What Fraction of Protons Interact in a Liquid Hydrogen Target?

[Annaino]

Homework Statement

A proton beam of energy E=7m_pc² 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/m_p. 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.

 

[Greg Bernhardt]

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?