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Homework Statement
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)?
Homework Equations
λ=1/nσ
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.