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    Radioactive dating sample problems

    The units of measure for time are dependent upon the unit of measure for the rate constant.The ratio of "N/N Carbon-14 is a radioisotope formed in our atmosphere by the bombardment of nitrogen-14 by cosmic rays.The Mayan calendar used 3114 BC as their reference.More recently is the radiocarbon date of 1950 AD or before present, BP.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.In a stratigraphical context objects closer to the surface are more recent in time relative to items deeper in the ground.Although relative dating can work well in certain areas, several problems arise.

    The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope.

    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.

    , where r is a measurement of the rate of decay, k is the first order rate constant for the isotope, and N is the amount of radioisotope at the moment when the rate is measured.

    The rate of decay is often referred to as the activity of the isotope and is often measured in Curies (Ci), one curie = 3.700 x 10" is the initial amount of radioisotope at the beginning of the period, and "k" is the rate constant for the radioisotope being studied.

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