Carbon 14 is used to determine the age of organic material. The procerdure is based on the formation of `.^(14)C` by neutron capture in the upper atmosphere.
`._(7)^(14)N + ._(0)^(1)n rarr ._(6)^(14)C + ._(1)n^(1)`
`.^(14)C` is abosorbed by living organisms during phostosythesis. The `.^(14)C` content is constant in living organisms 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 `.^(14)C` undergoes.
`._(6)^(14)C rarr ._(7)^(14)C + beta^(-)`
The half-life period of `.^(14)C` is 5770 years. The decay constant `(lambda)` can be calculated by using the following formula `lambda = (0.693)/(t_(1//2))`
The comparison fo the `beta^(-)` activity fo the dead matter with that of the carbon still in circulation enables measurement of the period of the isolation the materail form the living cycle. The method however, ceases to be accurate ever periods longer than `30,000` years. The proportaion of `.^(14)C` to `.^(12)C` living matter is `1:10^(12)`.
What should be the age of fossil for meainingful determination of its age?

Options

A. `6` years
B. `6000` years
C. `60,000` years
D. It can be used to calcualte any age

Answer

`b`

Explanation

After one half-life the change in concentration will be easily measurable, however after `60,000` years, the ratio to `C^(14)` to `C^(12)` is too low.