IIT JEE Advanced 2006 Paper 1

Paragraph for Questions 27–29: $^{14}\mathrm{C}$ is absorbed by living organisms during photosynthesis. The $^{14}\mathrm{C}$ content is constant in living organism once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of $^{14}\mathrm{C}$ in the dead being, falls due to the decay which $^{14}\mathrm{C}$ undergoes $^{14}_{6}\mathrm{C}$ → $^{14}_{7}\mathrm{N}+\beta^{-}$ The half-life period of ${}^{14}\mathrm{C}$ is 5770 years. The decay constant (λ) can be calculated by using the following formula λ = $\frac{0.693}{t_{1/2}}$ The comparison of the $\beta^{-}$ activity of the dead matter with that of the 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 $^{14}\mathrm{C}$ to $\,{}^{12}\mathrm{C}$ in living matter is 1 : $10^{12}$.