JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Self Evaluation Test - Nuclei

  • question_answer
    A piece of bone of an animal from a ruin is found to have \[^{14}C\] activity of 12 disintegrations per minute per gm of its carbon content. The \[^{14}C\] activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half-life of \[^{14}C\] is \[{{t}_{1/2}}=5760\] years)

    A)  1672 years

    B)  2391 years

    C)  3291 years

    D)  4453 years

    Correct Answer: B

    Solution :

    [b] Given, for \[^{14}C\] \[{{A}_{0}}=16\,\,dis\,\,{{\min }^{-1}}{{g}^{-1}}\] \[A=12\,\,dis\,\,{{\min }^{-1}}{{g}^{-1}}\] \[{{t}_{1/2}}=5760\,\,years\] Now, \[\lambda =\frac{0.693}{{{t}_{1/2}}}=\frac{0.693}{5760}\] per year Then, from, \[t=\frac{2.303}{\lambda }{{\log }_{10}}\frac{{{A}_{0}}}{A}\] \[=\frac{2.303\times 5760}{0.693}{{\log }_{10}}\frac{16}{12}\approx 2391\]years


You need to login to perform this action.
You will be redirected in 3 sec spinner