The half life for radioactive decay of `.^(14)C` is 5730 years. An archaeological artifact containing wood had only `80%` of the `.^(14)C` found in a living tree. Estimat the age of the sample.

Options

A. 1485 years
B. 1845 years
C. 530 years
D. 4767 years

Answer

B

Explanation

Radioactive decay follows first order kinetics.
Therefore,
Decau constant `(lambda) = (0.693)/(t_(1//2)) = (0.693)/(5730)`
Given `[R_(0)] = 100 :. [R] = 80`
and `t = (2.303)/(lambda) "log" ([R_(0)])/([R]) = (2.303)/((0.693)/(5730)) "log" (100)/(80)`
` = (2.303 xx 5730)/(0.693) xx 0.0969 = 1845` years