RAJASTHAN PMT Rajasthan - PMT Solved Paper-2007

  • question_answer
    In a sample of radioactive -material, what percentage of the initial number of active nuclei will decay during one mean life?

    A)  37%                                      

    B)  50%

    C)  63%                      

    D)         69.3%

    Correct Answer: C

    Solution :

    From Rutherford-Soddy law                 \[N={{N}_{0}}{{e}^{-\lambda \tau }}\] \[\therefore \]Using,\[\tau =\frac{1}{\lambda }\] we have                 \[N={{N}_{0}}{{e}^{-1}}=\frac{{{N}_{0}}}{e}\] Percentage decayed\[=\frac{{{N}_{0}}-N}{{{N}_{0}}}\times 100\]                                       \[=\frac{({{N}_{0}}-{{N}_{0}}/e)}{{{N}_{0}}}\times 100\]                                 63%


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