JEE Main & Advanced JEE Main Paper Phase-I (Held on 07-1-2020 Evening)

  • question_answer
    The activity of a radioactive sample falls from \[700\text{ }{{s}^{\,1}}\]to \[500\text{ }{{s}^{\,1}}\] in 30 minutes. Its half-life is close to [JEE MAIN Held on 07-01-2020 Evening]

    A) 66 min            

    B) 52 min

    C) 62 min

    D) 72 min

    Correct Answer: C

    Solution :

    [c] \[A={{A}_{0}}{{e}^{-\,t\ln \,2/{{T}_{1/2}}}}\] \[\Rightarrow \,500\,=700\,{{e}^{-\,t\ln \,2/{{T}_{1/2}}}}\] \[\Rightarrow \,\ln \,\frac{7}{5}\,=\frac{30\,\ln \,2}{{{T}_{1/2}}}\Rightarrow \,{{T}_{1/2}}\,=30\,\frac{\ln \,2}{\ln 1.4}\,=61.8\] \[\Rightarrow \,\,{{T}_{1/2}}\,\approx 62\] minutes

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