MGIMS WARDHA MGIMS WARDHA Solved Paper-2007

  • question_answer
    A radio isotope has half-life of 5 yr. The fraction of the atoms of this material that would decay in 15 yr will be

    A) 1                                             

    B) \[\frac{2}{3}\]

    C) \[\frac{7}{8}\]                                   

    D) \[\frac{5}{8}\]

    Correct Answer: C

    Solution :

    \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}={{\left( \frac{1}{2} \right)}^{15/5}}={{\left( \frac{1}{2} \right)}^{3}}\] \[\frac{N}{{{N}_{0}}}=\frac{1}{8}\] Fraction decayed \[={{N}_{0}}-N={{N}_{0}}-\frac{{{N}_{0}}}{8}\]                                 \[=\frac{8{{N}_{0}}-{{N}_{0}}}{8}=\frac{7}{8}{{N}_{0}}\]


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