# Rutherford scattering thin gold foil

1. Oct 21, 2013

### skate_nerd

1. The problem statement, all variables and given/known data
The fraction of 6.0 MeV protons scattered by a thin gold foil, of density 19.3 g/cm^3, from the incident beam into a region where scattering angles exceed 60° is equal to 2.0(10^-5). Calculate the thickness of the gold foil.

2. Relevant equations

$$N=(\frac{1}{4\pi\epsilon_o})^2\pi{I}\rho{t}(\frac{zZe^2}{Mv^2})^2\cot{\frac{\theta}{2}}$$

3. The attempt at a solution
I solved for t, giving
$$t=(\frac{1}{4\pi\epsilon_o})^{-2}\frac{1}{\pi\rho}\frac{N}{I}(\frac{zZe^2}{Mv^2})^{-2}\tan{\frac{\theta}{2}}$$

For Mv^2, I used 2*6 MeV, converted to joules. For ρ, I used the number of molecules in one cubic meter of gold, which is 98,000. For theta I used 60°. The ratio N/I is given: 2(10^-5). I used 8.988(10^9) m/F for 1/4piε. Z=79, and z=1, e=1.602(10^-9) coulombs.

I plugged in all known values and got 4.17(10^17). Obviously wrong, but I don't understand why I am so off. I check the units and everything. Anybody see what's wrong?

Last edited: Oct 21, 2013