JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Radioactivity

  • question_answer
    The half-life of a radioactive substance is 48 hours. How much time will it take to disintegrate to its \[\frac{1}{16}\]th part [BCECE 2003]

    A)            12 h                                          

    B)            16 h

    C)            48 h                                          

    D)            192 h

    Correct Answer: D

    Solution :

                       \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/T}}\Rightarrow \frac{1}{16}={{\left( \frac{1}{2} \right)}^{t/48}}\]                    \[\Rightarrow {{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{t/48}}\Rightarrow t=192\ hour.\]


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