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

  • question_answer
    The rest energy of an electron is 0.511 MeV. The electron is accelerated from rest to a velocity 0.5 c. The change in its energy will be                                                              [MP PET 1996]

    A)            0.026 MeV                             

    B)            0.051 MeV

    C)            0.079 MeV                             

    D)            0.105 MeV

    Correct Answer: C

    Solution :

               \[\Delta =m{{c}^{2}}-{{m}_{0}}{{c}^{2}}=\frac{{{m}_{0}}{{c}^{2}}}{\sqrt{1-({{v}^{2}}/{{c}^{2}})}}-{{m}_{0}}{{c}^{2}}\]                    \[={{m}_{0}}{{c}^{2}}\left( \frac{1}{\sqrt{1-({{v}^{2}}/{{c}^{2}})}}-1 \right)=0.511\,\left( \frac{1}{\sqrt{0.75}}-1 \right)\]                    = 0.079MeV


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