Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering (He) from gold-197 nuclei (197AU). The energy of the incoming helium nucleus was 7.09 x 10-13 J, and the masses of the helium and gold nuclei were 6 3.29 x 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.) (a) If a helium nucleus scatters to an angle of 115° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 120° He nucleus Gold nucleus 4He speed 14562052.73 x m/s 197Au velocity x m/s 1160023.058 197 Au direction -12.76 X ° counterclockwise from the +x-axis (b) What is the final kinetic energy (in J) of the helium nucleus?

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering (He) from gold-197 nuclei (197AU). The energy of the incoming helium nucleus was 7.09 x 10-13 J, and the masses of the helium and gold nuclei were 6 3.29 x 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.) (a) If a helium nucleus scatters to an angle of 115° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 120° He nucleus Gold nucleus 4He speed 14562052.73 x m/s 197Au velocity x m/s 1160023.058 197 Au direction -12.76 X ° counterclockwise from the +x-axis (b) What is the final kinetic energy (in J) of the helium nucleus?