How can i find the Potential difference?

[yy205001]

Homework Statement

Through what potential difference must an electron be accelerate, starting from rest, to acquire a speed of 0.99c?

vf=0.99c(m/s), vi=0(m/s), m=9.11e-31(kg), q=1.6e-19(C)

Homework Equations

E=γmc^2=V*q

The Attempt at a Solution

I plugged in all knowns in the equation and find V(emf).

What i got is 3.63e6 eV but the answer is 3.1e6 V.

What did i do wrong in the progress??

 

[ehild]

The voltage gives the electron extra energy over its rest energy, mc^2. So Vg=mc^2(γ-1).

ehild

 

[yy205001]

But how does (γ-1) come from??

 

[yy205001]

ehild, Never mind, i got it!

But should the unit be eV rather than V?

 

[ehild]

The question is potential difference, that is volts. But the change of energy of the electron is the same number in eV as the acceleration voltage: 1 elementary charge times U potential difference is 1*U =U eV.

ehild