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JEE Main & Advanced Chemistry Surface & Nuclear Chemistry / भूतल और नाभिकीय रसायन Question Bank Rate of decay and Half-life

  • question_answer
    A radioactive isotope decays at such a rate that after 96 minutes only \[\frac{1}{8}th\] of the original amount remains. The half-life of this nuclide in minutes is         [KCET 1992]

    A)                 12          

    B)                 24

    C)                 32          

    D)                 48

    Correct Answer: C

    Solution :

           \[\lambda =\frac{2.303}{t}\log \frac{[{{N}_{o}}]}{[N]}=\frac{2.303}{96}\log \frac{1}{1/8}\]                    \[=\frac{2.303}{98}\times 0.9=0.0216\]                                 \ \[{{t}_{1/2}}=\frac{0.693}{\lambda }=\frac{0.693}{0.0216}=32.0\,\,\min .\]


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