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Carbon Dating

Explore connections in mathematics and science with this article on carbon dating.
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Carbon Dating

How old are the Egyptian tombs? How long ago did the redwood trees begin growing? These and many similar questions can be answered by carbon dating, a method used by archaeologists and other scientists to discover the age of ancient remains and artifacts. But how does it work?

All living organisms on this planet are composed partially of carbon. A small amount of that carbon is in the form of a radioactive isotope called carbon-14. This isotope is created when solar radiation acts upon nitrogen in the upper atmosphere. The atmospheric carbon-14 is then absorbed by plants on the earth's surface, and any animal that eats the plants in turn absorbs some of that C-14 into its body. What makes carbon-14 useful to scientists is that it begins to break down at a known rate. Since this rate of decay is predictable, scientists can then measure the amount of carbon-14 in the remains of an organism or artifact, plug that value into a generalized equation, and calculate the age of those remains. This process, known as carbon dating, was developed by the American chemist Willard Libby in 1947 at the Institute for Nuclear Studies at Columbia University.

Carbon dating uses an exponential decay function, C(t) = 100 • e -.000121t, to show the percentage of carbon-14 remaining in an object that is t years old. In other words, this function takes in a number of years, t, as its input value and gives back an output value of the percentage of carbon-14 remaining. So, if you were asked to find out carbon's half-life value (the time it takes to decrease to half of its original size), you'd solve for t number of years when C(t) equals 50, because fifty percent represents one half.

Carbon dating does have certain limitations. After about 50,000 - 70,000 years, almost all of the carbon-14 in any remains will have broken down. So, objects older than that do not contain enough of the isotope to be dated. Conversely, the method doesn't work on objects that are too young. This method also cannot apply to the remains of aquatic life, because carbon-14 doesn't enter the ocean at an amount substantial enough for proper analysis. Carbon dating also does not work on fossils; usually they are too old, and they contain very little carbon. In general, other factors, such as changes in solar radiation or the burning of fossil fuels, affect the accuracy of carbon dating procedures, because they cause fluctuations in the relatively constant cycle of carbon-14 in the atmosphere. Scientific calculations, however, adjust for these minor inaccuracies.

Despite its limitations, carbon dating has proven to be an extremely useful way to determine the age of important archaeological discoveries, such as the Dead Sea Scrolls and the Iceman remains. It has also given scientific weight to arguments surrounding controversial objects and their dates of origin.