Determine the average `.^(14)C` activity in decays per minute per gram of natural carbon found in living organisms if the concentration of `.^(14)C` relative to that of `.^(12)C` is `1.4 xx 10^(-12)` and half life of `.^(14)C` is `T_(1//2) = 5730` years.

Explanation

`lambda = (0.693)/(T_(1//2))`
`= (0.693)/(5730xx365xx24xx60) = 2.30xx10^(-10)//min`
Number of nuclei in `1 g` of carbon is
`(1)/(12) xx 6.02xx10^(23) = 5xx10^(22)`
Concentration factor `= (.^(14)C)/(.^(12)C) = 1.4xx10^(-12)`
Number of `(.^(14)C)` nuclei per gram is
`(5xx10^(22))xx(1.4xx10^(-12)) = 7xx10^(10)`
`A = lambdaN = (2.30xx10^(-10))(7xx10^(10))`
`= 16.1 decays//g.min`