Answer
$5.2\times10^{-11}$m
Work Step by Step
For the force between charged particles we use $F = k\frac{Q_{1}Q_{2}}{r^{2}}$, where $k = 8.99\times10^{9}$.
For circular motion we use $F = \frac{mv^{2}}{r}$.
Combining these and solving for $r$ we get $r =k\frac{Q_{1}Q_{2}}{mv^{2}} $.
We then substitute for all of our known values: $r = (8.99\times10^{9})\frac{(1.602\times10^{-19})(1.602\times10^{-19})}{(9.11\times10^{-31})(2.2\times10^{6})^{2}}$
$r = 5.2\times10^{-11}$m