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 from gold-197 nuclei. the energy of the incoming helium nucleus was 8.00\times 10^{-13}~\text{j}8.00×10 −13 j, and the masses of the helium and gold nuclei were 6.68\times 10^{-27}~\text{kg}6.68×10 −27 kg and 3.29\times 10^{-25}~\text{kg}3.29×10 −25 kg, respectively (note that their mass ratio is 4 to 197). if a helium nucleus scatters to an angle of 120^\circ120 ∘ during an elastic collision with a gold nucleus, what is the final kinetic energy of the helium nucleus?