Electron microscope particle relativistic mass

[ForTheGreater]

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.

 

[ehild]

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

 

[ForTheGreater]

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 ?

 

[ehild]

γ=qV/m₀c²+1 ?

Yes, but you need to give the relativistic mass.

 

[ForTheGreater]

Yes, but you need to give the relativistic mass.

I was thinking γm₀=m_rel?

So (qV/m₀c2+1)m₀=m_rel?

From where do I get the v to answer b?

 

[ehild]

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.