The equation for the radioactive decay of 14 C is: During its life, a plant or animal is exchanging carbon with its surroundings, so the carbon it contains will have the same proportion of 14 C as the atmosphere. Once it dies, it ceases to acquire 14 Cbut the 14 C within its biological material at that time will continue to decay, and so the ratio of 14 C to 12 C in its remains will gradually decrease. The equation governing the decay of a radioactive isotope is: Measurement of Nthe number of 14 C atoms currently in the sample, allows the calculation of tthe age of the sample, using the equation above.
The above calculations make several assumptions, such as that the level of 14 C in bearshare dating download atmosphere has remained constant over time. The calculations involve several steps and include an intermediate value called the ""radiocarbon age"", which is the age in ""radiocarbon years"" of the sample: Calculating radiocarbon ages also requires the value of the half-life for 14 Cwhich for more than a decade after Libby's initial work was thought to be 5, years.
For consistency with these early papers, and to avoid the risk of a double correction for the incorrect half-life, radiocarbon ages are still calculated using the incorrect half-life value. A correction for the half-life is incorporated into calibration curves, so even though radiocarbon ages are calculated using a half-life value that is known to be incorrect, the final reported calibrated date, in calendar years, is accurate. When a date is quoted, the reader should be aware that if it is an uncalibrated date a term used for dates given in radiocarbon years it may differ substantially from the best estimate of the actual calendar date, both because it uses the wrong value for the half-life of 14 Cand because no correction calibration has been applied for the historical variation of 14 C in the atmosphere over time.
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