JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Radioactivity

  • question_answer
    The half-life of \[B{{i}^{210}}\]is 5 days. What time is taken by (7/8)th part of the sample to decay             [MNR 1986; Pb. PMT 2001]

    A)            3.4 days                                  

    B)            10 days

    C)            15 days                                   

    D)            20 days

    Correct Answer: C

    Solution :

                       By using\[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{t/T}};\] where \[N=\left( 1-\frac{7}{8} \right)\,{{N}_{0}}=\frac{1}{8}{{N}_{0}}\] So\[\frac{1}{8}{{N}_{0}}={{N}_{0}}{{\left( \frac{1}{2} \right)}^{t/T}}\]Þ\[{{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{t/5}}\]Þ t =15 days.


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