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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Self Evaluation Test - Nuclei

  • question_answer
    The nuclear fusion reaction\[2{{H}^{2}}{{\to }_{2}}H{{e}^{4}}+\text{Energy }\], is proposed to be used for the production of industrial power. Assuming the efficiency of process for production of power is 20%, find the ass of the deuterium required approximately for a duration of 1 year. Given mass of \[_{1}{{H}^{2}}\] nucleus = 2.0141 a.m.u and mass of\[_{2}H{{e}^{4}}\] nuclei = 4.0026 a.m.u and 1 a.m.u. = 31 MeV

    A)  165kg

    B)  138kg

    C)  180kg

    D)  60kg

    Correct Answer: B

    Solution :

    [b] Mass defect \[\Delta m=2\times 2.014-4.0026=0.0256\,a.m.u.\] Energy released when two \[_{1}{{H}^{2}}\] nuclei fuse \[=0.0256\times 931=23.8\text{ }MeV\] Total energy required to be produced by nuclear reaction in 1 year \[=2500\times {{10}^{6}}\times 3.15\times {{10}^{7}}=7.88\times {{10}^{16}}J\] No. of nuclei of \[_{1}{{H}^{2}}\] required \[=\frac{7.88\times {{10}^{16}}J}{23.8\times 1.6\times {{10}^{-13}}}\times 2=4.14\times {{10}^{28}}\] Mass of Deuterium required \[=\frac{4.14\times {{10}^{28}}}{6.02\times {{10}^{23}}}\times 2\times {{10}^{-3}}kg=138kg\]


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