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 ?xed 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?