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

  • question_answer
    A star initially has \[{{10}^{40}}\] deuterons. It produces energy via the processes            \[_{1}{{H}^{2}}{{+}_{1}}{{H}^{2}}{{\to }_{1}}{{H}^{3}}+p\]            \[_{1}{{H}^{2}}{{+}_{1}}{{H}^{3}}{{\to }_{2}}H{{e}^{4}}+n\]            The masses of the nuclei are as follows :            \[M({{H}^{2}})=2.014\ amu;\ M(p)=1.007\ amu;\]            \[M(n)=1.008\ amu;\ M(H{{e}^{4}})=4.001\ amu\]            If the average power radiated by the star is \[{{10}^{16}}W\],the deuteron supply of the star is exhausted in a time of the order of                                                                          [IIT 1993]

    A)            \[{{10}^{6}}\]sec                 

    B)            \[{{10}^{8}}\]sec

    C)            \[{{10}^{12}}\]sec              

    D)            \[{{10}^{16}}\]sec

    Correct Answer: C

    Solution :

               Mass defect =\[RV\propto n\]                    \[=0.026\ amu=0.026\times 931\times {{10}^{6}}\times 1.6\times {{10}^{-19}}J\]                    \[=3.82\times {{10}^{-12}}J\]                    Power of star =1016W                    Number of deuterons used \[=\frac{{{10}^{16}}}{\Delta M}=0.26\times {{10}^{28}}\]                    Deuteron supply exhausts in\[\frac{{{10}^{40}}}{0.26\times {{10}^{28}}}={{10}^{12}}s\].


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