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Symbolically, the process of radioactive decay can be expressed by the following differential equation, where N is the quantity of decaying nuclei and k is a positive number called the exponential decay constant.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.Through analysis, a bone fragment is determined to contain 13% of its original carbon-14.The half-life of carbon-14 is approximately 5,730 years. Since the quantity represents 13% (or 13/100ths) of , it follows that This is based on the decay of rubidium isotopes to strontium isotopes, and can be used to date rocks or to relate organisms to the rocks on which they formed.Although the time at which any individual atom will decay cannot be forecast, the time in which any given percentage of a sample will decay can be calculated to varying degrees of accuracy.The time that it takes for half of a sample to decay is known as the half life of the isotope.Due to the long half-life of uranium it is not suitable for short time periods, such as most archaeological purposes, but it can date the oldest rocks on earth.A proper radiometric date should read years before present (with 1950 being present) ± range/2 at x standard deviations (Xσ)', but is often reported as a single year or a year range, like 1260–1390 CE (the date for the Shroud of Turin).
are very much older than the approximately 6,000 to 10,000 years reckoned by young earth creationists.
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.
Given isotopes are useful for dating over a range from a fraction of their half life to about four or five times their half life.