The highest-energy cosmic ray protons produce charged pions colliding with the microwave background with the reaction p + γ → n + π⁺ (Greisen, Zatsepin,Kuzmin effect). The neutrinos from the decays of the pions have extremely high energies, say of the order of 10 EeV (Berezinsky, Zatsepin neutrinos). Their flux,however, is expected to be extremely small and they have not been detected yet.The neutrino–nucleon cross-sections are relatively large due to the huge number of open channels. Calculations give σ_NC = 3 x 10^-36 m². Calculate the average distance to interact in the Earth [ρ = 5 x 10³ kg m^-3].