Carbon 14 is used to determine the age of organic material. The procedure is based on the formation of 14C by neutron capture in the upper atmosphere ""_(7)N^(14) + _(0)n^(1)rarr ""_(6)C^(14)+ ""_(1)H^(1) ""^(14)C is absorbed by living organism during photosynthesis. The ""^(14)C content is constant in living organism once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of ""^(14)C in the dead being falls due to the decay which C^(14) undergoes. ""_(6)C^(14)rarr ""_(7)N^(14) + _(-1)e^(0) The half life period of ""^(14)C is 5770 years. The decay constant (lambda) can be calculated by using the following formulalambda = (0.693)/t_(1/2)The comparison of the beta –activity of the dead matter with that of carbon still in circulation enables measurement of the period of the isolation of the material from the living cycle. The method however, ceases to be accurate over periods longer than 30,000 years. The proportion of ""^(14)C to ""^(12)C in living matter is 1 : 10^(12 ) A nuclear explosion has taken place leading to increase in concentration of C^(14) in nearby areas. C^(14) concentration is C_(1) in nearby areas and C_(2) in areas far away. If the age of the fossil is determined to be t_(1) and t_(2) at the places respectively, then