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WB JEE Medical WB JEE Medical Solved Paper-2012

  • question_answer
    Two radioactive substances A and B have decay constants \[5\lambda \] and\[\lambda \] respectively. At \[t=0,\]they have the same number of nuclei. The ratio of number of nuclei of A to that of B will be \[{{(1/e)}^{2}}\] after a time interval of

    A)  \[\frac{1}{\lambda }\]

    B)  \[\frac{1}{2\lambda }\]

    C)  \[\frac{1}{3\lambda }\]

    D)  \[\frac{1}{4\lambda }\]

    Correct Answer: B

    Solution :

     We know that \[N={{N}_{0}}{{e}^{-\lambda t}}\] For A, \[{{N}_{A}}={{N}_{0}}{{e}^{-5\lambda t}}\] For B, \[{{N}_{B}}={{N}_{0}}{{e}^{-\lambda t}}\] Given, \[\frac{{{N}_{A}}}{{{N}_{B}}}=\frac{1}{{{e}^{2}}}\] \[\frac{N}{{{N}_{B}}}=\frac{1}{{{e}^{4\lambda t}}}\] \[t=\frac{1}{2\lambda }\]


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