Table 1: The different models of single-electron ion/atom.

 Model ® Bohr atom Planetary Relativistic Planetary- Relativistic Final Planetary- Relativistic a- Momentum Le = hn/2p Le + Lnu = hn/2p Le = hn/2p Le + Lnu = hn/2p Le + Lnu = hn/2p Centrifugal force Fe = me0ve2/Re - Fe = me0ve2/Re Fnu = M0vnu2/Rnu F1 = me0ve2/(1 - ve2/c2)1/2Re - F1 = me0ve2/(1 - ve2/c2)1/2Re F2 = M0vnu2/(1 - vnu2/c2)1/2Rnu F1 = me0ve2/(1 - ve2/c2)1/2Re F2 = M0vnu2/(1 - vnu2/c2)1/2Rnu Coulomb force FC = Ze2/[4pε0×Re2] FC = Ze2/[4pε0×(Re+Rnu)2] FC = Ze2/[4pε0×Re2] FC=Ze2/[4pε0×(Re+Rnu)2] FC = (Z+A×Z7/3)e2/[4pε0×(Re+Rnu)2] A » -2.81×10-6 Electron Ee = -meZ2e4/[8e02h2n2] Ee= -meM2Z2e4/[(me+M)28e02h2n2] Ee= me0c2×(1 - Z2e4/[4e02h2n2c2])1/2 - me0c2 Ee = me0c2×(1 - ve2/c2)1/2 - me0c2 Ee = me0c2×(1 - ve2/c2)1/2 - me0c2 Atomic nucleus - Enu = -me2M0Z2e4/[(me+M)28e0h2n2] - Enu = M0c2×(1 - vnu2/c2)1/2 - M0c2 Enu = M0c2×(1 - vnu2/c2)1/2 - M0c2 Electron- atomic nucleus bond E = -meZ2e4/[8e0h2n2] E = -meM0Z2e4/[8(me+M)e02h2n2] E = me0c2×(1–Z2e4/[4e02h2n2c2])1/2 - me0c2 E = me0c2×(1 - ve2/c2)1/2 - me0c2 + M0c2×(1 - vnu2/c2)1/2 - M0c2 E = me0c2×(1 - ve2/c2)1/2 - me0c2 + M0c2×(1 - vnu2/c2)1/2 - M0c2 H b- 0.0539% -0.0006% 0.0552% 0.00071% 0.000181% Kr35+ b- -1.6885% -1.6891% 0.0689% 0.06822% 0.000189% Maximum b- -1.6885% (Kr35+) -1.6891% (Kr35+) 0.0689% (Kr35+) 0.06822% (Kr35+) 0.00364% (Li2+) Average c- 0.5764% 0.5763% 0.0336% 0.02978% 0.001157%

Here Re and Rnu are distances between center of mass and electron and atomic nucleus, me0 and M0 are the rest mass of electron and atomic nucleus, ve, vnu and v the speed of electron, atomic nucleus and sum of speed electron and atomic nucleus, Z the number of element, e the electrical charge, ε0 and h are the dielectric and Planck’s constants, c the speed of light. a- v = (Z + A×Z7/3)e2/[2nh ε0]; thβe = ve/c = {(1 - [2cos(j/3) + 1]/[3ch2β])1/2 - (1 - [2cos(j/3 + 2p/3) + 1]/[3ch2β])1/2 + (1 - [2cos(j/3+ 4p/3) + 1]/[3ch2β])1/2}/2 + thβ /2; j = arccos(1 - 54sh2β ch4β ch2β Msh2β M); chβ M = [M2/(M2 - me2)]1/2; shβ M = [me2/(M2 - me2)]1/2; chβ = 1/[1 - (v/c)2]1/2; shβ = (v/c)/[1 - (v/c)2]1/2 ; thβ nu = thβ - thβ e; b- 100%×(E - Iexperim) /Iexperim; c- 100%×S½E - Iexperim½/Iexperim)/N, N = 36.