Final Velocity of Electron Accelerated from Rest Through Potential Difference

[Gyroscope]

Homework Statement

An electron is accelerated from rest through a potential difference of V volts. What is the final velocity?

I did:
$$qV=\frac{mc^2}{\sqrt{1-\frac{v_f^2}{c^2}}}$$

And solve for v, but I get an unreal answer. What am I doing wrong?!

Homework Equations

The Attempt at a Solution

 

[hage567]

Why are you using relativistic energy?

 

[Gyroscope]

Because there is an high potential difference. If I use non-relativistic energy it gives a speed higher than the speed of light.

 

[hage567]

Could you post more of the question and your work?

 

[ziad1985]

If I'm not mistaken(Memory sometimes betray me) qV=(Gamma-1)mc^2

 

[Gyroscope]

ziiad this is the relativistic kinetic energy, what I need is the relativistic change in kinetic energy.

 

[Gyroscope]

No, you are right. What a stupid mistake of mine. :( Thanks, mate.

 

[ziad1985]

Don't worry, we all make mistakes, they key part was "...accelerated from rest..."