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 192 minutes only \[1/16\] of the original amount remains. The half-life of the radioactive isotope is [Kerala CET 2004]

    A)                 32 min  

    B)                 48 min

    C)                 12 min  

    D)                 24 min

    Correct Answer: B

    Solution :

               \[\frac{N}{{{N}_{o}}}={{\left( \frac{1}{2} \right)}^{\frac{T}{{{t}_{1/2}}}}}\];  \[\left( \frac{1}{16} \right)={{\left( \frac{1}{2} \right)}^{\frac{192}{{{t}_{1/2}}}}}\];  \[{{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{\frac{192}{{{t}_{1/2}}}}}\]                                 \[{{t}_{1/2}}=48\,\min \]


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