Carbon dating accuracy range
In principle, any material of plant or animal origin, including textiles, wood, bones and leather, can be dated by its content of carbon 14, a radioactive form of carbon in the environment that is incorporated by all living things.
Because it is radioactive, carbon 14 steadily decays into other substances.
The decay of Carbon $ into stable Nitrogen $ does not take place in a regular, determined fashion: rather it is governed by the laws of probability and statistics formalized in the language of quantum mechanics.
As such, the reported half life of 30 \pm 40$ years means that $ years is the standard deviation for the process and so we expect that roughly $ percent of the time half of the Carbon $ in a given sample will decay within the time span of 30 \pm 40$ years.
Carbon 14 is thought to be mainly a product of bombardment of the atmosphere by cosmic rays, so cosmic ray intensity would affect the amount of carbon 14 in the environment at any given time.
#30,000-Year Limit The Lamont-Doherty group says uranium-thorium dating not only is more precise than carbon dating in some cases, but also can be used to date much older objects.
This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon $ to Carbon $.
The focus here is on the statistical nature of such dating.
The samples represented animals that lived at various times during the last 30,000 years. Alan Zindler, a professor of geology at Columbia University who is a member of the Lamont-Doherty research group, said age estimates using the carbon dating and uranium-thorium dating differed only slightly for the period from 9,000 years ago to the present.
Since 1947, scientists have reckoned the ages of many old objects by measuring the amounts of radioactive carbon they contain.
New research shows, however, that some estimates based on carbon may have erred by thousands of years.
They arrived at this conclusion by comparing age estimates obtained using two different methods - analysis of radioactive carbon in a sample and determination of the ratio of uranium to thorium in the sample.
In some cases, the latter ratio appears to be a much more accurate gauge of age than the customary method of carbon dating, the scientists said.
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This explains why the Wikipedia article on Carbon $14$ lists the half-life of Carbon 14 as $5730 \pm 40$ years.