JEE Main & Advanced Chemistry Surface & Nuclear Chemistry / भूतल और नाभिकीय रसायन Question Bank Rate of decay and Half-life

  • question_answer
    A radioactive sample is emitting 64 times radiations than nonhazardous limit. if its half-life is 2 hours, after what time it becomes non-hazardous              [DPMT 2005]

    A)                 16 hr     

    B)                 12 hr

    C)                 8 hr       

    D)                 4 hr

    Correct Answer: B

    Solution :

               \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\Rightarrow \frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]                    or \[\frac{1}{64}={{\left( \frac{1}{2} \right)}^{n}}\Rightarrow {{\left( \frac{1}{2} \right)}^{6}}={{\left( \frac{1}{2} \right)}^{n}}\Rightarrow n=6\]                    \[T={{t}_{1/2}}\times n=2\times 6=12\] hours.                                 After 12 hours, sample became non-hazardous.


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