Science Puzzle
How Old Is This Rock?
When a volcanic rock cools and crystallises, its minerals trap a little radioactive potassium-40. From that moment the potassium-40 slowly decays into other elements, including argon gas that stays trapped in the crystals. Half of any amount of potassium-40 decays in 1.25 billion years.
Measurements on a rock show that only a quarter of the potassium-40 it started with is left. How old is the rock?
The Answer
2.5 billion years. After one half-life, half the potassium-40 is left; after a second half-life, half of that half, a quarter.
The tempting answer is 3.75 billion years, reasoning that three quarters has gone and each quarter takes 1.25 billion years. Radioactive decay doesn't work like that. Each atom has a fixed chance of decaying in any given year, however long it has already existed, so the amount left halves over each equal stretch of time: a half, then a quarter, then an eighth, never quite reaching zero.
That steady halving makes a superb clock, and it's hard to upset: heat, pressure and chemistry barely change it. Geologists measure how much of the original element is left by comparing it with what it decayed into. Different clocks suit different ages. Carbon-14, with a half-life of about 5,700 years, dates bones and wood up to about 50,000 years old. Uranium, with half-lives of hundreds of millions to billions of years, dates the oldest rocks. The oldest known piece of Earth, a tiny zircon crystal from the Jack Hills of Western Australia, is about 4.4 billion years old.
The principle: Radioactive decay. Unstable atoms decay at a fixed rate that halves the amount left in each half-life, so the fraction remaining in a rock reveals its age.