Rutherford Scattering, relativistic

1. May 12, 2013

Physser

1. The problem statement, all variables and given/known data

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.
2. Relevant equations

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

3. 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 formular 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.

2. May 15, 2013

clamtrox

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
$$E = \frac{E_0}{ \sqrt{1-(v/c)^2}}$$