Radiometric Dating with Carbon 14

Carbon is one of the most common elements on Earth, and is one of the building blocks of every living thing. There is, however, more than one kind of carbon. An ordinary carbon atom has six protons and six neutrons inside its nucleus, for an atomic weight of 12. About one of every hundred carbon atoms has a seventh neutron, giving it an atomic weight of 13. These different carbon atoms are both stable isotopes, and they will always be carbon atoms.

A tiny percentage of carbon atoms-about one in a trillion-starts out as a nitrogen atom, until one of its protons is turned into a neutron by a collision with a cosmic ray. Atoms of this rare isotope of carbon, carbon-14, are unstable: they spontaneously turn back into nitrogen atoms over time. Cosmic-ray bombardment of the gases high in the atmosphere is constantly creating these unstable atoms, but carbon-14 decays rather slowly. It takes 5,730 years for half a sample of carbon-14 to change back into nitrogen; a time span scientists call the isotope’s half-life.

The ratio of unstable carbon-14 to all carbon atoms is small, but it is also constant. Scientists believe that the ratio of carbon-14 to all carbon atoms in the atmosphere is the same all over the world. No matter where you are, if you were to select a carbon atom at random from the atmosphere, the probability that it is a carbon-14 atom is identical.

Whether an isotope is stable or unstable makes no difference to a chemical reaction, so the percentage of carbon-14 atoms remains a constant even when the atoms become plugged into carbon dioxide or more complex molecules, such as sugar or protein. Every living organism constantly ingests carbon atoms from its environment and uses some of them to build its body.

As long as an organism lives, carbon atoms in its body are being swapped for fresh carbon atoms from the air and in plant and animal food. Since this exchange is constantly in progress, the ratio of carbon-14 atoms to all carbon atoms in a living organism’s body stays the same as the ratio in the atmosphere. When an organism dies, however, the exchange stops and all carbon atoms in its body become locked in place. Not only does the body decay, but the carbon-14 atoms decay as well – except that the carbon-14 atoms decay to nitrogen, and very slowly at that.

This process of radioactive decay follows an interesting pattern. After 5,730 years, half of the carbon atoms have turned back to nitrogen. If the rate of decay stayed constant, all of the carbon-14 would be gone after 11,460 years; but the decay of carbon-14 follows an exponential course instead of a straight line. After a second 5,730 years  (11,460 years total) half of the remaining carbon-14 has decayed, so one-fourth of the original amount is still present. After another 5,730 years (17,190 years), one-eighth remains.

Now you have three known facts. First, one of every trillion or so carbon atoms in the air is carbon-14; and second, the half-life of those unstable carbon-14 atoms is 5,730 years. The third fact is that when an organism dies, it no longer maintains the same ratio of carbon isotopes as the atmosphere. These three facts suggest that if you could separate every carbon atom from dead organic matter into little piles depending on the isotope, you could calculate the ratio of carbon atoms in your sample. If you know the carbon ratio, then-with some help from a calculator or a math whiz-you could calculate when that sample stopped living!

Of course, you can’t separate trillions of carbon atoms into little piles and weigh them, but there are other ways to measure the amount of carbon-14 in a sample. Laboratories like the Arizona Geochronology Center  prepare tiny samples of pure carbon, which are then placed in an accelerator mass spectrometer; a room-sized collection of electronics, powerful magnets, and computers. Different isotopes of carbon separate inside the accelerometer because of their slightly different masses. The accelerometer contains targets for each isotope that count the atoms that strike them; and the resulting counts are used to determine the ratio of carbon-14 to all carbon atoms.

Once you have a carbon-14 ratio, you can plug that number into a formula and get an estimate of when the organism that captured the carbon in your sample died. Using modern equipment, the upper limit of the age that can be calculated with carbon-14 dating is around 58,000 to 62,000 years. The lower limit is considerably younger: within the past twenty years, the Shroud of Turin and the Dead Sea Scrolls both have been assigned ages based on carbon-14 dating.

Geochronologists, scientists who use carbon-14 and other radiometric dating techniques, don’t give precise ages. Instead, they provide an estimate of the age and a range within it is most likely to lie. This uncertainty comes from many sources, including uncertainty in measurement of the carbon ratio. More uncertainty is introduced by the fact that scientists cannot state with certainty that the percentage of carbon-14 in all carbon is the same as it was 100 years ago, even less so 10,000 years ago. Though the principle of carbon-14 dating seems fairly simple, assuming you have a big lab with an accelerometer, in fact geochronologists must make many calculations and corrections during their processing, and must take extreme care not to contaminate their tiny samples with younger carbon while processing.

The technology of carbon-14 dating is only a few decades old, but in that short time the method has had profound impacts on a variety of sciences. Among the disciplines that have been enriched by carbon-14 dating are geology, archaeology, soil science, and anthropology.

For more information:

Arizona Geochronology Center: Basic Principles of Radiocarbon Dating
Center for Non-Destructive Testing: Carbon-14 Dating