_{1}

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The purpose of this contribution was to evaluate a recently published atom model for Helium, characterized by a double rotation of the electrons which exhibit perpendicular rotation axes. Thereby, each rotation is induced by the spin of one electron [1] . Hereto, a tangible mechanical model was used which facilitated to derive the mathematical formulae as the basics for two-dimensional projections, and—not least—for a digital animation yielding freeze images from different perspectives. The resulting shape of the electron shell turned out to be not spherical. In particular, the total velocity of the electrons is variable since the relative running direction may change—in contrast to the initial assumption—, even leading to an intermittent standstill, and implying a variable kinetic energy. Thus it can be concluded that this model describes a rotating rotor but not the Helium atom, and that it must be abandoned.

According to the conventional theory of quantum mechanics, the electron trajectories in atoms and in molecules are assumed as indeterminable and solely describable by probabilities of presence, implying Heisenberg’s uncertainty principle. In the case of Helium—the element with the most simple singular atoms—, the symmetry of the double-occupied 1s orbital is assumed as strictly spherical, exhibiting no asymmetry or anisotropy. The charge cloud model proposed by Kimball [

In contrast to this atom- and molecule-model where probabilities of presence are assumed, the author’s alternative approach is based on the assumption of well-defined electron trajectories. It proceeds from Bohr’s planar hydrogen model, published in 1913 [

As the author could point out in [_{2}-molecule known from X-ray-spectroscopic measurements, using normal physical laws and the condition of the constant orbital momentum for each electron. In the next step, a 3D atom model for the noble gases Helium and Neon was conceived [_{2}-model since no precise empiric data exist for its verification. Therein, the two electron orbits of the first shell were arranged as double cones, cf.

mechanical model which facilitated to derive the mathematical formulae as the basics for two-dimensional projections, and—not least—for a digital animation yielding freeze frames from different perspectives.

As outlined in [_{tot})^{2} = 2(u_{rot})^{2}.

In order to visualise the resulting electron trajectories, it was advantageous to construct a tangible mechanic model which can be manually stirred. Thereto, the kit of Stokys was used. The here applied model is shown from two different perspectives and at two different rotation angles in

In order to 2D-describe the electron trajectories in a Cartesian coordinate system (defined in

x = R ⋅ sin φ ( 1 + cos φ ) , y = − R ⋅ cos φ , z = R ( cos φ − ( sin φ ) 2 )

For the other electron, the formulas are identical equal except the sign. The respective diagrams for the two electrons are shown in the

Note: These formulas are analogous to those given in [

The availability of the x/y/z-parameters as a function of the rotation angle enables to easily determine the trajectory projections on the three possible planes, namely the x/y-, the x/z- and the y/z-plane. They are displayed in Figures 8-10. The respective shapes are exceptional and do not resemble to any known geometric figures. Obviously, they exhibit sharpened points which indicate standstills. Thus the motion is not continuous and constant.

In order to visualize the three dimensional shape of the electron trajectories, 3D-animations were made using a VPython computer program. The resulting images strongly depend on the—virtual—camera positions, implying different perspectives. From the numerous possibilities, the four examples shown in Figures 11-14 as freeze images were chosen.

The here presented figures yield a deepened and clearer comprehension of the recently published atom model of Helium [

I thank Dr Andreas Rüetschi-Isler for his critical objections enabling a distinct assessment and David Kummer for performing the 3D-animation and their freeze images.

The author declares no conflicts of interest regarding the publication of this paper.

Allmendinger, T. (2019) The Revision of the Alleged Spherical Atom Model of Helium. Journal of Applied Mathematics and Physics, 7, 1212-1219. https://doi.org/10.4236/jamp.2019.75081