# Accelerating electrons

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?!

## Answers and Replies

hage567
Homework Helper
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
Homework Helper
Could you post more of the question and your work?

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.

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