A beam of protons ( ) of kinetic energy (centre-of-mass frame) and rate strikes a…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Mechanics & Dynamical Systems · Calculus of change and accumulation

Action and Symmetry, Ch Scattering in a central field

Problem

A beam of protons (

Z_1=1

) of kinetic energy

2.0\ \mathrm{MeV}

(centre-of-mass frame) and rate

1.0\times10^7\ \mathrm{s^{-1}}

strikes a copper foil (

Z_2=29

, density

8.96\times10^3\ \mathrm{kg\,m^{-3}}

, molar mass

63.5\ \mathrm{g\,mol^{-1}}

) of thickness

1.0\ \mu\mathrm{m}

. Take

\mathrm{e}^2/4\pi\varepsilon_0 = 1.44\ \mathrm{MeV\,fm}

and

N_{\rm A}=6.022\times10^{23}\ \mathrm{mol^{-1}}

. Assume the copper nucleus is fixed and the scattering is pure Rutherford scattering. ((a)) Estimate the fraction of the protons scattered beyond

45^\circ

. ((b)) A detector of area

1.0\ \mathrm{cm^2}

is placed

25\ \mathrm{cm}

from the foil, centred at

45^\circ

. Estimate its count rate.

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