Energy of Electron in Each Orbit

For hydrogen atom, the energy of the revolving E, is the sum of its kinetic energy ( ½ mv²) and potential energy ( –e²/r).

E = ½ mv² – e²/r ----------- (4)

From equation (1)

mv² = e²/r

Substituting the value of mv² in (3)

E = ½ e²/r – e²/r

Or,

E = –e²/2r -------------(5)

Substituting the value of ‘r’ from equation (3) in (5),

E = – e²/2 × 4π2me²/n²h²

E = – 2 π²me⁴/n²h²

By using proper integer for ‘n’ (quantum number), we can get the energy for each orbit.