Ernest rutherford (the first new zealander to be awarded the nobel prize in chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4he) from gold-197 nuclei (197au). the energy of the incoming helium nucleus was 7.32 ✕ 10−13 j, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197. assume that the helium nucleus travels in the +x-direction before the collision.) if a helium nucleus scatters to an angle of 110° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus.