Alpha particles of kinetic energy (rest energy ) are fired at a thin gold foil

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Scales, units and the four-momentum

Problem

Alpha particles of kinetic energy

T = 5.00\,\mathrm{MeV}

(rest energy

mc^2 = 3727\,\mathrm{MeV}

) are fired at a thin gold foil. A gold nucleus has charge

79e

and a radius of about

7\,\mathrm{fm}

; treat it as fixed. ((a)) Find the momentum

|\mathbf p|c

of one incoming alpha particle. ((b)) In a head-on collision the alpha particle bounces straight back with its speed unchanged. What momentum does it transfer, and what length

\hbar c/(\Delta p\,c)

corresponds to that transfer? ((c)) A glancing collision deflects another alpha particle through a small angle and transfers only

\Delta p\,c = 20.0\,\mathrm{MeV}

. What length corresponds to that transfer? Explain why the beam energy alone does not fix the resolution. ((d)) Using

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

, find how close a head-on alpha particle comes to the centre of the gold nucleus. What does this say about reading the length in (b) as the size of structure this experiment resolves inside gold?

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