What fraction of the α particles in Rutherford's gold foil experiment are scattered at large angles? Assume the gold foil is two layers thick, as shown in the figure, and that the approximate diameters of a gold atom and its nucleus are 2.6 Å and 1.3×10−4Å, respectively. Hint: Calculate the cross-sectional area occupied by the nucleus as a fraction of that occupied by the atom. Assume that the gold nuclei in each layer are offset from each other.
Express your answer to two significant figures.