Classical Treatment of Rutherford Scatter
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Rutheford successfully used classical mechanics to account for the scattering pattern of alpha particles by heavy nuclei: he treated the alpha particle as a point mass that follows a hyperbolic trajectory under the repulsion of a fixed point nucleus. But the de Broglie view of the wave nature of particles raises some awkward questions about the validity of Rutherford's analysis.
(a) Calculate the de Broglie wavelength of a 6-McV alpha particle.
(b) Compare your result for (a) with the classical distance of closest approach in a head-on collision of a 6-MeV alpha particle with a gold nucleus (Z = 79). Neglect the recoil of the nucleus.
(c) Do you expert that classical mechanics will be valid describe this encounter? ls your conclusion strengthened or reversed if one takes account of the fact that the alpha particle loses momentum as it approaches the nucleus?
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Solution Summary
We use the classical model of Rutherford scattering to compute the distance of closest approach of a 6 MeV alpha particle to a gold nucleus, then we compare this distance to the de Broglie wavelength of a 6 MeV alpha particle to see if the classical model is a good approximation.
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(a) We wish to calculate the de Broglie wavelength of a 6-MeV alpha particle.
We have
(b) We wish to calculate the classical distance ...
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