Protons ( , mass ) of centre-of-mass kinetic energy scatter off gold nuclei ( , mass…

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Momentum, energy and conservation laws · Gravitation and central-force motion

Action and Symmetry, Ch Scattering in a central field

Problem

Protons (Z1=1Z_1=1, mass 1 u1\,\mathrm{u}) of centre-of-mass kinetic energy E=3.0 MeVE=3.0\,\mathrm{MeV} scatter off gold nuclei (Z2=79Z_2=79, mass 197 u197\,\mathrm{u}) in a thin foil. Take k=Z1Z2×1.44 MeV fmk=Z_1Z_2\times1.44\,\mathrm{MeV\,fm}. ((a)) Find the impact parameter bb giving a centre-of-mass deflection χ=25∘\chi=25^\circ. ((b)) A beam of 2.0×1052.0\times10^5 protons per second strikes the foil, which has 2.36×10222.36\times10^{22} gold atoms per square metre. A detector of solid angle 2.0×10−4 sr2.0\times10^{-4}\,\mathrm{sr} is set at χ=25∘\chi=25^\circ; because m1/m2m_1/m_2 is so small, the solid angles in the two frames differ by under 11 per cent, so treat them as equal. Find the count rate. ((c)) Find χlab\chi_{\rm lab} corresponding to χ=25∘\chi=25^\circ.

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