List four types of radiometric dating
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.
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.You find a bone fragment and through analysis you determine that it contains 13% of its original carbon-14.The half-life of carbon-14 is approximately 5,730 years. Start with the equation for continuous growth and decay: Thus the bone is approximately 17,000 years old.
This is consistent with the assumption that each decay event is independent and its chance does not vary over time.
where is the half-life of the element, is the time expired since the sample contained the initial number atoms of the nuclide, and is the remaining amount of the nuclide.