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

  • 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 \[-7.7\times {{10}^{-14}}J\], the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann?s constant \[k=1.38\times {{10}^{-23}}J/K\]] [AIEEE 2003]

    A)            \[{{10}^{9}}K\]                    

    B)            \[{{10}^{7}}K\]

    C)            \[{{10}^{5}}K\]                    

    D)            \[{{10}^{3}}K\]

    Correct Answer: A

    Solution :

               Kinetic energy of the molecules of a gas at a temp. T is \[\frac{3}{2}kT\]                    \[\therefore \]To initiate the reaction \[\frac{3}{2}kT=7.7\times {{10}^{-14}}J\]                    \[\Rightarrow \frac{3}{2}\times 1.38\times {{10}^{-23}}T=7.7\times {{10}^{-14}}\Rightarrow T=3.7\times {{10}^{9}}K\].                                  


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