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Speed of Free Electron Moving in Space

by quickclick330
Tags: electron, free, moving, space, speed
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quickclick330
#1
Dec14-07, 05:12 PM
P: 87
The total energy of a free electron moving through empty space is E=1.5mc^2, where m is the mass of the electron and c is the speed of light. What is this electronís speed?

1. c (the speed of light)
2. 0.7453c
3. 0.8660c
4. 0.9428c
5. 0.9950c
6. 0.9999c


I thought since that Etotal = 1.5mc^2 then....

Etotal = KE = .5mv^2

1.5mc^2 = .5mv^2 and solve for v (masses would cancel which is what I was looking for)

What is wrong about this approach?
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Doc Al
#2
Dec14-07, 05:29 PM
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Using KE = .5mv^2 is only good when v << c.

Hint:
[tex]E = \gamma m c^2[/tex]
kudoushinichi88
#3
Dec14-07, 05:40 PM
P: 133
I believe that the proper relativistic kinetic energy equation would be

[tex]E_k = (\gamma - 1)mc^2[/tex]

Or did you make that mistake on purpose, Doc Al?

quickclick330
#4
Dec14-07, 05:41 PM
P: 87
Speed of Free Electron Moving in Space

oh shoot...i forgot about that. Do I need to use the non-approximated version of KE? (I can never remember it.. but i'm looking it up right now)
Doc Al
#5
Dec14-07, 05:42 PM
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E is total energy, of course.

(There's no need to find kinetic energy.)
quickclick330
#6
Dec14-07, 05:44 PM
P: 87
okay
quickclick330
#7
Dec14-07, 05:46 PM
P: 87
so mc^2 would cancel out on both sides and I would be solving 1.5 = gamma right?
Doc Al
#8
Dec14-07, 05:47 PM
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Quote Quote by quickclick330 View Post
so mc^2 would cancel out on both sides and I would be solving 1.5 = gamma right?
Yep. That's all you need to do.
quickclick330
#9
Dec14-07, 05:51 PM
P: 87
ahh...got it, thank you :-)
kudoushinichi88
#10
Dec14-07, 05:52 PM
P: 133
Oh, I get it... the total energy of the free electron is the sum of its kinetic energy and the energy from the mass-energy equivalence? The potential energy of the electron is zero, since it's free, right?

[tex]E_{total}= (\gamma - 1)mc^2 + mc^2[/tex]
[tex]\ \ \ = \gamma mc^2[/tex]

Is this so?
Doc Al
#11
Dec14-07, 05:58 PM
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Quote Quote by kudoushinichi88 View Post
Oh, I get it... the total energy of the free electron is the sum of its kinetic energy and the energy from the mass-energy equivalence? The potential energy of the electron is zero, since it's free, right?

[tex]E_{total}= (\gamma - 1)mc^2 + mc^2[/tex]
[tex]\ \ \ = \gamma mc^2[/tex]

Is this so?
Yep.
kudoushinichi88
#12
Dec14-07, 06:00 PM
P: 133
Ah, thanks...


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