Why Do Scientists Measure Things by Half-Life?

Reader @Procrustes tweeted at us to ask: “Why do scientists measure things like radioactive elements in half-life? Why not just measure the whole life?”

If you’re not familiar with the term “half-life,” maybe you’ve heard one of your nerd friends use it. If they weren’t complaining about a guy named Gabe and ranting about steam and a valve, they were probably using it in reference to radiometric dating, a technique that uses measurement of radioactive decay to figure out the age of archaeological artifacts and dinosaur fossils.

Decay and Dating

At the center of every atom is a dense region called a nucleus, which consists of protons and neutrons. In some atoms, the forces in the nucleus are balanced and the nucleus is stable. In others, the forces are unbalanced and the nucleus has an excess of internal energy; it’s unstable, or radioactive. These unstable atoms essentially self-destruct because of the imbalance and break down, or decay. When they do this, they lose energy by emitting energetic subatomic particles (radiation).

These particles can be detected, typically with a Geiger counter. In the case of radiocarbon dating, a common dating method for organic matter that uses carbon-14 (an isotope, or variant, of the element carbon) to estimate age, one radioactive “beta particle” is produced for every carbon-14 atom that decays. By comparing the normal abundance of carbon-14 in a living creature (which is the same concentration in the atmosphere) with the amount left in the material being dated, based on the known decay rate, scientists can figure out roughly how long ago whatever they’re looking at was still alive.

Half-life steps onto the scene in the decay process. While the lifespan of any individual atom is random and unpredictable, the probability of decay is constant. You can’t predict when an unstable atom will break down, but if you have a group of them, you can predict how long it will take. Atoms that have an equal probability of decaying will do so at an exponential rate. That is, the rate of decay will slow in proportion to the amount of radioactive material you have.

“Many will disappear early on in the process but some will last for much longer time periods,” says Dr. Michael Dee, a researcher at Oxford University’s radiocarbon lab. “It’s a bit like putting (a lot) of coins out in the rain. Although they all have an equal probability of being hit by raindrops, many will be struck immediately and others will remain dry, perhaps for an extended period of time.”

It’s easy misinterpret half-life to mean “one half of the time it takes for whatever atoms you’re looking at to decay,” but it actually means “the length of time it takes for one half of the atoms you’re looking at to decay.” The measurement is useful in radiometric dating, says Dee, because exponential decay means “it doesn’t matter how much radioactive material you have, the time taken until half of it is gone [the half-life] is always the same.”

The whole life of the material, on the other hand, would be equal to the lifespan of the last atom in the group to decay. Since an atom’s lifespan is random, inestimable and essentially infinite, the whole life would be, too. It winds up being a not-very-useful measurement. “It’s a bit like one coin sitting out in the rain,” says Dee. “And never getting hit, ever.”