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KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • question_answer
    A radioactive sample of \[{{\operatorname{U}}^{238}}\] decay to Pb through a process for which half-life is \[4.5\times {{10}^{9}}\] years. The ratio of number of nuclei of Pb to \[{{\operatorname{U}}^{238}}\]after a time of \[1.5\times {{10}^{9}}\] years (given \[{{2}^{1/3}}=1.26\])

    A) 0.12

    B) 0.26

    C) 1.2       

    D) 0.37

    Correct Answer: B

    Solution :

    \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}={{\left( \frac{1}{2} \right)}^{1/3}}=\frac{1}{1.26}\]
    Also \[\frac{N}{{{N}_{0}}}=\frac{1}{1.26}\Rightarrow \frac{{{N}_{u}}}{{{N}_{Pb}}+{{N}_{0}}}=\frac{1}{2.26}\]\[\Rightarrow \]\[{{N}_{Pb}}=0.26{{N}_{0}}\Rightarrow \frac{{{N}_{Pb}}}{{{N}_{0}}}=0.26\]


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