How can radioactive atoms work as a clock if each one decays at random?

Radioactive atoms make a good clock because, although each one decays at random, a big crowd of them behaves with perfect regularity. Every unstable atom has the same 50 percent chance of decaying within a fixed stretch of time, called its half-life. You can't predict when one particular atom will go, but with billions of them, almost exactly half will have decayed after one half-life, half of what's left after the next, and so on. Count what remains and you can read off how much time has passed.

It works like flipping a mountain of coins and removing every head. You never know which coin will land heads, yet each round removes about half of them, and the pile shrinks on a reliable schedule. And the schedule never speeds up or slows down: the half-life is the same whether the sample is fresh or ancient.

Each kind of atom has its own clock speed. Carbon-14 has a half-life of about 5,700 years. Uranium-238 takes about 4.46 billion years. Ernest Rutherford hit on the idea in 1907 and soon used it to date rocks. The cover of the Voyager Golden Record even carries a plated sample of pure uranium-238, so that anyone who finds it could measure how much uranium remains and work out how old the record is.