If an alpha particle (two protons and two neutrons) is given an initial (nonrelativistic) velocity vvv at a very far distance and is aimed directly at a gold nucleus (Z=79Z=79), what is the closest distance ddd the alpha particle will come to the nucleus? In this problem you can estimate that the mass of the proton mpmpm_p is equal to the mass of the neutron and only consider the effects of a single gold nucleus. Assume that the alpha particle comes close enough so that the nucleus is not substantially screened by inner-shell electrons. Express your answer in terms of mpmpm_p, the permittivity