical limit of any dating method.

Explanation

Each nucleus decays with a constant probability per unit time, so the population follows $N(t) = N_0 e^{-\lambda t}$ with $\lambda = \ln 2 / T_{1/2}$ . Because the decay law is exponential, the fraction left after $n$ half-lives is always $2^{-n}$ , regardless of when you start counting — that is why T½ alone characterises a nuclide and why radiometric dating just measures the remaining fraction to infer time.

Chemists behind it

Marie Curie Frederick Soddy