Question: Cosmic rays are mainly protons. Their energy spectrum decreases with increasing energy. Their interactions with the atmospheric nuclei produce mesons, which give rise, by decaying,

Cosmic rays are mainly protons. Their energy spectrum decreases with increasing energy. Their interactions with the atmospheric nuclei produce mesons, which give rise, by decaying, to v_μ and v_e. In a sample of N_v =106 v_μs with 1 GeV energy, how many interact in crossing the Earth along its diameter? [Note: σ 7 fb, ρ≈ 5 x10³ kg m^-3, R≈ 6000 km.]

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