Photo: AFP
Photo: AFP

The carbon tells the tale

The speed of decay of radioactive substances helps us determine the age of an artifact that contains such substances

I’m reading a fascinating book (Mary Beard’s SPQR) that teases out the history of ancient Rome. From the writings of Roman historians, the generally accepted date for when the city was founded is 753 BCE. But this book says “arguments still rage about the age of almost every major find".

Such “finds" are usually analysed by a process of archaeological deduction. It relies on clues such as “wheel-made pottery (assumed to be later than handmade) [and] the occasional presence in graves of Greek ceramics". Such analysis dates back the remains of early huts in Rome to about 750 BCE, which the book says is “excitingly close to 753 BCE".

But the same findings were also subjected to “radiocarbon dating", which suggested they are a full century older still.

So, the arguments will continue, I suspect. But radiocarbon dating results are hard to ignore, because they rely on a mechanism much like a ticking clock. So, in a sense, you simply have to read off the elapsed time, much like you might look at your wall-clock to find it’s been seven hours since you woke and you have accomplished nothing.

But how does this ticking clock work? Carbon appears widely in nature—in coal, vegetables, animals and all kinds of other organic material. Importantly, it appears in a few different “isotopes", or avatars. The everyday isotope—accounting for the great majority of carbon—is called Carbon 12, because each of its atoms contain six protons and six neutrons. But sprinkled amid all that C12 are tiny deposits of a mutant variety called Carbon 14, whose atoms have two extra neutrons.

Never mind what protons and neutrons are. What’s important is that because of the extra neutrons, the C14 atom (strictly, its nucleus, but never mind) is unstable and thus decays. That is, it steadily loses matter and energy by emitting certain kinds of sub-atomic particles. This decay process is called radioactivity.

C14 is formed high up in our atmosphere by cosmic rays. These are themselves atomic particles, zooming through the universe at great speed. Many enter the Earth’s atmosphere and it’s estimated that about half a million of them hit each of us humans each hour. But cosmic rays also smash into high-flying nitrogen atoms and turn them into C14 atoms. (It’s a little more complicated, but, again, never mind). These atoms team up with oxygen and form carbon dioxide (CO2).

Plants absorb CO2, and that’s how they come to contain C14. Humans and other animals eat plants, which is how C14 turns up in our bodies. In fact, it’s in our bodies at about the same concentration—one part in a trillion of carbon, I did say “tiny deposits"—as it appears elsewhere.

When plants die, they suddenly stop absorbing C14. When we die, we suddenly stop eating plants, and therefore ingesting C14. So, since C14 is radioactive and decays, the amount of C14 in any organic matter—a neem tree, the mosquito you slapped into oblivion last night, a poor soul who dies in a car crash—begins dropping as soon as it is dead.

With me so far? Well, this drop in level of radioactive isotopes is the very foundation of radiocarbon dating. If we know the speed at which radioactive substances decay, we can use that to determine the age of an artifact that contains such substances.

In the case of C14, we know that a given amount of it will reduce by half in about 5,700 years. This is called C14’s “half-life". So, if we measure the C14 in a sample of long-dead organic matter—a fossil, a bone fragment, a beam from a wooden hut—and find one part C14 in two trillion of carbon, that’s half the concentration we would expect to find in living things. That is, half the C14 in the sample has decayed away. Therefore, the sample is about 5,700 years old: C14’s half-life. If we find one part in four trillion, the sample is about 11,400 years old.

In general, if we have to estimate the age of some archaeological discovery, we only have to compare the concentration of C14 in it to the 1 in a trillion figure and stack that up against the half-life.

In that sense, decaying C14 is the ticking clock I mentioned above. It ticks well for objects up to about 60,000 years old—or 10 C14 half-lives, down to about 1 part in a quadrillion. Older than that, and C14 levels drop too low to measure accurately. We would have to use another radioactive substance, with a longer half-life. Aluminium 26, for example, has a half-life of over 700,000 years, and is used to determine the age of certain kinds of rocks.

Back at ancient Rome: radiocarbon dating tells us those huts date from about 850 BCE, or about 2,850 years ago. Call it half of C14’s half-life. Puzzle for you: what was the concentration of C14 detected in samples from the huts?

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers explores the joy of mathematics, with occasional forays into other sciences.

Comments are welcome at dilip@livemint.com. To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza

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