Carbon forms the foundation for the life on Earth, starting from the microbes that appeared 3.7 billion years ago to humans that appeared around 2 million years ago. C-12 is constantly stored within the bodies of every biotic component of the biosphere through several life processes. Along with C-12, a radioactive isotope of carbon C-14 is found in every living organism in a ratio of one C-14 atom for every trillion C-12 atoms. Did you know, that even this trace amount of C-14 can help determining the archeological age of a fossil? Let us find out how.
C-14 is naturally produced in the atmosphere by the interaction of cosmic rays and atmospheric Nitrogen as shown in the reaction 1 above. C-14 radioisotope spontaneously decays using Beta decay pathway as shown in equation 2, and has a half life of 5730 years.
The ratio of abundance of C-12 to C-14 is given by :
For all living beings, this ratio between the isotopes remains constant as the carbon within their bodies are constantly getting replenished because of life processes. However, after an organism dies the carbon accumulation stops and the C-14 count keeps reducing as time elapses.
By Radioactive Decay Law we can say,
Where is number of active nuclei of C-14 in a sample, is the amount of active nuclei when it was living and is the decay constant.
Half life of C-14 is
We can determine the decay constant using the half life equation,
Rearranging the decay law and using the value of the decay constant we can write
can be estimated by the natural ratio of C-14 in atmosphere and sample size.
Hence, we can determine the age t of a sample. Ideally, radiocarbon dating is accurate with fossils with an age of 40,000 years or above.