5  Conclusions.

In this second paper concerning the resurrection of the Bohr/Sommerfeld theory of atomic structure, the primary objective was to incorporate the mechanical aspects of electron spin. The accomplishment of this objective can be summarised as follows.

5.1   Electron Spin Cause.

Because this theory is one in which the electron especially is treated as a real physical particle, and is postulated to possess real physical spin, it is necessary to also propose a cause of that spin. Also, because it has been ëstablished" from empirical data that certain orbital transitions involve a change in the direction of spin, it is necessary that any proposed mechanism for electron spin must include a natural means to induce spin reversals. The mechanism proposed here, based upon the Lorentz-Fitzgerald relativistic contraction of the electron due to its high orbital velocity, meets both of the above requirements without incurring anomalies in the energy or emission characteristics of the atom.

5.2   Spin Angular Momentum Quantisation.

The quantisation of electron spin was accomplished in an identical manner to that of the principle quantum number for the orbital motion in [1]. This was possible because the two motions, albeit driven by the same source are completely independent. Consequently the spin quantum number must be treated as a principle quantum number in its own right. This helped to define its unique value.

5.3   Spin Mechanical Effects.

Having established the need, a proposed mechanism and the quantisation of electron spin, it was possible to establish the mechanical effects of this motion on the spectral signature of the atom.

5.3.1   Electron Orbital Transition Initiation.

The first effect is the inherent condition that causes an electron to initiate an orbital transition. Irrespective of the direction of the spin, its magnitude is sufficient to cause the circumferential velocity to exceed the terminal velocity of D0, ( ~ the velocity of light). The electron will then shed a number of energy quanta in the form of a photon emission to avoid that anomaly. The direction of photon emission does not appear to depend upon the direction of electron spin because both forward and backward emissions can take place from an electron with either spin direction. This is a question which would need further investigation. The Compton recoil that the photon emission imparts to the electron then determines the nature of the change to its orbital angular momentum and spectral emission. Despite the detail that has been presented here on this effect, the mechanism so described is still incomplete. It will be finalised in a future paper in which the cause of the Lamb Shift is introduced.

5.3.2   Spin Relativistic Mass Increase.

The mass increase incurred as a result of electron spin will be relativistically significant because of the high spin rate, such that the quantum criteria level is approached. This mass increase augments that due to the orbital motion to result in the total relativistic mass of the electron. However, in determining the orbital path rotation due to relativistic effects it is only that part of the relativistic mass increase due to the orbital motion that is taken into account. This is because the matter wave associated with that motion, and used in the determination of the principle and azimuth quantum numbers, is a representation of the kinetic energy of the orbital motion only. The spin relativistic mass increase is similarly treated in isolation when quantising that motion. The consequence is that although the spin relativistic mass increase contributes to the overall mass increase of the electron, and therefore the atom, it does not contribute to the electron's orbital bound energy and is therefore not an influence in the spectral signature.

5.3.3   Mechanical Spin Energy.

In a similar manner to the relativistic mass increase discussed above, the mechanical spin energy of the electron, while contributing to the overall energy of the atom, would not form part of the orbital bound energy of the electron. It would not therefore be involved in defining spectral emission wavelengths.

5.3.4   Selection Rules.

In treating the electron as a real physical particle, it has been possible to derive, in detail, the Selection Rules for electron orbit shell transitions, in terms of orbit geometry and the direction of photon emission. All of the so-called permitted orbit transitions have been so derived. This includes those for which a spin reversal is involved. The reason for the appearance/non-appearance of spin reversal is also clear and is seen to be a consequence of the spin relationships to the orbital quadrants involved in the transition. Furthermore, for those transitions that are not permitted, the reasons have also been determined. The only one for which a potential disagreement exists between the current quantum theory and that proposed here is for those excluded transitions for which Dnj = ±2. This condition exists because the spin reversal incumbent in these potential transitions incurs a spin angular momentum change that is in the same direction as the associated orbital angular momentum change. Because the spin and orbital motions are completely separate there should not be any quantum reason why the angular momentum associated with these two motions could not change in the same direction during a transition. The exclusion of the two transitions in question is therefore believed to be for orbital geometrical reasons alone. The Dnj condition must obviously be associated with this geometrical limitation but is not believed to be the primary factor involved.

The overriding conclusion drawn from the results of this paper, is that the mechanical aspects of the spin of a real physical electron particle have been satisfactorily incorporated into the resurrected Bohr/Sommerfeld theory of atomic structure presented here and have thereby provided a clearer insight into some of the mechanisms involved. However, it is noted that on several occasions, to progress matters smoothly, it has been necessary to introduce results that will only be fully developed in future papers. Recourse to future results in this fashion is frequently necessary in the development of complex, lengthy concepts. The results so used here will, in the next two papers, be adequately developed to fully justify such premature use. The first of these papers will cover the magnetic dipole coupling of electron orbit and spin to produce the fine structure splitting of the spectra.

One final, but significant point of a philosophical nature needs to be mentioned. Although the mechanical aspects of electron spin are not involved in producing the spectral signature, it is believed to be one of the most important features of atomic structure. Without it there could be no electron orbital transitions and consequently the nature of matter throughout the entire Cosmos, and all chemical and biological processes within it, would be very severely restricted. It is an astounding consequence that the nature of all things should be largely governed by the spinning of a simple elementary particle less than 6E-13 centimetres in diameter.



P3 Version 1.0.2
Ó P.G.Bass, April 2008

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