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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Mock Test - Modern Physics

  • question_answer
    A radioactive substance has a half-life of 60 minutes. After 3 hours, the fraction of atom that have decayed would be

    A) 12.5%  

    B) 87.5%

    C) 8.5%                

    D) 25.1%

    Correct Answer: B

    Solution :

    [b] \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{\frac{t}{{{T}_{1/2}}}}}\] Hence, fraction of atoms decayed \[=1-\frac{N}{{{N}_{0}}}=1-{{\left( \frac{1}{2} \right)}^{\frac{t}{{{T}_{1/2}}}}}=1-{{\left( \frac{1}{2} \right)}^{\frac{3\times 60}{60}}}=\frac{7}{8}\] In percentage it is \[\frac{7}{8}\times 100=87.5%\]


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