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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Mock Test - Modern Physics

  • question_answer
    A star initially has 1040 deuterons. It produces energy via the processes \[_{1}{{H}^{2}}+{}_{1}{{H}^{2}}\to {}_{1}{{H}^{3}}+p\] \[_{1}{{H}^{2}}+{}_{1}{{H}^{3}}\to {}_{2}{{H}^{4}}+n\] 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

    A) \[{{10}^{6}}\]            

    B) \[{{10}^{8}}\sec \]

    C) \[{{10}^{12}}\sec \]    

    D) \[{{10}^{16}}\sec \]

    Correct Answer: C

    Solution :

    [c] Mass defect \[=3\times 2.014-4.001-1.007-1.008\] \[=0.026amu=0.026\times 931\times {{10}^{6}}\times 1.6\times {{10}^{-19}}J\]\[=3.82\times {{10}^{-12}}J\] Power of star \[={{10}^{16}}W\] 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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