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Question

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.

  1. 0.28 MeV    
  2. 0.34 MeV    
  3. 0.39 MeV    
  4. 0.46 MeV    

The correct answer is: 0.34 MeV


    Given m0c2 = 0.51 MeV and v = 0.8 c
    K.E. of the electron = mc2– m0c2
    But m equals fraction numerator m subscript 0 end subscript over denominator square root of 1 minus fraction numerator v to the power of 2 end exponent over denominator c to the power of 2 end exponent end fraction end root end fraction equals fraction numerator m subscript 0 end subscript over denominator square root of 1 minus open parentheses fraction numerator 0.8 c over denominator c end fraction close parentheses to the power of 2 end exponent end root end fraction equals fraction numerator m subscript 0 end subscript over denominator square root of 0.36 end root end fraction equals fraction numerator m subscript 0 end subscript over denominator 0.6 end fraction
    Now, m c to the power of 2 end exponent equals fraction numerator 0.51 over denominator 0.6 end fraction MeV = 0.85 MeV
    \ K.E. = (0.85 – 0.51)MeV = 0.34 MeV

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