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

  • question_answer
    A sample of radioactive substance has \[{{10}^{6}}\] nuclei. If half-life is 20 seconds, the number of nuclei left in the sample after 10 second is

    A)  \[{{10}^{4}}\]

    B)  \[2\times {{10}^{5}}\]

    C)  \[7\times {{10}^{5}}\]

    D)  \[11\times {{10}^{5}}\]

    Correct Answer: C

    Solution :

    [c] \[N={{N}_{0}}{{e}^{-\lambda /t}}={{10}^{6}}{{e}^{-\left[ \frac{In\,\,2}{20}\times 10 \right]}}\] \[={{10}^{6}}{{e}^{-In\,\,\sqrt{2}}}=\frac{{{10}^{6}}}{\sqrt{2}}=\,\,\approx \,\,7.07\times {{10}^{5}}\]


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