JEE Main & Advanced Sample Paper JEE Main - Mock Test - 8

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

A) 1485 years

B) 1845 years

C) 530 years

D) 4767 years.

Correct Answer: B

Solution :

Radioactive decay follows first order kinetics, there-fore,

Decay constant \[(\lambda )=\frac{0.693}{{{t}_{1}}/2}=\frac{0.693}{5730}\]

Given, \[{{R}_{0}}=100\] \[\therefore \,\,\,R=80\]

and \[t=\frac{2.303}{\lambda }\log \frac{{{[R]}_{0}}}{[R]}=\frac{2.303}{\left( \frac{0.693}{5730} \right)}\log \frac{100}{80}\]

\[=\frac{2.303\times 5730}{0.693}\times 0.0969=1845\,years\]