Borel's model How the potential energy of the electron is derived

First of all, the hydrogen atom is the best specimen because it has only 1 electron, and this electron has no orbital angular momentum, which means that this electron moves in a uniform circular motion around the hydrogen nucleus: the Coulomb gravitational force provides the centripetal force: ke?/r?=mv?/r......①.

Electron's potential energy Ep in Coulomb field is derivative of gravitational force to distance, Ep=dF/dr=-ke?/r......② to infinity as zero potential energy surface

Electron's kinetic energy Ek=0.5mv?......③ , substituting ① into ③, we have Ek=0.5ke?/r=ke?/2r......④.

Total electron energy E=Ek+Ep=-ke?/2r≈-9×(10^9)Nm?/C?×[1.6×10^(-19)C]? ÷ [2 × 5.292 × 10^(-11)m] ≈ -2.17687 × 10^(-18)J ≈ -13.60544eV

Where 9 × (10^9)Nm?/C? is the Coulomb constant, 1.6 × 10^(-19)C is the electron charge, and 5.292 × 10^(-11)m is the first Bohr radius of the hydrogen atom, the radius of electron rotation in the ground state of the hydrogen atom.