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Haryana PMT Haryana PMT Solved Paper-2005

  • question_answer
    Two radioactive materials A and B 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 A to that of B will be 1/e after a time :

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

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

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

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

    Correct Answer: B

    Solution :

                    \[{{N}_{A}}=No{{e}^{-10\lambda t}}\] and        \[{{N}_{B}}=No{{e}^{-\lambda t}}\] \[\Rightarrow \]               \[\frac{{{N}_{A}}}{{{N}_{B}}}=\frac{1}{e}={{e}^{(-10\lambda +\lambda )t}}\] or            \[9\lambda t=1\] \[\therefore \]  \[t=\frac{1}{9\lambda }\]


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