hydrogen atom frequency and wavelength

Derivation of Formula for the Calculation  of the frequency of radiation in hydrogen atom, bohr’s theory

According to bohr’s quantum condition when an electron is revolving around a nucleus in an atom , it does not emit radiation, when it got excited , it jump from one energy level (lower) to another energy level (higher) . Therefore when it return back to its ground state(original unexcited energy level) it emit energy inform of radiation, the difference between the two energy level is given as ∆E = hf where E1 and E2 are energies of the electron in 1st and 2nd orbit respectively h is the plank constant and f is the frequency f the radiation. total energy of an electron is the sum of its potential and kinetic energy , the  kinetic energy is given as ½[mv2] while potential energy is given as the workdone in bringing  an electron of charge e from infinity at a distance r to nucleus of charge Ze,