The relative width of the red calibration curve indicates the range of uncertainty: In October 2012, a team led by Christopher Ramsey of Oxford University published a new study, based on analyses of varves (alternating light/dark bands in sediments) from Lake Suigetsu, which is located about 350 kilometers west of Tokyo, near the coast of the Sea of Japan.
These researchers collected core samples 70 meters deep, and then painstakingly counted the layers, year by year, to obtain a direct record stretching back 52,000 years.
Since it is chemically indistinguishable from the stable isotopes of carbon (carbon-12 and carbon-13), radiocarbon is taken by plants during photosynthesis and then ingested by animals regularly throughout their lifetimes.
When a plant or animal organism dies, however, the exchange of radiocarbon from the atmosphere and the biosphere stops, and the amount of radiocarbon gradually decreases, with a half-life of approximately 5730 years.
I don't know the chemistry behind it, but as I understand it we know that simply because, based on the rate of decay of the Carbon-14 isotope.
Radiocarbon dating is based on the decay of carbon-14 into carbon-12, the stable isotope.
For instance, even in the 1950s, when Willard Libby first developed the process, it was recognized that the scheme assumes that the level of carbon-14 in the atmosphere is constant.
But researchers have known at least since 1969 that the carbon-14 level has not been constant, so that the radiocarbon clock needs to be "calibrated." As a result, various schemes are used to correct and calibrate radiocarbon dates, including: In each case, radiocarbon dates, determined by well-established procedures and calculations, are compared directly with dates determined by the above methods, thus permitting the radiocarbon dates to be accurately calibrated with distinct and independent dating techniques.
I get that radiocarbon dating can account for discrepancies in the atmospheric concentration of carbon-14/carbon-12 through the Carbon curve wherein other dating methods were able to verify the accuracy of carbon dating.
Carbon-14 decays at a rate known as its half-life; by calculating the ratio of C-14 to C-12 in a sample and using the half-life formula you can figure out how old it is.