The KE of the electron in an orbit of radius r in hydrogen atom is (e = electronic charge) e²/r, e²/2r, e²/4r, e²/2r²

The centrifugal force acting on the revolving electron is balanced by the electrostatic force acting between the electron and the nucleus of hydrogen atom so that the electron revolves in a certain fixed orbit.
∴Fcentrifugal=Felectrostatic
OR
mv²/r=ke²/r²
We get
mv²=ke²/r
Thus kinetic energy of electron
K.E=1/2mv²=ke²/2r=e²/2r (putting k=1 in some unit)