Show that the largest scattering angle one can expect from a single atom is θ = 2 Z 2 e 2 4 π ε 0 K R .

Question

Consider the scattering of an alpha particle from the positively charged part of the Thomson plumpudding model. Let the kinetic energy of the∝ particle be K (nonrelativistic) and let the atomic radius be R. (a) Assuming that the maximum transverse Coulomb force acts on the ∝ particle for a time∆ t = 2R/v (where v is the initial speed of the ∝ particle), show that the largest scattering angle we can expect from a single atom is (b) Evaluate θ for an 8.0-MeV ∝ particle scattering from a gold atom of radius 0.135 nm.

Answer 1

Question

Chapter 4, Problem 12P

(a)

To determine

Show that the largest scattering angle one can expect from a single atom is θ=2Z2e24πε0KR .

(b)

To determine

Evaluate θ for an alpha particle scattering from a gold atom.

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Consider the scattering of an alpha particle from the positively charged part of the Thomson plumpudding model. Let the kinetic energy of the∝ particle be K (nonrelativistic) and let the atomic radius be R. (a) Assuming that the maximum transverse Coulomb force acts on the ∝ particle for a time∆ t = 2R/v (where v is the initial speed of the ∝ particle), show that the largest scattering angle we can expect from a single atom is (b) Evaluate θ for an 8.0-MeV ∝ particle scattering from a gold atom of radius 0.135 nm.

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