JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Critical Thinking

  • question_answer
    Rest mass energy of an electron is 0.51 MeV. If this electron is moving with a velocity 0.8 c (where c is velocity of light in vacuum), then kinetic energy of the electron should be.

    A)            0.28 MeV                               

    B)            0.34 MeV

    C)            0.39 MeV                               

    D)            0.46 MeV

    Correct Answer: B

    Solution :

                       Given m0c2 = 0.51 MeV and v = 0.8 c                    K.E. of the electron = mc2? m0c2                    But \[m=\frac{{{m}_{0}}}{\sqrt{1-\frac{{{v}^{2}}}{{{c}^{2}}}}}=\frac{{{m}_{0}}}{\sqrt{1-{{\left( \frac{0.8\,c}{c} \right)}^{2}}}}=\frac{{{m}_{0}}}{\sqrt{0.36}}=\frac{{{m}_{0}}}{0.6}\]                    Now, \[m{{c}^{2}}=\frac{0.51}{0.6}\] MeV = 0.85 MeV                    \ K.E. = (0.85 ? 0.51)MeV = 0.34 MeV.


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