A Rutherford scattering experiment is performed in which alpha particles are directed at a flat sheet of carbon. This sheet contains a single layer of carbon atoms arranged on a square grid (Fig. P30.82), with an atomic spacing of 0.25 nm. Estimate the probability that an alpha particle will collide with a carbon nucleus. Assume the carbon nuclei have a diameter of 2.0 fm and that the center of an alpha particle must overlap with a carbon nucleus for a collision to occur (since the strong force has a very short range). Your answer will give an estimate for the probability that an alpha particle will scatter back toward its source in Rutherford’s experiment. These scattering events were the ones that puzzled Rutherford and led him to infer the existence of the nucleus.