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Electron accelerated through a PD

  1. Oct 16, 2009 #1
    An electron is accelerated from rest through a potential difference of 2 X 10^6 V. I need the velocity of the electron in order to calculate the energy of the particle. Using 1/2mv^2=u doesn't work because you get v > c. I can't seem to find an eqn to make the relativistic correction. Could someone help me find the velocity?
     
  2. jcsd
  3. Oct 17, 2009 #2

    tiny-tim

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    Hi hockeyhoser23! :smile:

    I need the velocity of the electron in order to calculate the energy of the particle. Using 1/2mv^2=u doesn't work because you get v > c. I can't seem to find an eqn to make the relativistic correction.[/QUOTE]

    Use energy = m/√(1 - v2/c2) :smile:
     
  4. Oct 17, 2009 #3
    just mass over the gamma factor?
     
  5. Oct 17, 2009 #4

    tiny-tim

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    oops! I missed out a c2. :redface:

    Yes, just mc2/gamma … when v is small, that's approximately mc2 + (1/2)mv2 :wink:
     
  6. Oct 17, 2009 #5

    gabbagabbahey

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    He means [itex]\gamma mc^2[/itex]

    EDIT: tinytim beat me to it:smile:
     
    Last edited: Oct 17, 2009
  7. Oct 17, 2009 #6
  8. Oct 17, 2009 #7

    gabbagabbahey

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    Errr... you mean "mc2 times gamma" right?
     
  9. Oct 17, 2009 #8

    tiny-tim

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    no idea … never use it … was just copying hockeyhoser23 :smile:
     
  10. Oct 17, 2009 #9
    ^ yeah sorry, gamma = 1 / (1-v^2/c^2)^1/2, so it would be gamma*mc^2
     
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