Clocks Made of Decay: How Radiocarbon Dating Works

A clock that cannot be reset

Some atomic nuclei are unstable and fall apart, or decay, at a rate that nothing can change. Not heat, not pressure, not chemistry. A given kind of unstable nucleus has a fixed half-life, the time it takes for half of any sample to decay, and that half-life is a constant of nature. This is what makes radioactive decay such a good clock. An ordinary clock can be stopped, sped up, or reset, but the decay of a nucleus marches at its own pace regardless of what happens to the rock or bone or wood it sits inside. If you know the half-life, and you can measure how much of the unstable material is left, you can read off how much time has passed. Radiometric dating is just the careful application of that idea, and the most famous version uses carbon.

Where the carbon clock comes from

The clever part of radiocarbon dating is how the clock gets wound in the first place. High in the atmosphere, cosmic rays from space strike nitrogen atoms and convert a few of them into a rare, unstable form of carbon called carbon-14. This carbon-14 mixes into the air as carbon dioxide, chemically identical to ordinary carbon dioxide, and from there it enters the living world. Plants absorb it during photosynthesis, animals eat the plants, and so every living thing is constantly taking in carbon-14 along with ordinary carbon, maintaining the same small ratio of the unstable kind to the stable kind as the atmosphere itself.

That equilibrium lasts exactly as long as the organism is alive. The moment it dies, it stops taking in new carbon. The ordinary carbon already in its body stays put, but the carbon-14 keeps decaying, and now nothing replaces it. From the moment of death, the carbon-14 in the remains begins to dwindle on a fixed schedule, with a half-life of about 5,730 years. The proportion of carbon-14 left behind is therefore a measure of how long ago the organism died.

Reading the remaining fraction

The arithmetic is the arithmetic of halving. After one half-life, half the original carbon-14 remains; after two, a quarter; after three, an eighth, and so on down a curve that falls steeply at first and then flattens as it approaches zero.

 fraction of carbon-14 remaining
 1.00 *
      |  \
 0.50 +    *
      |      \ .
 0.25 +        '  *
      |             ' .
 0.12 +                  '  *  .
      |                         '  '  *  .  .
 0.06 +                                       '  '  *  .  .  .
      +----+----+----+----+----+----+----+----+----+----+----
       0   5730  11460 17190 22920 ...    years before present

Measure that a bone retains a quarter of the expected carbon-14, and you read across to two half-lives, roughly 11,500 years since the animal died. The shape of the curve also explains the method’s limit. Because the amount left keeps halving, after about ten half-lives, somewhere around fifty thousand years, so little carbon-14 remains that it can no longer be measured reliably against the background. Radiocarbon dating works well for things tens of thousands of years old, which happens to cover the whole span of human civilization and the end of the last ice age, but it cannot reach deeper than that.

The method was developed by Willard Libby around 1949, and it transformed archaeology by giving, for the first time, absolute ages for organic remains rather than guesses based on style and stratigraphy. Libby received the Nobel Prize in Chemistry in 1960. One refinement proved necessary: the atmospheric level of carbon-14 has not been perfectly constant over the millennia, so raw radiocarbon ages must be calibrated against independent records, most importantly the rings of long-lived trees, which provide a year-by-year check going back thousands of years.

Beyond carbon

Carbon-14 is only one clock in a whole set, and the others reach much further back, because they use isotopes with far longer half-lives. To date rocks rather than once-living things, geologists turn to systems like uranium decaying to lead, with a half-life measured in billions of years, locked inside crystals of the mineral zircon. These long clocks are how we know the deep history of the planet. The oldest rocks and meteorites dated this way put the age of the Earth at about 4.54 billion years, a figure that comes directly from counting the slow conversion of uranium into lead. The principle is identical to the carbon case: a parent isotope decaying at a fixed rate into a daughter product, with the ratio between them recording the elapsed time.

What ties all of this together is the reliability of the underlying physics. The constancy of the half-life is not an assumption of convenience; it has been tested exhaustively, and decay rates do not budge under any conditions found in nature. That is what lets a handful of atoms inside a scrap of charcoal, or a uranium-bearing crystal in an ancient rock, serve as an honest clock, ticking at a rate set when the universe made the elements, indifferent to everything that has happened to the sample since.