JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Critical Thinking

  • question_answer
    A radioactive sample of U238 decay to Pb through a process for which half life is 4.5 ´ 109 years. The ratio of number of nuclei of Pb to U238 after a time  of 1.5 ´ 109 years (given 21/3 = 1.26)        [Based on IIT-JEE (Mains) 2004]

    A)            0.12                                          

    B)            0.26

    C)            1.2 

    D)            0.37

    Correct Answer: B

    Solution :

                Here \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}={{\left( \frac{1}{2} \right)}^{1/3}}\]                    where n = Number of half lives \[=\frac{1}{3}\]                    Þ \[\frac{N}{{{N}_{0}}}=\frac{1}{1.26}\] Þ \[\frac{{{N}_{U}}}{{{N}_{Pb}}+{{N}_{U}}}=\frac{1}{1.26}\]                    Þ \[{{N}_{Pb}}=0.26\,{{N}_{U}}\] Þ \[\frac{{{N}_{Pb}}}{{{N}_{U}}}=0.26\]


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