# Dating calculation

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The following equation gives the quantitative relationship between the original number of nuclei present at time zero () and the number () at a later time : To see how the number of nuclei declines to half its original value in one half-life, let in the exponential in the equation . For integral numbers of half-lives, you can just divide the original number by 2 over and over again, rather than using the exponential relationship.For example, if ten half-lives have passed, we divide by 2 ten times. For an arbitrary time, not just a multiple of the half-life, the exponential relationship must be used. Carbon-14 has a half-life of 5730 years and is produced in a nuclear reaction induced when solar neutrinos strike in the atmosphere.Samples were tested at three independent laboratories, each being given four pieces of cloth, with only one unidentified piece from the shroud, to avoid prejudice.All three laboratories found samples of the shroud contain 92% of the found in living tissues, allowing the shroud to be dated (see [link]).It has not been determined how the image was placed on the material.(credit: Butko, Wikimedia Commons) Calculate the age of the Shroud of Turin given that the amount of found in it is 92% of that in living tissue.Its remarkable negative imprint of an apparently crucified body resembles the then-accepted image of Jesus, and so the shroud was never disregarded completely and remained controversial over the centuries.Carbon-14 dating was not performed on the shroud until 1988, when the process had been refined to the point where only a small amount of material needed to be destroyed. In one half-life , the number decreases to half of its original value.Thus, if you know the number of carbon nuclei in an object (perhaps determined by mass and Avogadro’s number), you multiply that number by to find the number of nuclei in the object.When an organism dies, carbon exchange with the environment ceases, and is not replenished as it decays.Radioactive carbon has the same chemistry as stable carbon, and so it mixes into the ecosphere, where it is consumed and becomes part of every living organism.Carbon-14 has an abundance of 1.3 parts per trillion of normal carbon.