Answer
$v = 2.2\times 10^6~m/s$
Work Step by Step
We can find the speed of the electron:
$\frac{mv^2}{r} = \frac{k~q^2}{r^2}$
$v^2 = \frac{k~q^2}{m~r}$
$v = \sqrt{\frac{k~q^2}{m~r}}$
$v = \sqrt{\frac{k~q^2}{m~(\frac{\hbar^2}{m~k~q^2})}}$
$v = \sqrt{\frac{k^2~q^4}{\hbar^2}}$
$v = \frac{k~q^2}{\hbar}$
$v = \frac{(9.0\times 10^9~N~m^2/C^2)(1.6\times 10^{-19}~C)^2}{1.0546\times 10^{-34}~J~s}$
$v = 2.2\times 10^6~m/s$
