This is a formula which helps you to date a fossil by its carbon.If a fossil contains 60% of its original carbon, how old is the fossil? That means this is how long it takes for half the nuclei to decay.Using this measurement also corrects for any mass-dependent fractionation within the AMS system.The Fraction Modern corrected for δC of a sample 10 separate times over the course of a run.Although one can simply measure older samples for longer times, there are practical limits to the minimum sample activity that can be measured.At the present time, for a 1 milligram sample of graphite, this limiting age is about ten half-lives, or 60,000 years, if set only by the sample size.The limiting age is then calculated as -8033 * ln(2sigma) and rounded according to conventions outlined above.If you have a fossil, you can tell how old it is by the carbon 14 dating method.

In order to remove the effects of isotopic fractionation, the Fraction Modern is then corrected to the value it would have if its original δC value to which all radiocarbon measurements are normalized.) The fractionation correction is done using the 13/12 ratio measured by the AMS system.In AMS, the filiamentous carbon or "graphite" derived from a sample is compressed into a small cavity in an aluminum "target" which acts as a cathode in the ion source.The surface of the graphite is sputtered with heated, ionized cesium and the ions produced are extracted and accelerated in the AMS system.After 5600 years, if we start with a gram, we end up with half a gram.This rather complex formula shows you how to solve this puzzle using accepted scientific methods.Due to variability in sample homogeneity, sample collection, and sample processing, the variability of replicate samples (reproducibility) is generally greater than the reported error for a single sample.

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