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

  • question_answer
    Two radioactive substances A and B have decay constants \[5\lambda \]and \[\lambda \]respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become\[{{\left( \frac{1}{e} \right)}^{2}}\]will be : [JEE Main 10-4-2019 Afternoon]

    A) \[1/4\lambda \]            

    B) \[1/\lambda \]

    C) \[1/2\lambda \]

    D) \[2/\lambda \]

    Correct Answer: C

    Solution :

    \[{{N}_{A}}={{N}_{0}}{{e}^{-5\lambda t}}\] \[{{N}_{B}}={{N}_{0}}{{e}^{-\lambda t}}\] \[\frac{{{N}_{A}}}{{{N}_{B}}}=\frac{{{e}^{-5\lambda t}}}{{{e}^{-\lambda t}}}=\frac{1}{{{e}^{2}}}\] \[\Rightarrow {{e}^{-4\lambda t}}={{e}^{-2}}\] \[\Rightarrow 4\lambda t=2\] \[\Rightarrow t=\frac{1}{2\lambda }\]                      


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