Accuracy range of carbon dating
Radiocarbon, or Carbon-14, dating is probably one of the most widely used and best known absolute dating methods. Radiocarbon dating relies on a simple natural phenomenon.
This allowed for the establishment of world-wide chronologies.
As the Earth's upper atmosphere is bombarded by cosmic radiation, atmospheric nitrogen is broken down into an unstable isotope of carbon - carbon 14 (C-14).
The unstable isotope is brought to Earth by atmospheric activity, such as storms, and becomes fixed in the biosphere.
It's development revolutionized archaeology by providing a means of dating deposits independent of artifacts and local stratigraphic sequences.
Libby in 1949, and has become an indispensable part of the archaeologist's tool kit since.
Much of the information presented in this section is based upon the Stuiver and Polach (1977) paper "Discussion: Reporting of C14 data". 1890 wood was chosen as the radiocarbon standard because it was growing prior to the fossil fuel effects of the industrial revolution.
A copy of this paper may be found in the Radiocarbon Home Page The radiocarbon age of a sample is obtained by measurement of the residual radioactivity. T (National Institute of Standards and Technology; Gaithersburg, Maryland, USA) Oxalic Acid I (C). The activity of 1890 wood is corrected for radioactive decay to 1950.
This explains why the Wikipedia article on Carbon $ lists the half-life of Carbon 14 as 30 \pm 40$ years.
Other resources report this half-life as the absolute amounts of 30$ years, or sometimes simply 00$ years.
Because it reacts identically to C-12 and C-13, C-14 becomes attached to complex organic molecules through photosynthesis in plants and becomes part of their molecular makeup.