The electron revolves in a circular orbit of radius r around a nucleus with a charge Ze.

The electron revolves in a circular orbit of radius r around a nucleus with a charge Ze. What is the speed and period of rotation of an electron?

The force acting on an electron is determined by Coulomb’s law:
F = 1 / 4πέέ0 * e * Ze / r ^ 2, where e is the electron charge.
According to Newton’s second law F = m * a, then we get:
a = 1 / 4πέέ0 * e * Ze / r ^ 2 * m, where m is the electron mass.
since a = v ^ 2 / r we get v = √a * r = √1 / 4πέέ0 * e * Ze / r * m
orbital period T = 2πr / v