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

  • question_answer
    Rest mass energy of an electron is 0.54 MeV. If velocity of the electron is 0.8 c, then K.E. of the electron is

    A)            0.36 MeV

    B)            0.41 MeV

    C)            0.48 MeV                               

    D)            1.32 MeV

    Correct Answer: A

    Solution :

                       \[{{m}_{0}}{{c}^{2}}=0.54\,MeV\]and K.E. = \[m{{c}^{2}}-{{m}_{0}}{{c}^{2}}\] Also \[m=\frac{{{m}_{0}}}{\sqrt{1-\frac{{{v}^{2}}}{{{c}^{2}}}}}=\frac{{{m}_{0}}}{\sqrt{1-{{(0.8)}^{2}}}}=\frac{{{m}_{0}}}{0.6}\] \ \[E=m{{c}^{2}}=\frac{{{m}_{0}}}{0.6}{{c}^{2}}=\frac{{{m}_{0}}c}{0.6}=\frac{0.5\,H}{0.6}=0.9\,MeV\] \ K.E.= (0.9 ? 0.54) = 0.36 MeV.     


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