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? Why do we use the carbon dating to calculate the age of the fossil?A. Rate of exchange of carbon beween atmosphere and living is slower than decay of `C""^(14)`B. It is not appropriate to use `C""^(14)` dating to determine imageC. Rate of exchange of `C""^(14)` between atmosphere and living organism is so fast that an equilibrium is set up between the intake of `C""^(14)` by organisms and its exponential decayD. None of these