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How can i find the Potential difference?

  1. Apr 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Through what potential difference must an electron be accelerate, starting from rest, to acquire a speed of 0.99c?

    vf=0.99c(m/s), vi=0(m/s), m=9.11e-31(kg), q=1.6e-19(C)
    2. Relevant equations

    E=γmc^2=V*q

    3. The attempt at a solution
    I plugged in all knowns in the equation and find V(emf).

    What i got is 3.63e6 eV but the answer is 3.1e6 V.

    What did i do wrong in the progress??
     
  2. jcsd
  3. Apr 28, 2012 #2

    ehild

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    The voltage gives the electron extra energy over its rest energy, mc^2. So Vg=mc^2(γ-1).

    ehild
     
  4. Apr 28, 2012 #3
    But how does (γ-1) come from??
     
  5. Apr 28, 2012 #4
    ehild, Never mind, i got it!

    But should the unit be eV rather than V?
     
  6. Apr 28, 2012 #5

    ehild

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    The question is potential difference, that is volts. But the change of energy of the electron is the same number in eV as the acceleration voltage: 1 elementary charge times U potential difference is 1*U =U eV.

    ehild
     
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