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Radiocarbon dating

Deflection

The process of dating an ancient object by measuring the proportion of 6C12 to its radioisotope 6C14 . in a specimen is known as carbon dating.

            The atmosphere contains carbon 6C12 and its radioisotope 6C14. Neutron by cosmic rays reacts with nitrogen in the air to form  6C14 as below:

                            7N14   + 0n1----------------------------------   6C14 + 1H1

  The ratio of 6C14 to  6C12 in the atmosphere is about 10-12. Both  6C12 and   6C14     combine with oxygen to from carbon dioxide that is absorbed by the living plants during photosynthesis process. But  6C14  is a beta emitter and decays back into nitrogen as 

             6C14 ---------------------------------     7N14   + -1e0

Hence, the amount of   6C14 goes on decaying. As the living plant performs photosynthesis, the deacy of      6C14    is compensated by a new supply of it from atmospheric air and a radioactive equilibrium is reached where there is a fixed ratio of 6C14 to 6C12

          When the plant dies, no more 6C14is taken in and that inside the plant begins to decay at a known rate without any replacements.   6C14  has half life of 5730 years. By determining the carbon content of a sample and measuring its activity, we can determine when the organism died or the life of that object.

         Suppose the activity of some dead material was R0 at the time of death and it has been reduced to R after t years. Then, according to law of radioactive decay, we have

                        

                     Butwhere T= 5730 years, the half-life of the radioactive carbon. SO, 

                   

Hence by measuring the activity R0 of the living plant and activity R of its dead material, the age t of that object can be determined.