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The half-life of an isotope like C14 is the time it takes for half of it to decay away: in C14, every 5,730 years, half of it is gone.
So, if you measure the amount of C14 in a dead organism, you can figure out how long ago it stopped exchanging carbon with its atmosphere.
What you need is a ruler, a reliable map to the reservoir: in other words, an organic set of objects that you can securely pin a date on, measure its C14 content and thus establish the baseline reservoir in a given year.
Fortunately, we do have an organic object that tracks carbon in the atmosphere on a yearly basis: tree rings.
But before that, only fragmentary data is available, making it very difficult to definitively date anything older than 13,000 years.Radiocarbon dating was invented in the 1950s by the American chemist Willard F.Libby and a few of his students at the University of Chicago: in 1960, he won a Nobel Prize in Chemistry for the invention.Given relatively pristine circumstances, a radiocarbon lab can measure the amount of radiocarbon accurately in a dead organism for as long as 50,000 years ago; after that, there's not enough C14 left to measure. Carbon in the atmosphere fluctuates with the strength of earth's magnetic field and solar activity.
You have to know what the atmospheric carbon level (the radiocarbon 'reservoir') was like at the time of an organism's death, in order to be able to calculate how much time has passed since the organism died.Since that time, CALIB, now renamed Int Cal, has been refined several times--as of this writing (January 2017), the program is now called Int Cal13.