Speed parameter β and Lorentz factor γ

  • #1
rlc
128
1

Homework Statement


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

Homework Equations


KE=(γ-1)*511 KeV
SQRT(1/(1-β^2))=γ

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.
 

Answers and Replies

  • #2
phyzguy
Science Advisor
4,651
1,587
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?
 
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  • #3
224
35
Nope your just fine,
√(1/1-β^2) = γ
Express β in function of γ and you'll get it,
Hope this helps :)
 
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  • #4
rlc
128
1
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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