MGIMS WARDHA MGIMS WARDHA Solved Paper-2008

  • question_answer
    The\[{{t}_{0.5}}\]of a radioactive isotope is 1.5 h. How long will it take for its activity to be reduced to\[\frac{1}{16}\]of its original value?

    A) 3.0 h                                     

    B) 360 min

    C) 4.5 h                                     

    D) 600 min

    Correct Answer: B

    Solution :

    \[\lambda =\frac{0.693}{{{t}_{1/2}}}\] \[=\frac{0.693}{1.5}{{h}^{-1}}=0.462\,{{h}^{-1}}\] \[{{N}_{0}}=1;\,N=\frac{1}{16}\] \[t=\frac{2.303}{\lambda };\log \frac{{{N}_{0}}}{N}\] \[=\frac{2.303}{0.462}\log 16\]   \[=6\text{ }h=360\text{ }\min \]


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