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 8.00×10−13J
, and the masses of the helium and gold nuclei were 6.68×10−27kg
and 3.29×10−25kg
, respectively (note that their mass ratio is 4 to 197).
a. If a helium nucleus scatters to an angle of 120°
during an elastic collision with a gold nucleus, calculate the helium nucleus’s final speed and the final velocity (magnitude and direction) of the gold nucleus.