Ernest Rutherford (the first New Zealander to be awarded theNobel Prize in Chemistry) demonstrated that nuclei were very smalland dense by scattering helium-4 nuclei (4He) from gold-197 nuclei(197Au). The energy of the incoming helium nucleus was 7.78 ✕ 10−13J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is4 to 197). (Assume that the helium nucleus travels in the +xdirection before the collision.)
(a)
If a helium nucleus scatters to an angle of 130° during anelastic collision with a gold nucleus, calculate the heliumnucleus' final speed (in m/s) and the final velocity (magnitude inm/s and direction counterclockwise from the +x-axis) ofthe gold nucleus.
4He speed _________ m/s
197Au velocity_________ m/s
197Au direction__________ ° counterclockwise from the+x-axis
(b)
What is the final kinetic energy (in J) of the heliumnucleus?
_________ J
