A beam of alpha particles ( ) of kinetic energy (centre-of-mass frame) and rate…

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Gravitation and central-force motion · Gravitation and central-force motion

Action and Symmetry, Ch Scattering in a central field

Problem

A beam of alpha particles (Z1=2Z_1=2) of kinetic energy 6.0 MeV6.0\ \mathrm{MeV} (centre-of-mass frame) and rate 5.0×105 s−15.0\times10^5\ \mathrm{s^{-1}} strikes a lead foil (Z2=82Z_2=82, density 11.34×103 kg m−311.34\times10^3\ \mathrm{kg\,m^{-3}}, molar mass 207.2 g mol−1207.2\ \mathrm{g\,mol^{-1}}) of thickness 200 nm200\ \mathrm{nm}. Take e2/4πε0=1.44 MeV fm\mathrm{e}^2/4\pi\varepsilon_0 = 1.44\ \mathrm{MeV\,fm} and NA=6.022×1023 mol−1N_{\rm A}=6.022\times10^{23}\ \mathrm{mol^{-1}}. Assume the lead nucleus is fixed and the scattering is pure Rutherford scattering. ((a)) Estimate the fraction of the alphas scattered beyond 40∘40^\circ. ((b)) A detector of area 4.0 cm24.0\ \mathrm{cm^2} is placed 50 cm50\ \mathrm{cm} from the foil, centred at 40∘40^\circ. Estimate its count rate.

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