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BHU PMT BHU PMT (Mains) Solved Paper-2010

  • question_answer
    In a sample of radioactive material, what fraction of the initial number of active nuclei will remain disintegrated after half of a half-life of the sample?

    A)  \[\frac{1}{4}\]                                  

    B)  \[\frac{1}{2\sqrt{2}}\]

    C)  \[\frac{1}{\sqrt{2}}\]                                    

    D)  \[\sqrt{2}-1\]

    Correct Answer: C

    Solution :

                     According to radioactive decay, \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/{{T}_{1/2}}}}\] According to question,                 \[t=\frac{{{T}_{1/2}}}{2}\] Then,    \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{1/2}}=\frac{1}{\sqrt{2}}\]        


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