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VIT Engineering VIT Engineering Solved Paper-2009

  • question_answer
    Two radioactive materials \[{{X}_{1}}\] and \[{{X}_{2}}\] have decay constants \[10\lambda \] and \[\lambda \] 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)  \[1/(11\lambda )\]

    C)  \[11/(10\lambda )~\]

    D)  \[1/(9\lambda )\]

    Correct Answer: D

    Solution :

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


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