In the Rutherford scattering experiment, $4\mathrm{.}00-$MeV alpha particles scatter off gold nuclei $($containing $79$ protons and $118$ neutrons$).$ Assume a particular alpha particle moves directly toward the gold nucleus and scatters backward at $180,$ and that the gold nucleus remains fixed throughout the entire process.

$($a$)$ Determine the distance of closest approach of the alpha particle to the gold nucleus.

$1m$

$($b$)$ Determine the maximum force exerted on the alpha particle.

magnitud

direction