Since carbon is fundamental to life, occurring along with hydrogen in all organic compounds, the detection of such an isotope might form the basis for a method to establish the age of ancient materials.
Libby, a Professor of Chemistry at the University of Chicago, predicted that a radioactive isotope of carbon, known as carbon-14, would be found to occur in nature.
The ensuing atomic interactions create a steady supply of c14 that rapidly diffuses throughout the atmosphere.
Plants take up c14 along with other carbon isotopes during photosynthesis in the proportions that occur in the atmosphere; animals acquire c14 by eating the plants (or other animals).
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.
This discovery meant that there are three naturally occurring isotopes of carbon: Whereas carbon-12 and carbon-13 are stable isotopes, carbon-14 is unstable or radioactive.
Carbon-14 is produced in the upper atmosphere when cosmic rays bombard nitrogen atoms.
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.It is naturally unstable and so it will spontaneously decay back into N-14 after a period of time.It takes about 5,730 years for half of a sample of radiocarbon to decay back into nitrogen.C-14 is produced in the upper atmosphere when nitrogen-14 (N-14) is altered through the effects of cosmic radiation bombardment (a proton is displaced by a neutron effectively changing the nitrogen atom into a carbon isotope).The new isotope is called "radiocarbon" because it is radioactive, though it is not dangerous.