Electron microscope particle relativistic mass

AI Thread Summary
The discussion revolves around calculating the relativistic mass of electrons in an electron microscope that accelerates them to 25% of the speed of light using a 40 kV voltage. Participants clarify that the relativistic kinetic energy formula is not 1/2 mv², emphasizing that the correct approach involves using the invariant mass and the Lorentz factor, γ. The relationship between the accelerating voltage and the relativistic mass is explored, with suggestions to derive velocity from momentum. Additionally, there are corrections to the equations presented, particularly regarding the energy-momentum relationship. The conversation highlights the importance of understanding relativistic concepts to solve the problem effectively.
ForTheGreater
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Homework Statement


They were going to purchase an electron microscope, and wanted the electrons velocity to be as high as 25% of the speed of light after acceleration. There was a microscope at hand that had an accelerating voltage of 40 kV.
a) How large is the electrons relativistic mass when it hits the target expressed in m0?
b) Is the voltage high enough to reach at least25% of the speed of light?

Homework Equations


qV=K
mv2/2=K
E2=m2c2+p2c2
E=K+mc2
p=mvγ

The Attempt at a Solution


Don't know where you use the rest mass and where you get the relativistic mass? Not sure how to figure this out.
 
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ForTheGreater said:

Homework Statement


They were going to purchase an electron microscope, and wanted the electrons velocity to be as high as 25% of the speed of light after acceleration. There was a microscope at hand that had an accelerating voltage of 40 kV.
a) How large is the electrons relativistic mass when it hits the target expressed in m0?
b) Is the voltage high enough to reach at least25% of the speed of light?

Homework Equations


qV=K
mv2/2=K
E2=m2c2+p2c2
E=K+mc2
p=mvγ

The Attempt at a Solution


Don't know where you use the rest mass and where you get the relativistic mass? Not sure how to figure this out.
The equation in red is wrong. The relativistic kinetic energy is not 1/2 mv2. In the other formulae, m means the invariant mass (called also rest mass). The relativistic mass is γm. http://www.britannica.com/science/relativistic-mass
 
ehild said:
The equation in red is wrong. The relativistic kinetic energy is not 1/2 mv2. In the other formulae, m means the invariant mass (called also rest mass). The relativistic mass is γm. http://www.britannica.com/science/relativistic-mass

γ=qV/m0c2+1 ?
 
ForTheGreater said:
γ=qV/m0c2+1 ?
Yes, but you need to give the relativistic mass.
 
ehild said:
Yes, but you need to give the relativistic mass.

I was thinking γm0=mrel?

So (qV/m0c2+1)m0=mrel?

From where do I get the v to answer b?
 
ForTheGreater said:

Homework Equations


qV=K
E2=m2c2+p2c2
E=K+mc2
p=mvγ
There is an error also in the equation in red.
It should be E2=(mc2)2+p2c2
Determine p, and you get v from it.
 
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