Electron accelerated through a potential difference

AI Thread Summary
To find the velocity of an electron accelerated through a potential difference of 1x10^6 V, the kinetic energy (K) must be calculated using the relativistic formula, as the situation is highly relativistic. The initial approach used the classical kinetic energy equation, which is not valid at such high speeds. Instead, the correct kinetic energy for the electron is K = eV, where e is the charge of the electron and V is the potential difference. The momentum can then be calculated using relativistic equations, which account for the increase in mass at high velocities. The key takeaway is that relativistic effects must be considered when dealing with particles accelerated to significant fractions of the speed of light.
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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(2x1x106[/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?
 
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An electron passing through a 1x10^6 V potential is a highly relativistic situation. The kinetic energy you wrote down is no longer true.
 
So, how do i find K, or the momentum for that matter?
 

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