# Fraction of protons scattering

1. Oct 27, 2014

### Annaino

1. The problem statement, all variables and given/known data
A proton beam of energy E=7mpc2 is incident on a cylindrical volume (V=20 cm3) of liquid hydrogen (density ρ=0.071 g cm-3) at rest. The spot area of the beam is A=4 cm2 and the total cross section is σ=30 mb. What fraction of the protons entering the target will interact? What is the mean free path (collision length)?

2. Relevant equations
λ=1/nσ

3. The attempt at a solution
I found the number of protons in the given volume, N = ρV/mp. I then computed the fraction as f=Nσ /A=ρVσ/mA=6.4E-6. I don't like the order of magnitude I am getting from this approach. I found the mean free path from the equation above. Again, with a weird order of magnitude. λ=m/ρσ=7.84 km.

2. Nov 2, 2014

### Staff: Admin

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

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