# Carbon dating calculation

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This correction is performed as follows: $$Fm_ = Fm_ ( Fm_ - Fm_b)\frac$$ Where $$M$$ is sample mass, and $$M_b$$ and $$Fm_b$$ are the mass and Fm of the blank.Fraction Modern is a measurement of the deviation of the C is also affected by natural isotopic fractionation.Fractionation is the term used to describe the differential uptake of one isotope with respect to another.While the three carbon isotopes are chemically indistinguishable, lighter C, reflecting the difference in mass.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.Thus, ages are limited by the age of the process blanks (more on that below) and by the statistical uncertainty of the C ratios of the blank, the sample and the modern reference, respectively.For small samples, blank contribution as a fraction of sample mass becomes a more important term, so a mass balance blank correction is applied.

It is expected then, for a 5,570 year (1 half-life) or 11,140 year old (2 half-lives) sample that 125 or 63 counts per second would be obtained.

Ages are calculated using 5568 years as the half-life of radiocarbon and are reported without reservoir corrections or calibration to calendar years.

For freeware programs, we suggest that you look at the following web site for a list of programs that will calibrate radiocarbon results to calendar years (including making reservoir corrections).[ Radiocarbon-Related Information Sources] The error in the age is given by 8033 times the relative error in the Fm .

The limiting age is then calculated as -8033 * ln(2sigma) and rounded according to conventions outlined above.

It has been determined that the rate of radioactive decay is first order.