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.