The typical energy of a neutrino in the cosmic neutrino background, as pointed out in Chapter 5, is Eν∼kTν∼5×10−4eV. What is the approximate interaction cross-section σw for one of these cosmic neutrinos? Suppose you had a large lump of 56Fe (with density ρ=7900kgm−3). What is the number density of protons, neutrons, and electrons within the lump of iron? How far, on average, would a cosmic neutrino travel through the iron before interacting with a proton, neutron, or electron? (Assume that the cross-section for interaction is simply σw, regardless of the type of particle the neutrino interacts with.)