# Electron microscope particle relativistic mass

1. Oct 4, 2015

### ForTheGreater

1. The problem statement, all variables and given/known data
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?

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

3. 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.

2. Oct 4, 2015

### ehild

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

3. Oct 4, 2015

### ForTheGreater

γ=qV/m0c2+1 ?

4. Oct 4, 2015

### ehild

Yes, but you need to give the relativistic mass.

5. Oct 4, 2015

### ForTheGreater

I was thinking γm0=mrel?

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

From where do I get the v to answer b?

6. Oct 4, 2015

### ehild

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.