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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.Therefore, the number of radioactive nuclei decreases from to in one half-life, then to in the next, and to in the next, and so on. Thus, if is reasonably large, half of the original nuclei decay in a time of one half-life.If an individual nucleus makes it through that time, it still has a 50% chance of surviving through another half-life.By comparing the abundance of 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. There are instances in which the date of an artifact can be determined by other means, such as historical knowledge or tree-ring counting.
This is an exponential decay, as seen in the graph of the number of nuclei present as a function of time.
Even if it happens to make it through hundreds of half-lives, it still has a 50% chance of surviving through one more.
The probability of decay is the same no matter when you start counting. The chance of heads is 50%, no matter what has happened before.
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.