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Half life and radiocarbon dating

One of the most famous cases of carbon-14 dating involves the Shroud of Turin, a long piece of fabric purported to be the burial shroud of Jesus (see Figure 22.28).This relic was first displayed in Turin in 1354 and was denounced as a fraud at that time by a French bishop.(a) The decay constant shows that 0.0568 percent of the nuclei in a carbon-11 sample will decay each second.Another way of considering the decay constant is that a given carbon-11 nuclei has a 0.0568 percent probability of decaying each second.Half of what remains decays in the next half-life, and half of that in the next, and so on.This is exponential decay, as seen in the graph of the number of nuclei present as a function of time. Radioactive carbon has the same chemistry as stable carbon, and so it mixes into the biosphere, 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, so if you know the number of carbon nuclei in an object (perhaps determined by mass and Avogadro’s number), you can multiply that number by in an artifact, such as mummy wrappings, with the normal abundance in living tissue, it is possible to determine the artifact’s age (or time since death).Carbon-14 dating can be used for biological tissues as old as 50 or 60 thousand years, but is most accurate for younger samples, since the abundance of nuclei in them is greater.

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The time in which half of the original number of nuclei decay is defined as the .The values obtained at the three independent laboratories gave a weighted average date of 1320 ± 60.That uncertainty is typical of carbon-14 dating and is due to the small amount of 14 C in living tissues, the amount of material available, and experimental uncertainties (reduced by having three independent measurements).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.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.It has not been determined how the image was placed on the material.(credit: Butko, Wikimedia Commons) Carbon-11 has a half-life of 20.334 min. If 1 kg of carbon-11 sample exists at the beginning of an hour, (b) how much material will remain at the end of the hour and (c) what will be the decay activity at that time?That said, is it notable that the carbon-14 date is consistent with the first record of the shroud’s existence and certainly inconsistent with the period in which Jesus lived.There are other noncarbon forms of radioactive dating.Its remarkable negative imprint of an apparently crucified body resembles the then-accepted image of Jesus.As a result, the relic has been remained controversial throughout the centuries.


  1. Dec 8, 2016. Theoretically, if one could detect the amount of carbon-14 in an object, one could establish that object's age using the half-life, or rate of decay.

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