An alpha particle with a kinetic energy of $10.0 \mathrm{MeV}$ makes a head-on collision with a gold nucleus at rest. What is the distance of closest approach of the two particles? (Assume that the gold nucleus remains stationary and that it may be treated as a point charge. The atomic number of gold is $79,$ and an alpha particle is a helium nucleus consisting of two protons and two neutrons.)