Closest approach ...

When an alpha particle approaches a heavy nucleus (gold) on the line of centers, the distance of closest approach gives an upper limit on the size of the nucleus. It is a relatively simple matter to calculate this minimum distance by equating the kinetic energy of the alpha particle with the maximum potential energy in the field of the target nucleus.

PE in an inverse square force field is given by ...

If the energy of an alpha particle is 5.5 MeV, the distance of closest approach to a gold nucleus (atomic number 79) is given by....