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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    Two radioactive materials \[{{X}_{1}}\] and \[{{X}_{2}}\] have decay constants \[10\lambda \] and \[2\lambda ,\] respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \[{{X}_{1}}\] to that of \[{{X}_{2}}\] will be \[1/e\] after a time

    A) \[1/(10\lambda )\]             

    B) \[1/(8\lambda )\]  

    C) \[11/(10\lambda )\]           

    D) \[1/(9\lambda )\]

    Correct Answer: B

    Solution :

    [b] \[{{N}_{1}}={{N}_{0}}{{e}^{-10\lambda t}}\] and \[{{N}_{2}}={{N}_{0}}{{e}^{-2\lambda t}}\] \[\Rightarrow \,\,\,\frac{{{N}_{1}}}{{{N}_{2}}}=\frac{1}{e}={{e}^{-1}}={{e}^{(-10\lambda +2\lambda )\,t}}={{e}^{-8\lambda t}}\] \[\Rightarrow \,\,\,\,\,\,\,t=\frac{1}{8\lambda }\]          


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