RAJASTHAN PMT Rajasthan - PMT Solved Paper-2005

  • question_answer
    A radioactive element has half life of 3.6 days. In what time will it be left 1/32nd undecayed?

    A)  4 days                                 

    B)  12 days

    C)  18 days               

    D)         24 days

    Correct Answer: C

    Solution :

    Here : Half life\[{{T}_{1/2}}\]= 3.6 days Amount left after time t, \[N=\frac{1}{32}\times {{N}_{0}}\] Number of half lives is given by \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]             or                \[\frac{\frac{{{N}_{0}}}{32}}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]             or                \[\frac{1}{32}=\frac{1}{{{2}^{n}}}\]             or                \[n=5\]             or                \[\frac{t}{{{t}_{1/2}}}=5\]             Hence, time of decay


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