Chapter 8, Problem 68GP

The structure of the atom. During 1910–1911, Sir Ernest Rutherford performed a series of experiments to determine the structure of the atom. He aimed a beam of alpha particles (helium nuclei, of mass 6.65 × 10⁻²⁷ kg) at an extremely thin sheet of gold foil. Most of the alphas went right through with little deflection, but a small percentage bounced directly back. These results told him that the atom must be mostly empty space with an extremely small nucleus. The alpha particles that bounced back must have made a head-on collision with this nucleus. A typical speed for the alpha particles before the collision was 1.25 × 10⁷ m/s, and the gold atom has a mass of 3.27 × 10⁻²⁵ kg. Assuming (quite reasonably) elastic collisions, what would be the speed after the collision of a gold atom if an alpha particle makes a direct hit on the nucleus?