An alpha particle $($charge $2$e and mass $6\mathrm{.}64\backslash$times $10^27$ kg $)$ is shot towards a stationary gold nucleus $($charge $79$e$).$ When the two particles are $10$cm apart, the alpha particle moves with a speed of $1000$m$/$s: a$)$ The speed of the alpha particle when it is $1\mathrm{.}00$mm away from the gold nucleus. b$)$ The distance of closest approach before the alpha particle bounces back.