(a) A gold nucleus contains 197 nucleons packed tightly against each other. A single nucleon (proton or neutron) has a radius of about 1.310-15 m. Calculate the approximate radius of the gold nucleus. (Hint: Remember that the volume of a sphere is (4/3)r3.)
_____ m
(b) Also calculate the approximate radius of the alpha particle, which consists of 4 nucleons.
_____ m
(c) Rutherford correctly predicted the angular distribution for 10-MeV (kinetic energy) alpha particles colliding with gold nuclei (1 MeV = 1106 eV). What initial kinetic energy in MeV must alpha particles have (when far from the nucleus) in order to make contact with a gold nucleus? An alpha particle consists of 2 protons and 2 neutrons; a gold nucleus consists of 79 protons and 118 neutrons. Assume that the massive gold nucleus hardly moves in this interaction. (If contact is made, the strong interaction will come into play, and the angular distribution will deviate from that predicted by Rutherford, which was based solely on electric interactions.)
_____ MeV