Radioactive decay is random, but for a large number of nuclei it follows a steady pattern described by the half-life.
What half-life means
The half-life is the time taken for half the radioactive nuclei in a sample to decay, or equally for the activity (count rate) to fall to half its value. Activity is measured in becquerels (Bq), where 1 Bq is one decay per second. Half-life is a fixed property of a nuclide and does not change with temperature, pressure or chemistry.
Key idea
After n half-lives, the fraction remaining is (½)n. So after 1, 2, 3 half-lives: ½, ¼, ⅛ of the original remains.
Worked example
A source has an activity of 1600 Bq and a half-life of 4 days. After 8 days two half-lives have passed. Activity = 1600 → 800 (after 4 days) → 400 Bq (after 8 days). So the activity is 400 Bq.
Using half-life
Half-life explains how long radioactive waste stays dangerous and is the basis of radioactive (carbon) dating. To find a half-life from a graph, read off the time for the count rate to fall from any value to half of it.
Remember
- Half-lives range from fractions of a second to billions of years.
- The count rate never quite reaches zero; it keeps halving.
- We cannot say when one nucleus will decay, only the average behaviour of many.