Electron accelerated through a potential difference

[seanc12]

Homework Statement

I am trying to get the velocity of an electron which has been accelerated through a potential difference of 1x10⁶ V, so that i can find its momentum.

Homework Equations

K=(1/2)mv²
v=sqrt(2K/m)

The Attempt at a Solution

So , K = 1x10⁶eV and m = 0.511x10⁶eV/c²

v=sqrt(2x1x10⁶/.511x10⁶eV/c²)

then the c² comes out and I am left with

v=sqrt(2x1x10<sup>6[/SUPeV]/.511x106eV)c

v=1.98c

which is clearly wrong since v can't be higher than the speed of light,
what am i overlooking?</sup>

 

[Pengwuino]

An electron passing through a 1x10^6 V potential is a highly relativistic situation. The kinetic energy you wrote down is no longer true.

 

[seanc12]

So, how do i find K, or the momentum for that matter?