Chapter 9, Problem 44P

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 $\text{8}.00\text{×1}{0}^{-13}\text{ J}$ , and the masses of the helium and gold nuclei were $6.68\text{×1}{0}^{-27}\text{ kg}$ and $3.29\text{×1}{0}^{-25}\text{ kg}$ , respectively (note that their mass ratio is 4 to 197).

a. If a helium nucleus scatters to an angle of $\text{12}0°$ 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.

b. What is the final kinetic energy of the helium nucleus?