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The time that it takes for half of a sample to decay is known as the half life of the isotope.Some isotopes have half lives longer than the present age of the universe, but they are still subject to the same laws of quantum physics and will eventually decay, even if doing so at a time when all remaining atoms in the universe are separated by astronomical distances.Various elements are used for dating different time periods; ones with relatively short half-lives like carbon-14 (or C) are useful for dating once-living objects (since they include atmospheric carbon from when they were alive) from about ten to fifty thousand years old. Longer-lived isotopes provide dating information for much older times.The key is to measure an isotope that has had time to decay a measurable amount, but not so much as to only leave a trace remaining.Within the nucleus, we find neutrons and protons; but for now, let's just focus on the neutrons.These neutrons can become unstable, and when they do, they release energy and undergo decay. Radioactivity occurs when the nucleus contains an excess amount of neutrons. The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists.

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A new, more stable isotope, called the decay or daughter product, takes its place.There's a small amount of radioactive carbon-14 in all living organisms.When they die no new carbon-14 is taken in by the dead organism.The meaning of this equation is that the rate of change of the number of nuclei over time is proportional only to the number of nuclei.This is consistent with the assumption that each decay event is independent and its chance does not vary over time.Radioactive dating uses the ratios of isotopes and their specific decay products to determine the ages of rocks, fossils and other substances.