In 1911, Ernest Rutherford developed a planetary model of the atom, in which a small positively charged nucleus is orbited by electrons. The model was motivated by an experiment carried out by Rutherford and his graduate students, Geiger and Marsden. In this experiment, they fired alpha particles with an initial speed of 1.75 x 107 m/s at a thin sheet of gold. (Alpha particles are obtained from certain radioactive decays. They have a charge of +2e and a mass of 6.64 x 10-27 kg.) How close can the alpha particles get to a gold nucleus (charge = +79e) along a head-on trajectory, assuming the nucleus remains stationary and ignoring the effects of the gold atom's electrons? (This calculation sets an upper limit on the size of the gold nucleus.)