Half-life

Decay is random

Radioactive decay is a random process. Every unstable nucleus of a particular isotope has exactly the same chance of decaying in the next second, and that chance never changes. A nucleus doesn't "age" or "wear out": one that has existed for a million years is no more likely to decay next than one that formed a moment ago. It is a bit like a huge crowd each tossing a coin every minute and sitting down when they get heads. You can't say who will sit down next, but you can say that about half the crowd will be sitting after the first minute.

What half-life means

The half-life of a radioisotope is the time it takes for half of the radioactive nuclei in a sample to decay. After one half-life, half the original nuclei are left; after two half-lives a quarter; after three an eighth, and so on. The amount never quite reaches zero, but it soon becomes too small to measure. The activity (the number of decays per second, measured in becquerels, Bq) also halves every half-life, because fewer nuclei are left to decay.

Half-life calculations

To find how much is left: work out how many half-lives have passed (time ÷ half-life), then halve the starting amount that many times.

Worked example: A hospital receives 80 mg of technetium-99m (half-life 6 hours). How much is left after 24 hours?
Number of half-lives = 24 ÷ 6 = 4. So 80 → 40 → 20 → 10 → 5 mg.

Worked example: A Geiger counter reads 1600 counts per minute from a sample. Two days later it reads 400 counts per minute. What is the half-life?
1600 → 800 → 400 is two halvings, so two half-lives = 2 days, and the half-life is 1 day. (In real measurements, remember to subtract the background count first.)

A useful rule: after about 10 half-lives, less than 0.1% of the original nuclei remain.

Radiocarbon dating

Cosmic rays hitting the upper atmosphere turn some nitrogen into carbon-14. It mixes into the air as carbon dioxide, and plants take it in during photosynthesis, so every living thing has about the same tiny proportion of carbon-14 as the air (about one carbon atom in a trillion). When an organism dies, it stops taking in carbon, and its carbon-14 steadily decays with a half-life of 5730 years. By measuring how much carbon-14 is left compared with carbon-12, scientists can work out how long ago it died.

A piece of charcoal with a quarter of the carbon-14 of living wood has been through two half-lives, so the tree died about 2 × 5730 = 11 460 years ago. Radiocarbon dating works on things that were once alive (wood, charcoal, bone, shell, cloth) and up to about 50 000 years. For older objects and rocks, isotopes with longer half-lives are used, such as potassium-40 and uranium-238.

Radiocarbon dates are part of the evidence for the long history of people in Australia. Charcoal and shell from sites such as Lake Mungo in NSW show people were there more than 40 000 years ago, and the Gunditjmara eel traps at Budj Bim in Victoria have been dated to at least 6600 years old, older than the Egyptian pyramids. For the oldest sites, such as Madjedbebe in Arnhem Land (about 65 000 years), scientists use luminescence dating, which measures how much radiation sand grains have absorbed from natural radioactive elements since they were last in sunlight.