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Speed parameter β and Lorentz factor γ

  1. Apr 8, 2015 #1

    rlc

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    1. The problem statement, all variables and given/known data
    Find the speed parameter β and Lorentz factor γ for an electron that has a kinetic energy of:

    a) 6.00 keV
    b) 2.00 MeV
    c) 4.00 GeV

    2. Relevant equations
    KE=(γ-1)*511 KeV
    SQRT(1/(1-β^2))=γ

    3. The attempt at a solution
    a) 6 KeV=(y-1)*511
    y=1.0117
    1.0117=SQRT(1/(1-β^2))
    β=0.152

    b) 2 MeV=(y-1)*0.511
    y=4.91
    4.91=SQRT(1/(1-β^2))
    β=0.979

    c) 4000 MeV=(y-1)*0.511
    y=7828
    My issue with this problem is I can't figure out how to calculate β. I was able to calculate the other betas by guessing and checking what beta was...I don't know how to simplify the equation to make solving for beta easier.
    I can't use this method for this particular problem because y is so large. If someone could point out to me where my issue is, and how to go about getting around this problem, I would be very thankful.
     
  2. jcsd
  3. Apr 8, 2015 #2

    phyzguy

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    Science Advisor

    You have:
    [tex] \gamma = \sqrt{\frac{1}{1-\beta^2}}[/tex]
    If you square both sides you have:
    [tex] \gamma^2 = \frac{1}{1-\beta^2}[/tex]

    Can't you take this and solve for β in terms of γ?
     
  4. Apr 8, 2015 #3
    Nope your just fine,
    √(1/1-β^2) = γ
    Express β in function of γ and you'll get it,
    Hope this helps :)
     
  5. Apr 10, 2015 #4

    rlc

    User Avatar

    Thank you! The answer ended up being 1.00
    It's pretty clear I haven't taken a math class in a while... :)
     
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