Several short-lived radioactive species have been used to determine the age of wood or animal fossils. One of the most intresting substance is `""_(6)C""^(14)`(half-life fossils, etc.). Carbon-14 is produced by the bombardment of nitrogen atoms present in the upper atmosphere with neutrons (from cosmic rays). `""_(7)N""^(14)+""_(0)n""^(1)to""_(6)C""^(14)+""_(1)H""_(1)` Thus carbon-14 is oxidised, to `CO""_(2)` and eventually lingested by land animals. The death of plants or animals put an end to the intake of `C""_(14)` from the atmosphere. After this the amount of `C""_(14)` in the dead tissues starts decreasing due to its disintegration as per the following reaction : `""_(6)C""^(14)to""_(7)N""^(14)+""_(-1)beta""^(0)` The `C""^(14)` isotope enters the biosphjere when carbon dioxide is taken up in plant photosynthesis. Plants are eaten by animals, which exhale `C""^(14)` as `CO""_(2)`. Eventually, `C""^(14)` participates in many aspects of carbon cycle. The `C""^(14)` lost by radioactive decay-replenishment process, a dynamic rquillibrium is established whereby the ratio of `C""^(14)` to `C""^(12)` remains constant in living matter. But when an individual plant or an animal dies, the `C""^(14)` isotpe inn it is no longer replenished, so the ratio decreases as `C""^(14)` decays. So, ther number `C""^(14)` nuclei after time t (after the death of living matter) would be less than in a livingthe following formula, `t""_(1//2)=0.693`/? The intensity of the cosmic rays have remain the same for 30,000 years. But since some years changes in this are observed due to excessive burning of fossil fuel and nuclear test? A nuclear explosion has taken place leading to increase in concentration of `C""^(14)` in nearby areas. `C""^(14)` concentration is `C""_(1)` in nearly 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 respective places thenA. The age of the fossil will inrease at the where explosion has taken place and `T""_(1)-T""_(2)=1/lamda"in"C""_(1)/(C""_(2))`B. The age of the fossil will decrease at the place where explosion has taken place and `T""_(1)-T""_(2)=1/lamda"in"C""_(1)/(C""_(2))`C. The age of the fossil will determined to be sameD. `T""_(1)/T""_(2)=C""_(1)/C""_(2)`