Please provide the formulae and complete derivation of energy of electron in nth orbit (En)

The energy of electron revolving in a stationary orbit is of two types:

Kinetic energy which is due to velocity and potential energy which is due to position of electron.

From the first postulate of Bohr’s atom model:

Where m is mass of electron, v is linear velocity, r is radius of orbit in which e revolves around the nucleus.

Necessary centripetal force for revolution of electron is provided by the electrostatic force of attraction between electron and nucleus whose charge is Ze where Z is the atomic number of the atom.

So,