Equilateral Spherical Triangles and Electrons in the Atom
editWhen drawn on a sphere’s surface, an equilateral spherical triangle with the area of a third of its sphere’s area, automatically divides the total surface area into three identical triangles. This special case locates their three shared vertices in three-dimensional space. These vertices are equidistant from each other and the same distance from the center point. The three identical angles linking the center points to the vertices are of 120 three-dimensional degrees. This is exactly as the Quarks in Hadrons are arranged. There are no direct links between the configurations of the theoretical triangles and the physical Quarks, but the coincidence is not surprising.
Both have concerns with efficiency, symmetry, change and distribution of responsibility. (If you can forgive the anthropomorphisms).
Any odd number of equilateral spherical triangles with the same area characteristic as three divides the total area of any sphere into that odd number’s number of equilateral spherical triangles. Other examples relevant to the atom are five and seven but the limit is infinite.
If radii of the sphere are drawn from the center point of each equilateral spherical triangle these take the same form as virtual lines to the center point through the three lobes of Electrons that support the first set of atom’s nuclei. This is the same in the five lobes of the following thirty-six and seven in the remainder. Instability of ultra heavy atoms prevents nine being realistic.
Physical Implication
This development of an effective and economic energy configuration was crucial in the Hadron’s stabilization phase of the beginning of the Universe and still is crucial in the functioning of Atoms.
During the expansion phase, the external spherical energy layers reached the point where the first Quarks formed, initially dropping to the energy levels of “Down” where they could begin to combine to form multi-particle structures, the first versions of which were unstable. As they fell further, a proportion morphed into “Up” and the first mixed trios of structural Quarks began to naturally collect at the vertices of a virtual sphere with the Quarks that formed the Gluons and Mesons collecting at the central point of that sphere. These latter Quarks reacted with structural Quarks to create the process that stabilizes atomic nuclei.
The minute energy produced by the process of Neutrons changing to Protons appeared as Electrons that facilitated the production of stable atoms. Thus, the dimensions of the virtual sphere of the first experimental conjunction of Quarks became standard for all the Hadrons that have followed.
The three structural Quarks set their equidistant positions in space as these points minimized their mutual conflict and allowed the Gluons and Mesons, that appeared at the same time, to become tied into a communal survival team that formed the Hadrons.
Hydrogen is the archetypal atom consisting of a Proton and an Electron. The positive Electric Charge leaks from the nucleus of the Proton in a three-dimensional manner and, due to its need to maintain a value of one throughout its range, extends a proportionally long distance from the nucleus. The Electron, before it was captured, was incapable of any movement being dependant on an atom being close enough to reach out for it. When they make contact the Electron’s movements are controlled by variations in the positive charge which are due to the activity within the nucleus to keep its Quarks from the brink of instability.
Should the Proton encounter a Neutron before an Electron a Deuteron nucleus is created. When another Deuteron or another Proton and Neutron connects to it a Helium nucleus is formed. The shape of the Nucleus is not simple as the four Hadrons involved connect at 120 three dimensional degrees. The resulting pool of Electric Charge’s shape reflects this and its need to maintain its value at plus one to match the Electrons of minus one. When an Electron is in range, once connected to the pool of charge, its motion is determined by the constant change in the pool’s shape
The first connections between Quarks occurred when the initial Deuterons atoms’ nuclei, based on a Proton/Neutron union, appeared. The junction between the two occurs between complementary “facets” that are one of the three the virtual equilateral spherical triangles that look outward from the main internal activity. The two facets, one from each Hadron, overlap with each virtual equilateral spherical triangle making a perfect seal, the external energies merging and their survival activity synchronizing to mutual benefit. The vast energies involved are those that make it almost impossible to separate them.
The new entity had four unused facets and, in the absence of Electrons, enjoined with others using two from the Deuteron nucleus, or one each of a lone Proton and Neutron, to form a Helium nucleus.
In the absence of Electrons, the Helium nucleus attracts Hadrons. If that absence is maintained over a suitable time interval the nucleus will sequentially step through the other element configurations adding the appropriate Hadrons until sufficient Electrons are encountered to create an element. As the second of the first two, Lithium and Beryllium, is formed, the pair of Electrons that convert it from nucleus to element must have opposite “spins.” If that does not happen one of them will alter its spin.
Taking Beryllium as an example, its conversion from nucleus to element involves the capture of four Electrons, two that could have made a Helium atom, one that could have made Lithium and one for itself. The Electrons would inhabit two concentric three-dimensional rings of space around the Nucleus, each containing a pair. The inner ring contains what would have been a Helium atom’s Electrons if the heavier nucleus of Lithium had not bonded to the Helium nucleus before Electrons were encountered
The cumulative Electric Charge due to the next atom in the sequence, Boron, was the foundation for a more efficient usage in the increase in three-dimensional space that was made available by the addition of nuclei as they were added.
The extra space that built up as Carbon, Nitrogen, Oxygen and Fluorine and Neon appeared was sufficient for suitable pairs of Electrons to operate in one of the three “lobes” that evolved. These first lobes are separated by 120 three-dimensional angles and Electric Charge that reflects the shape of each nucleus. The resulting variations in charge controls Electrons with no interference between lobes taking place.
After Neon, the second non-reactive atom, another space for a spherical concentric ring of two Electrons followed by a similar run of six elements was completed by Argon. The Electrons added by each new element extended the existing lobes. The number of elements between the non-reactive elements depended on how many there were until there were no “facets” available for connection.
After Argon the arrangement of elements before the next one with no facets to allow connection rose to eighteen, including a pair making a base spherical concentric ring of two Electrons. This growth in numbers drove the volume of positive charge as the number of elements grew. The increase in the space made available allowed the development of five lobes. After the next non-reactive element, Krypton, a similar run of eighteen elements terminated with Xenon. The next string of consisted of thirty-two elements terminating with Radon and developed seven lobes. This pattern would have continued with nine lobes of electrons but the theoretical resulting elements are non-viable.
If the detail of the Electrons surrounding a heavy metal such as Gold could be made visible the nearest thing that it would resemble is a spherical Sea Urchin with three layers of offset spikes surrounding a small spherical core.
The whole organization of atoms from the structure of individual nuclei, the structure of groups of nuclei and the clusters of Electrons that surround them are based on the equilateral spherical triangle. The fundamental reason for this is that the positions up taken in three dimensions by Quarks in the atom are the most efficient possible and shape any edifice that is built upon them.
Sources
editAll sources came from Wikikpedia
1/ Spherical Trigonometry - other than the effect of curvature on angles its content is not relevant to the atom.
2/ A document that no longer exists in Wikipedia showed the Electrons in Sub-shells for each element against their atomic symbols.
3/ Quark
4. Electronic Structure