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Journal of Modern Physics

The Spinning Period of a Free Electron and the Periods of Spin and Orbital Motions of Electron in Atomic States

Ziya Saglam, M. Sağlam, Servet Bayram, Tim Horton

Published Jan 1, 2015• 1 citation
Publisher

Abstract

The spinning period for a free electron and the periods of spin and orbital motion of the electron in an atomic state have been calculated. We have shown that for a free electron the spinning period is: (Ts)free=1.9×10-20s. But in the atomic case we show that, both the spin and the orbital periods depend on the quantum numbers n, ml, ms and the effective Landé-g factor, g* which is a function of the quantum number l of the atomic state given in Dirac notation. We have also calculated these periods for the ground state and some excited states—hydrogen and hydrogen-like atoms. For atomic states the approximate values of spinning period are and the related orbital periods are: (T0)atomic=(10-16-10-15)s. Therefore atto-second processes which are related to the pulse of 10-18 s will filter the orbital motion of the electron but will be long enough to detect the details of the spin motion, such as flip-flops.

DOI
10.4236/jmp.2015.615229

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The spinning period for a free electron and the periods of spin and orbital motion of the electron in an atomic state have been calculated. We have shown that for a free electron the spinning period is: (Ts)free=1.9×10-20s. But in the atomic case we show that, both the spin and the orbital periods depend on the quantum numbers n, ml, ms and the effective Landé-g factor, g* which is a function of the quantum number l of the atomic state given in Dirac notation. We have also calculated these periods for the ground state and some excited states—hydrogen and hydrogen-like atoms. For atomic states the approximate values of spinning period are and the related orbital periods are: (T0)atomic=(10-16-10-15)s. Therefore atto-second processes which are related to the pulse of 10-18 s will filter the orbital motion of the electron but will be long enough to detect the details of the spin motion, such as flip-flops.
The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time.The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae.The quantization of the spin motion has been done on the basis of the old quantum theory.It gives a quantum number n = 1/2 as the index of the spin state acceptable for both the electron and proton particle.In effect of the spin existence the electron motion in the hydrogen atom can be represented as a drift motion accomplished in a combined electric and magnetic field.More than 18,000 spin oscillations accompany one drift circulation performed along the lowest orbit of the Bohr atom.The semiclassical theory developed in the paper has been applied to calculate the doublet separation of the experimentally well-examined D line entering the spectrum of the sodium atom.This separation is found to be much similar to that obtained according to the relativistic old quantum theory.
Based solely on internationally recognized laboratory measured data of the ground-state hydrogen atom, this paper conducts complete calculation and logical derivation of the whole process of electron orbital motion. The whole process includes all core parameters and derivation processes, such as orbital circumference, revolutions per second, equivalent plane square calculation of flattened spherical surface, total number of orbital positions and spatial traversal times, abandoning all subjective assumptions and complex solid geometry disputes. The research clearly shows that the electron has a unique and fixed orbital position at every moment, without quantum superposition state or spontaneous transition. The so-called electron cloud is only the trajectory coverage effect formed by the ultra-high-speed motion of electrons; the so-called quantum superposition state and quantum transition are both misunderstandings of classical deterministic orbital motion. Based on measured data, this paper negates the core hypotheses of electron cloud, superposition state and quantum transition in quantum mechanics with verifiable calculation and logic, proving that electrons are always in deterministic orbital motion, and the stability of atoms is completely governed by classical mechanical rules.
The motion of circular wave packets for one electron in a central Coulomb field with a high atomic number Z is calculated. The wave packet is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects, in particular the spin-orbit potential. A time scale is defined within which spin dynamics must be taken into account, mainly in atoms with high Z. Within this time scale there exists a mechanism of collapses and revivals of the spin, already shown by the authors for harmonic oscillator potential and called the spin-orbit pendulum. Though this effect does not have the exact periodicity of the simpler model, the wave packet spatial motion is nevertheless quite similar.
The fine structure of hydrogen energy was calculated by using the usual momentum-wavefunction relation directly, rather than establishing the well-known Dirac wave equation. As the results, the energy levels are completely the same as that of the Dirac wave equation, while the wavefunction is single component that is quite different from Dirac's four component wavefunction, the most important thing is that the present calculation brings out electronic spin in a new way which has never been reported and indicates that the electronic spin is a kind of orbital motion.
Abstract 1. In a recent paper Dirac* has brilliantly removed the defects before existing in the mechanics of the electron, and has shown how the phenomena usually called the “ spinning electron ” fit into place in the complete theory. He applies to he problem the method of q-numbers and, using non-commutative algebra, exhibits the properties of a free electron, and of an electron in a central field of electric force. In a second paper † he also discusses the rules of combination and the Zeeman effect. There are probably readers who will share the present writer’s feeling that the methods of non-commutative algebra are harder to follow, and certainly much more difficult to invent, than are operations of types long familiar to analysis. Wherever it is possible to do so, it is surely better to present the theory in a mathematical form that dates from the time of Laplace and Legendre, if only because the details of the calculus have been so much more thoroughly explored. So the object of the present work is to take Dirac’s system and treat it by the ordinary methods of wave calculus. The chief point of interest is perhaps the solution of the problem of the central field, which can be carried out exactly and leads to Sommerfeld’s original formula for the hydrogen levels. But it is also of some interest to exhibit the relationship of the new theory to the previous equations which were derived empirically by the present writer.* It appears that those equations were an approximation to the new ones, derived by an approximate elimination of two of Dirac’s four wave functions. We shall also review a few other points connected with the free electron, the emission of radiation from an atom and its magnetic moment, and shall outline a discussion of the Zeeman effect.
The detailed motion of a free Dirac electron is investigated by examining the expectation values of the position r and of r×ṙ in a wave packet. It is shown that the well-known zitterbewegung may be looked upon as a circular motion about the direction of the electron spin, with a radius equal to the Compton wavelength (divided by 2π) of the electron. It is further shown that the intrinsic spin of the electron may be looked upon as the “orbital angular momentum” of this motion. The current produced by the zitterbewegung is seen to give rise to the intrinsic magnetic moment of the electron.