Radioactive dating is a technique which allows for accurate determination of the age of materials. The most common type of radioactive dating is called radiocarbon dating, which can be used to find the age of organic materials. A long-lived isotope of carbon, 14 C, is similar chemically to the stable isotope of carbon, 12 C. Living organisms exchange carbon with their environments constantly, so they accumulate 14 C. The amount contained in an organism quickly reaches the same abundance that is found on the earth, about one atom of 14 C for every 7 x 1011 atoms of 12 C. When the organisms die, they stop accumulating 14 C, and the abundance of 14 C decreases due to radioactive decay. By measuring the radioactivity of the sample, the abundance of 14 C relative to the amount of 12 C can be found, thus determining how long the organism has been dead.
14 C is produced in the upper atmosphere from nuclear reactions caused by cosmic rays. It combines with oxygen atoms, just as 12 C atoms do, to form carbon dioxide. Eventually, 14 C beta decays to a 14 N atom, a beta particle (electron), and an electron antineutrino. The decay rate for this process in a living organism is about 15 decays per minute per gram of carbon. This process has a half-life of approximately 5,730 years. After this amount of time, the amount of 14 C and the radioactivity of a given sample is reduced by half.
To determine the age of a sample, the amount of carbon in the sample is found through chemical analysis. The number of decays expected if the sample was a living organism is calculated by multiplying the decay rate by the mass of the carbon sample. Next, the actual number of decays is measured using a Geiger counter. After N half-lives, the decay rate decreases by a factor of (1/2)N . This is the same of the ratio of the number of decays measured to the number of decays for a living organism. In this way, the number N of half-lives that have elapsed can be found, determining the age of the sample.
One of the most familiar applications of radioactive dating is determining the age of fossilized remains, such as dinosaur bones. Radioactive dating is also used to authenticate the age of rare archaeological artifacts. Because items such as paper documents and cotton garments are produced from plants, they can be dated using radiocarbon dating. Without radioactive dating, a clever forgery might be indistinguishable from a real artifact. There are some limitations, however, to the use of this technique. Samples that were heated or irradiated at some time may yield by radioactive dating an age less than the true age of the object. Because of this limitation, other dating techniques are often used along with radioactive dating to ensure accuracy.
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