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.