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

  • question_answer
    In the nuclear fusion reaction \[_{1}^{2}H+_{1}^{3}H\to _{2}^{4}He+n\] given that the repulsive potential energy between the two nuclei is- \[\sim 7.7\times {{10}^{-14}}J\], the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's Constant \[k=1.38\times {{10}^{-23}}J/K\]]

    A)  \[{{10}^{7}}K\]

    B)  \[{{10}^{5}}K\]

    C)  \[{{10}^{3}}K\]

    D)  \[{{10}^{9}}K\]

    Correct Answer: D

    Solution :

    [d] average kinetic energy per molecule \[=\frac{3}{2}kT\] This kinetic energy should be able to provide the repulsive potential energy \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\frac{3}{2}kT=7.7\times {{10}^{-14}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,T=\frac{2\times 7.7\times {{10}^{-14}}}{3\times 1.38\times {{10}^{-23}}}=3.7\times {{10}^{9}}K\]


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