Rutherford Scattering, relativistic

[Physser]

Homework Statement

Asked to calculate the relativistic correction, to the differential scattering cross section which is given by the equation below in terms of E, E₀ and θ where E₀= .511 MeV.
with 100MeV electrons from an Au nuclei at certain angles θ.

Homework Equations

Relativistic correction = [ 1 - (v₀)²/c².sin²(θ/2)]

The Attempt at a Solution

I figure the electron energy is kinetic so 100MeV = 1/2 m v²

and by re-arranging for v i get; v = 200/E₀

then plugging into the formula for v gives, (at 20°=θ)

[1 - 200/E₀c².0.03 ]

I'm not sure, first of all if this is correct do far and second of all how to express in terms of E, could it be to use;

E = √(1-(v/c)²).mc² and somehow re-arrange?

Any help would be greatly appreciated.
Cheers.

 

[clamtrox]

I figure the electron energy is kinetic so 100MeV = 1/2 m v²

It's not appropriate at all to use the non-relativistic approximation for kinetic energy here.

I think you should try to solve v/c from
$$E = \frac{E_0}{ \sqrt{1-(v/c)^2}}$$