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

  • question_answer
    Average life of a radioactive sample is 4ms. Initially the total number of nuclei is \[{{N}_{0}}\]. A charged capacitor of capacity \[20\mu F\] is connected across a resistor R. The value of R such that ratio of number of nuclei remaining to charge on capacitor remains constant with time is

    A)  100\[\Omega \]

    B)  200 \[\Omega \]

    C)  300 \[\Omega \]

    D)  400 \[\Omega \]

    Correct Answer: B

    Solution :

    [b] \[N={{N}_{0}}{{e}^{-\lambda t}}q={{q}_{0}}{{e}^{-t/RC}}\] and \[\frac{N}{q}=\] constant when \[{{e}^{-\lambda t}}={{e}^{t/RC}}\Rightarrow \lambda =\frac{1}{RC}\,\,\,R=200\Omega \].


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