Alpha particles (

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

Alpha particles (Z1=2Z_1 = 2, mass 4 u4\,\mathrm{u}) of centre-of-mass kinetic energy E=5.0 MeVE = 5.0\,\mathrm{MeV} scatter off aluminium nuclei (Z2=13Z_2 = 13, mass 27 u27\,\mathrm{u}) free and initially at rest in a thin foil. Take k=Z1Z2 e2/4πε0=Z1Z2×1.44 MeV fmk = Z_1 Z_2\,\mathrm{e}^2/4\pi\varepsilon_0 = Z_1 Z_2 \times 1.44\,\mathrm{MeV\,fm}. ((a)) Find the impact parameter bb that gives a centre-of-mass deflection χ=40∘\chi = 40^\circ. ((b)) Find χlab\chi_{\rm lab} corresponding to χ=40∘\chi = 40^\circ. ((c)) A beam of 1.0×1061.0\times10^6 alphas per second strikes the foil, which has 6.0×10226.0\times10^{22} aluminium atoms per square metre. A detector subtending 1.0×10−3 sr1.0\times10^{-3}\,\mathrm{sr} in the laboratory is placed at that laboratory angle. Using the frame relation for the cross-section, with cos⁡χlab=(cos⁡χ+m1/m2)/1+(m1/m2)2+2(m1/m2)cos⁡χ\cos\chi_{\rm lab}=(\cos\chi+m_1/m_2)/\sqrt{1+(m_1/m_2)^2+2(m_1/m_2)\cos\chi}, find the count rate.

Browse the problem library