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The Entropy Reduction Laboratory

Tetrahedral Sphere and the PSE
The TETRAHEDRON is one of the platonic bodies. It has four corners and four regular triangles as sides. There are three pairs of othogonal edges, the total number of edges is six.
The TETRAHEDRAL SPHERE is the central projection of the tetrahedron onto the surface of the unit sphere. The triangular sides of the tetrahedron become spherical triangles on the surface of the sphere.
the PSE

The four electrons sit at the corners of a tetrahedron. Alternatively, if the electronic charges are assumed to be spread out evenly - in this highly symmetric static model - each electron covers one of the four spherical triangles on the surface of the sphere.
The element with Z=4 electrons is the element Beryllium.
in space
and the
    In the periodic system of the elements, for high atomic numbers Z the central Coulomb potential, as seen by a shell electron, is modified by the interaction with all the other shell electrons. Therefore, it appears reasonable that the filling of states is not realized any more in accordance with the Hydrogen spectrum. For low Z, the Coulomb potential will be far less modified than in the high Z case and the indicated argument fails. Therefore, the crucial question is: What effect produces the fourfold degeneracy of the electronic state constituting the lowest double shell of the PSE ? By the Pauli Principle, due to electronic spin, only a twofold degeneray of electronic states is expected. For explanation of the fourfold degeneracy, the following model is offered:

    Two electrons define a line, three a plane. This plane may have any orientation in space. Therefore, to define three-dimensional isotropic space, four electrons are required. Since under the supposition that the nucleus, consisting of different kinds of particles, does not contribute to the definition of three-dimensional isotropic space, in case of the atomic shell electrons also at least four electrons are required for granting highest symmetry. In the state of highest symmetry, the electrons are arranged to form a tetrahedron. Each two of the four electrons at the corners of the tetrahedron may be viewed as having opposite spin and sitting on one of two orthogonal edges. Thus, in addition to the spin quantum number s, for full classification, a new quantum number, which shall be called the topical quantum number c , is required. A visualization of a pair of electron pairs with orthogonal spin axis is presented in Electron's 3D space and spin (Java applet).
    Since the tetrahedron is a self related Platonic body and the Platonic spheres are of the same symmetry as the Platonic bodies, the electronic charges may be considered to be spread out evenly over the surface of the Tetrahedral Sphere, where each electron covers one of the four spherical triangles. By this tranformation, the role of the topical quantum number is not changed.If spin and topical quantum number cause the fourfold degeneracy of the lowest state in the PSE, one might infer, that this degeneracy will extend to the higher states and cause the Occupation of States accordingly.
    In summary, the fourfold degeneracy appears to be a consequence of the inherent degree of freedom a particle with spin experiences in isotropic space. The resulting Double Shell Periodic System images directly the sequence of occupation of electronic states.

Rotation To rotate the spheres, click on a selected sphere and drag the mouse.
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Last update of the page: April 20, 2003