JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Morning)

  • question_answer Two radioactive materials A and B have decay constants\[10\lambda \]and\[\lambda ,\]respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time : [JEE Main 10-4-2019 Morning]

    A) \[\frac{11}{10\lambda }\]                              

    B) \[\frac{1}{9\lambda }\]

    C) \[\frac{1}{10\lambda }\]                                

    D) \[\frac{1}{11\lambda }\]

    Correct Answer: B

    Solution :

    \[{{N}_{1}}={{N}_{0}}{{e}^{-10\lambda t}}\]           \[{{N}_{2}}={{N}_{0}}{{e}^{-\lambda t}}\]           \[\frac{1}{e}=\frac{{{N}_{1}}}{{{N}_{2}}}={{e}^{-9\lambda t}}\] \[\Rightarrow 9\lambda t=1\] \[t=\frac{1}{9\lambda }\]

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