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JEE Main & Advanced Chemistry Surface & Nuclear Chemistry / भूतल और नाभिकीय रसायन Question Bank Artificial Transmutation

  • question_answer
    A piece of wood was found to have \[{{C}^{14}}/{{C}^{12}}\] ratio 0.7 times that in a living plant. The time period when the plant died is (Half-life of \[{{C}^{14}}=5760\,yrs)\]            [Pb. PMT 1999]

    A)                 2770 yrs               

    B)                 2966 yrs

    C)                 2980 yrs               

    D)                 3070 yrs

    Correct Answer: B

    Solution :

           Given \[{{N}_{o}}=1,{{N}_{t}}=0.70\] and \[{{t}_{1/2}}=5760\] yrs.                              \[k=\frac{0.693}{{{t}_{1/2}}}=\frac{0.693}{5760}\] .                              We also know, \[k=\frac{2.303}{t}\]\[\log \frac{{{N}_{0}}}{{{N}_{t}}}.\frac{0.693}{5760}\]                                 or \[t=\frac{2.303\times 5760\times 0.155}{0.693}=2966yrs.\]


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