# Homework Help: Electron accelerated through a PD

1. Oct 16, 2009

### hockeyhoser23

An electron is accelerated from rest through a potential difference of 2 X 10^6 V. I need the velocity of the electron in order to calculate the energy of the particle. Using 1/2mv^2=u doesn't work because you get v > c. I can't seem to find an eqn to make the relativistic correction. Could someone help me find the velocity?

2. Oct 17, 2009

### tiny-tim

Hi hockeyhoser23!

I need the velocity of the electron in order to calculate the energy of the particle. Using 1/2mv^2=u doesn't work because you get v > c. I can't seem to find an eqn to make the relativistic correction.[/QUOTE]

Use energy = m/√(1 - v2/c2)

3. Oct 17, 2009

### hockeyhoser23

just mass over the gamma factor?

4. Oct 17, 2009

### tiny-tim

oops! I missed out a c2.

Yes, just mc2/gamma … when v is small, that's approximately mc2 + (1/2)mv2

5. Oct 17, 2009

### gabbagabbahey

He means $\gamma mc^2$

EDIT: tinytim beat me to it

Last edited: Oct 17, 2009
6. Oct 17, 2009

### leright

7. Oct 17, 2009

### gabbagabbahey

Errr... you mean "mc2 times gamma" right?

8. Oct 17, 2009

### tiny-tim

no idea … never use it … was just copying hockeyhoser23

9. Oct 17, 2009

### hockeyhoser23

^ yeah sorry, gamma = 1 / (1-v^2/c^2)^1/2, so it would be gamma*mc^2