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Math behind carbon dating

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In his article Light Attenuation and Exponential Laws in the last issue of Plus, Ian Garbett discussed the phenomenon of light attenuation, one of the many physical phenomena in which the exponential function crops up. In this second article he describes the phenomenon of radioactive decay, which also obeys an exponential law, and explains how this information allows us to carbon-date artefacts such as the Dead Sea Scrolls. In the previous article, we saw that light attenuation obeys an exponential law. To show this, we needed to make one critical assumption: that for a thin enough slice of matter, the proportion of light getting through the slice was proportional to the thickness of the slice. Exactly the same treatment can be applied to radioactive decay. However, now the "thin slice" is an interval of time, and the dependent variable is the number of radioactive atoms present, N t.
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BioMath: Carbon Dating

Radiocarbon dating is a method that provides objective age estimates for carbon-based materials that originated from living organisms. The impact of the radiocarbon dating technique on modern man has made it one of the most significant discoveries of the 20th century. Archaeology and other human sciences use radiocarbon dating to prove or disprove theories. Over the years, carbon 14 dating has also found applications in geology, hydrology, geophysics, atmospheric science, oceanography, paleoclimatology and even biomedicine. Radiocarbon, or carbon 14, is an isotope of the element carbon that is unstable and weakly radioactive.
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Carbon 14 Dating of Organic Material

Radiocarbon dating also referred to as carbon dating or carbon dating is a method for determining the age of an object containing organic material by using the properties of radiocarbon , a radioactive isotope of carbon. The method was developed in the late s at the University of Chicago by Willard Libby , who received the Nobel Prize in Chemistry for his work in It is based on the fact that radiocarbon 14 C is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.
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Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material. The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles. Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon. At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.
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