Question

The kinetic energy of the electron in hydrogen atom is ______________. (εo is permittivity of free space, 'e' is charge of an electron and 'r' radius of orbit of an electron)

Answer 1

There is an electrostatic Force exist between nucleas and electron
It’s given by F_electrostatic = [1/(4πε₀)] × e²/r²

Centripetal Force of rotating electron is
F_centripetal = mv²/r

By using above two relations I’ve solved kinetic energy of electron in hydrogen atom.
See 2nd image for derivation.