Half-life

Section 3 of 5

A carbon-14 nucleus holds too many neutrons to stay as it is. Sooner or later it breaks down.

When it does, one of its neutrons turns into a proton and shoots out a fast electron. The nucleus now has 7 protons and 7 neutrons, so the atom is nitrogen-14 again, the atom it was made from. This breaking down is radioactive decay.

Nobody can say when one particular carbon-14 atom will decay: it might be tomorrow, or in 20,000 years. In a crowd of billions, though, the numbers are very steady. In any 5,700 years, half of the carbon-14 atoms decay. That time is carbon-14's half-life.

Carbon-14 halves every 5,700 years A bar chart of the share of carbon-14 left against time. At 0 years the bar is 100%. Each bar after it is half as tall as the one before: 50% at 5,700 years, 25% at 11,400 years, 12.5% at 17,100 years and 6.25% at 22,800 years. 0% 25% 50% 75% 100% carbon-14 left 100% 0 50% 5,700 25% 11,400 12.5% 17,100 6.25% 22,800 years
Start with any amount of carbon-14. After one half-life, half of it is left. After two, a quarter. Each half-life halves whatever is left.

The halving goes on however little is left: a half, a quarter, an eighth, a sixteenth. After ten half-lives, 57,000 years, about a thousandth of the carbon-14 remains.

How well it is known

Scientists have measured the half-life many times, and the value they accept today is 5,700 years, give or take 30. Willard Libby, who invented carbon dating, used 5,568 years. Laboratories still work out a first radiocarbon age with Libby's number, so that ages measured since the 1950s can all be compared, and calibration, at the end of this lesson, turns it into a calendar date.

Quick check

A piece of charcoal holds one eighth of the carbon-14 that fresh wood holds. About how old is it?