Chemistry · Chapter 21

Half-Life Lab

Run a sample of 400 nuclei forward through twelve half-lives and watch the count fall. Then work the same maths backwards and read an age off the fraction that is left.

The sample 400 nuclei to start

A sample of 400 nuclei, with the decayed ones faded out

The decay curve the same shape for every isotope

Fraction of the sample remaining against half-lives elapsed

The curve halves on every step, so it keeps falling without ever reaching zero.

Live numbers

100percent left fresh
Isotope: carbon-14, half-life 5,730 years
Time elapsed: 0 years
Nuclei left in the grid: 400 of 400
Decay constant k: 1.21 × 10−4 per year
From 1.000 mol you still have: 6.022 × 1023 nuclei
Activity, as a share of the start: 100 percent

Pick the isotope

Only the width of one step changes. The shape of the fall never does.

Date a find work the maths backwards

5,094years old
Dating clock
Try a measured find

What this tells you

Reading the result
Just under one half-life
A sample holding 54.0 percent of its carbon-14 has not quite lost half, so it is a little younger than 5,730 years.