A beam of particles of kinetic energy E = 10 MeV and intensity I = 1

A beam of α particles of kinetic energy E = 10 MeV and intensity I = 1 μ A hits a lead target [A = 207, Z = 82, ρ = 1.14 x 10⁴ kg m^-3] of thickness t = 0.2 mm. We locate a counter of area S = 1 cm² at a distance of l = 0.5 m beyond the target at the angle θ = 40°. Neglecting, when necessary, the variation of the angle on the detector find: (a) the number of incident particles per second R_i, (b) the solid angle ΔΩ under which the target sees the detector, (c) the differential cross-section at the detector, and (d) how many hits the detector counts per second.