Electron accelerated through a PD

[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?

 

[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)

 

[hockeyhoser23]

just mass over the gamma factor?

 

[tiny-tim]

oops! I missed out a c².

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

 

[gabbagabbahey]

just mass over the gamma factor?

He means [itex]\gamma mc^2[/itex]

EDIT: tinytim beat me to it

 

[leright]

you don't need the velocity to calculate the energy. The kinetic energy is just (voltage)*(charge). The charge of an electron is 1.6E-19 C.

But if you want to calculate the velocity from the KE (which is what I assume you want to do) then you need a relativistic formula.

http://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies

There's a relativistic KE formula in the wiki article.

 

[gabbagabbahey]

oops! I missed out a c².

Yes, just mc²/gamma …

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

 

[tiny-tim]

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

no idea … never use it … was just copying hockeyhoser23

 

[hockeyhoser23]

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