Electron microscope particle relativistic mass

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Homework Help Overview

The discussion revolves around the relativistic mass of electrons in the context of an electron microscope, specifically examining the effects of an accelerating voltage of 40 kV and whether it can achieve a velocity of at least 25% of the speed of light.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about the application of rest mass versus relativistic mass in calculations. There are questions regarding the correct equations to use for determining relativistic mass and kinetic energy. Some participants suggest that the relativistic kinetic energy formula is incorrectly stated and discuss the relationship between relativistic mass and rest mass.

Discussion Status

Participants are actively questioning the equations presented and exploring the definitions of relativistic mass. There is a recognition of errors in the equations being discussed, and some guidance is offered regarding the relationship between kinetic energy and relativistic mass. However, there is no explicit consensus on the correct approach or final answer.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a focus on ensuring the accuracy of the equations related to relativistic mass and energy.

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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