#### Answer

The number of revolutions that the electron makes per second is $6.6\times 10^{15}~rev/s$

#### Work Step by Step

The centripetal force is the net force which keeps an object moving in a circle. In this case, the electric force provides the centripetal force to keep the electron moving in a circle. We can find the speed of the electron.
$F = \frac{mv^2}{r}$
$v^2 = \frac{F~r}{m}$
$v = \sqrt{\frac{F~r}{m}}$
$v = \sqrt{\frac{(8.2\times 10^{-8}~N)(5.3\times 10^{-11}~m)}{9.1\times 10^{-31}~kg}}$
$v = 2.185\times 10^6~m/s$
We can use the speed to find the number of revolutions per second. Let $N$ be the number of revolutions per second.
$N = (v)(\frac{1~rev}{2\pi ~r})$
$N = (2.185\times 10^6~m/s)(\frac{1~rev}{(2\pi)(5.3\times 10^{-11}~m)})$
$N = 6.6\times 10^{15}~rev/s$
The number of revolutions that the electron makes per second is $6.6\times 10^{15}~rev/s$