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) fromgold-197 nuclei (197Au). The energy of the incominghelium nucleus was 7.39 ✕ 10−13 J, and the masses of thehelium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕10−25 kg, respectively (note that their mass ratio is 4to 197). (Assume that the helium nucleus travels in the +xdirection before the collision.)
(a)
If a helium nucleus scatters to an angle of 102° 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?
