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

  • question_answer
    The disintegration rate of a certain radioactive sample at any instant is 4750 disintegrations per minute. Five minutes later the rate becomes 2700 disintegrations per minute. Calculate half-life of the sample.

    A)  \[9.1\,\min \]

    B)  \[6.1\,\min \]

    C)  \[2.3\,\min \]

    D)  \[1.1\,\min \]

    Correct Answer: B

    Solution :

    [b] We know that the rate of integration \[\left| -\frac{dN}{dt} \right|=A\] \[\therefore \,\,\,\,\,\,\,\,\,A={{A}_{0}}{{e}^{-\lambda t}}\] or \[2700=4750\,{{e}^{-\lambda \times 5}}\] or \[\lambda =0.1131\] per minute Half-life   minute


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