Carbon-14 dating has proven valuable to many sciences, especially to archaeology and geology. Although this radiocarbon dating thing seems complex and it requires a well-equipped modern laboratory, both the science behind the technique and the mathematics involved are fairly simple.
A Scary-Looking Chemistry Picture
To begin, carbon is among the most common elements and, more important, carbon is found in every living thing. What makes radiocarbon dating possible is that there is more than one "kind" of carbon, kinds called called isotopes. Ordinary carbon has six protons and six neutrons inside each nucleus, giving it an atomic weight of 12. This most common isotope of carbon is carbon-12 (12C). Around one of every one hundred carbon atoms is a different isotope: it has an extra neutron, making it carbon-13. These two isotopes are both stable, so they will always be carbon.
A tiny percentage of carbon, about one of every trillion atoms, begins as nitrogen. It stays a nitrogen atom, isotope nitrogen-14, until it's smacked by a passing cosmic ray, which turns one of its protons into a neutron. This very rare carbon isotope, carbon-14 (14C), is not stable: over time, every atom spontaneously turns back into nitrogen. Cosmic-ray bombardment of the gases high in the atmosphere constantly creates these unstable atoms, but 14C decays slowly. It takes 5,730 years for half a sample of 14C to turn back to nitrogen; a time span scientists call its half-life.
Why Carbon-14 Dating Works
The ratio of unstable carbon-14 to all carbon is small, but it is assumed constant, and scientists also believe that the ratio of 14C to all carbon is the same world-wide. No matter where you go, if you select an atom at random from the atmosphere, the probability that it is 14C remains the same.
Whether an isotope is stable or not makes no difference to chemical reactions, so the percentage of 14C remains the same even when the atom gets plugged into CO2 or complex molecules like proteins or sugar. Every living organism constantly eats or breathes in carbon atoms from its environment, and uses them to build its body.
As long as an organism is alive, carbon from its body is swapped for fresh atoms from the air and from food. Since this exchange is constantly in progress, the ratio of 14C to all carbon in a living organism remains the same as that ratio in the atmosphere. When an organism dies, however, the exchange stops and all carbon in its body becomes locked in place. The body decays, and the 14C atoms it contains decay as well; except that they very slowly decay into nitrogen.
An Important Curve
How Carbon-14 Dating Works
Radioactive decay like this follows an interesting pattern. After 5,730 years, half of the original carbon-14 has turned back to nitrogen. If the rate of decay were constant, all 14C atoms would have decayed after 11,460 years; but the decay process follows an exponential curve instead of a straight line. So, in the second 5,730 years (11,460 years total) half of the remaining 14C has decayed, leaving one-fourth of the original amount. After another 5,730 years (17,190 years), one-eighth is still around.
Now, we have three useful facts. First, about one of every trillion carbon atoms is 14C; and second, the half-life of 14C is 5,730 years. The third fact is that when an organism dies, it stops maintaining the same isotope ratio as the atmosphere. These facts suggest that if you could sort all carbon from dead organic matter into little piles of atoms depending on the isotope, you could determine the ratio of the isotopes present. If you know the ratio, then--with some help from a calculator, a math whiz, or a simple graph--you can calculate when that sample stopped living!
The Laboratory Setting
The Nuts and Bolts
Naturally, you can't separate billions of atoms into little piles and count them, but there are other ways to separate the carbon isotopes in a sample. Laboratories like the Arizona Geochronology Center prepare tiny, pure samples and process them in an accelerator mass spectrometer; a room-sized collection of computers, powerful magnets, and assorted electronics. The slight differences in mass between the different isotopes allows the accelerometer to separate them from each other. The accelerometer contains a target for each isotope, which counts the atoms that strike it. The resulting counts are used to determine the percentage of carbon that is 14C.
Once you have determined the ratio, you can plug the number into a formula or use a graph to estimate when whatever captured the carbon in your sample died. Using modern equipment, the maximum age that can be calculated with 14C dating is around 58,000 to 62,000 years. The lower limit is much younger: within the past two decades, both the Shroud of Turin and the Dead Sea Scrolls have been dated with this process.
How Results are Used
The technology of carbon-14 dating is just decades old, but in that short time this tool has proven highly important to several scientific disciplines. Among sciences that have been enriched by 14C dating are geology, archaeology, soil science, and anthropology.