Question

A proton (mass m, charge +e) and an alpha particle (mass 4m, charge +2e) approach one another with the same initial speed v from an initially large distance. How close will these two particles get to one another before turning around?

Answer 1

The kinetic energy of the moving particles is completely transformed into electric potential energy at the point of closest approach.

$U_e = K\\ \frac{k(e)(2e)}{r^2} = \frac12 (m)v^2 + \frac12 (4m)v^2$

$r=\frac{4ke^2}{5mv^2}$