The fraction of incident particles scattered through an angle greater than θ is given by f = σnt, where σ is the cross-sectional area, n is the number of atoms per volume and t is the thickness of the foil. Taking that the large angles are angles more than 90 degrees, θ = 90°. The differential cross-section in Rutherford scattering model is given by
where KE is the kinetic energy (one can be derived from the energy of alpha-particles).
Therefore, in order to calculate the fraction of the α particles in Rutherford's gold foil experiment that are scattered at large angles, the energy of beam required.
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