# How to calculate thickness of the wall in a wire chamber

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1. Nov 28, 2014

### Kyrios

1. The problem statement, all variables and given/known data
This is a question on multiple coulomb scattering in a wire chamber

momentum p = 500MeV/c
wire resolution = 120 microns
distance from wall to wire = 0.01m
radiation length of wall material X_0 = 2E-3 m
mass of charged particle $m_{\pi}$ = 139.6 MeV/c^2
charge z = 1

How thick is the wall if 68% of the particles are scattered less than the wire resolution?

2. Relevant equations

$$\theta = \frac{13.6}{\beta p} z \sqrt{\frac{x}{x_0}}$$

3. The attempt at a solution

What I am trying to find is x, but am uncertain of where exactly the 120 microns and 68% comes in.
I looked up a distribution table and for z=0.68, the area below z = 0.7517. (I think this is what you have to do for 68% scatter less than the resolution?)
The gaussian distribution forms a triangle to work out theta, with the side opposite to the angle. I assume the mean would be zero, so would this side just be 0.7517x120microns?

Last edited: Nov 28, 2014
2. Nov 29, 2014