The Particle - The wrong turn that led physics to a dead end

Engineer Xavier Borg - Blaze Labs


Development of the new model

A proper model has to be compliant with experimental evidence and so be in perfect agreement with the spectral data for each atom. It is evident from our previous discussions that each shell is equivalent to a polyhedra shell, and getting the right sequence of shells is of primary importance in order to further develop the correct sequence of polyhedra transformations for each equivalent quantum number. If quantum numbers are unique, it then follows from our knowledge about the 6 unique basic platonics (5+dual tetra), that all basic elements can be described by no more than 6 pricipal quantum numbers.

Let us first see what the present theory says. Conventionally, the maximum number of electrons in the set of orbitals, defined by the principal quantum number n = 1, 2, 3, 4 etc., (also known by their spectroscopic designation K, L, M, N, etc., ) is given by the formula Z max = 2n2 and it is presented in table below.

Principal
quantum
number
Number of electrons
in a subshell
Maximum number of electrons in a shell
n> symbol s (l=0) p (l=1) d (l=2) f (l=3) g (l=4) h (l=5) Z max
1 K 2 - - - - - 2
2 L 2 6 - - - - 8
3 M 2 6 10 - - - 18
4 N 2 6 10 14 - - 32
5 O 2 6 10 14 18 - 50
6 P 2 6 10 14 18 22 72

Electron configuration

The electron configuration of an atom might be presented by the number of electrons in each subshell, by the order of filling.

The conventional electron occupancy of the subshells of all atoms is as follows:

1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s, 5p, 5d, 5f, 5g,

giving maximum shell capacity sequence 2,8,18,32,50... etc. Theoretically, with such a theory, additional subshells such as the g, h and so on, can exist, but they are not required for any real atoms. See the scheme below:

1 1s   2
2 2s 2p   8
3 3s 3p 3d   18
4 4s 4p 4d 4f   32
5 5s 5p 5d 5f 5g   50
6 6s 6p 6d 6f 6g 6h   72
7 7s 7p 7d 7f 7g 7h 7i 98

But, by just observing the electron shells of heavy atoms, one can observe that we soon run into problems, because higher shells start to be filled up before the respective lower shell has attained its full capacity. It is a well known nightmare for chemistry teachers, that, beginning with Z=19, a vivid struggle between normal filling and exeptional filling of subshells starts. Also, according to the experimental spectral data, in the ground state, electrons fill the quantum states in the order:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d ...
respectively, giving maximum shell capacity sequence 2,8,8,18,18,32,32. If you try to follow this sequence on the above table, you will encounter 'jumping' back and forth between quantum levels, which does not make sense, since quantum levels must be filled in the same sequential order as the shells.

If you imagine building up nested platonic shapes, it makes no sense for a sequence to start within the inner structure of a completed platonic to compose the next higher shell. Once an inner structure is complete (shell filled up or 'sealed'), higher shells cannot add any part within it. We therefore see, that the conventional way of shell capacity sequencing s->p->d->f is wrong. The scheme below shows a new way, which although still uses the conventional shell & electron method, describes in a different way which shells go with each respective quantum number, and as you see it is exactly the same order shown by the sequence we got from the experimental spectral data!

1 1s   2
2 2s 2p 8
3 3s   3p 8
4 4s   3d 4p 18
5 5s   4d 5p 18
6 6s   4f 5d 6p 32
7 7s   5f 6d 7p 32

The above table matches the sequence given from spectral data, and also the maximum number of elements of 118 matches the conventional periodic table. But if we try to analyse it in terms of shell build up, there seems to be something still wrong. For example, lets take shell number 7, first we find subshell 7s (l=0), then instead of moving to the next subshells in the order s,p,d,f (l=0,1,2,3..) we see that we are first filling subshell s, and then the remaining subshells in the reverse order f,d,p. It makes sense that higher subshells (lower energy levels) get filled up before the lower subshells (higher energy levels) for each quantum shell number. This means that the table has to be shifted all by one term, in order to move the 's' subshells at the end of each shell build, thus making all shells fill up in the same order f,d,p,s as follows:

1   1s 2
2   2s 2
3   2p 3s 8
4   3p 4s 8
5   3d 4p 5s 18
6   4d 5p 6s 18
7   4f 5d 6p 7s 32
8   5f 6d 7p 8s 32

With the new scheme the quantum numbers will match the lowest energy level subshell of the shell. Quantum number 1 will thus match those subshells with total electron count of 2, quantum number 2 will match those subshells with electron count of 8 and so on. This new quantum numbering scheme now has the same filling order of the subshells and the problem of jumping is totally eliminated during the subshells' filling, with the electrons in full accordance to the present experimental data. In the conventional model, this problem occurs for example at the filling of element with atom no. 19 Calcium, instead of 3d subshell filling, the subshell 4s is filled. The same surprise occurs at the elements with atom no.37 - Rubidium and atom no.55 - Cesium). Also, in contrary to the conventional way of electron shell configuration, with this new scheme, up to 56 basic elements can be contained within the first 6 shells or 3 principle quantum numbers, and up to 120 basic elements can be contained within 8 shells or 4 principle quantum numbers. The new model, apart from being much neater, can thus contain all known elements by using just s,p,d,f shells, without the need to resort to higher shells g,h.. whose existence is not proven. Below is a table summarising the proposed model.

Principal quantum number Shell quantum number Number of electrons in a subshell Maximum number of electrons in a shell Maximum number of electrons in a level Maximum number of electrons in atom
n symbol ns f (l=3) d (l=2) p (l=1) s (l=0) Zsmax Zlmax Zmax
1 K 1 - - - 2 2 4 2
L 1' - - - 2 2 4
2 M 2 - - 6 2 8 16 12
N 2' - - 6 2 8 20
3 O 3 - 10 6 2 18 36 38
P 3' - 10 6 2 18 56
4 Q 4 14 10 6 2 32 64 88
R 4' 14 10 6 2 32 120

This new sequence is totally in agreement with experimental spectral data sequence:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s ... , which with the new quantum shell renumbering becomes:

1s, 1s', 2p, 2s, 2p', 2s', 3d, 3p, 3s, 3d', 3p', 3s', 4f, 4d, 4p, 4s, 4f', 4d', 4p', 4s' ...
Renumbering the quantum shell levels does not change the original basic sequence:

2, 2, 6, 2, 6, 2, 10, 6, 2, 10, 6, 2, 14, 10, 6, 2, 14, 10, 6, 2 ...

Note that the sequence is now very simple and no non-sense jumping between quantum levels is required to agree with experimental spectral data. Also, a new kind of symmetry now becomes evident. It becomes very noticable the fact that each principle quantum level is now composed of a paired structure, a double shell, which must be fully filled before the level can be 'sealed'. Once 'sealed' or completed, the next quantum level will have no effect on the sealed level during its growth. Since every two consequtive shells are composed exactly the same, quantum numbers can now be halved, and each quantum number is given a property of 'spin' where the first shell of each level shall be arbitrarily be the positive quantum spin denoted by the usual notations 1s, 2s, etc.. and the second shell will be the negative quantum spin and is denoted by 1s', 2s', etc.. The new sequence thus becomes:

(1s 1s') (2p 2s, 2p' 2s') (3d 3p 3s, 3d' 3p' 3s') (4f 4d 4p 4s, 4f' 4d' 4p' 4s')

Thus the electron configuration now consists of only four shells, each shell being a double-structure with twice as many electrons per shell as in the conventional electron configuration. This double quantum structure is clearly shown by plotting various physical characteristics for the elements. Similar graphs for density, ionisation energy, electronegativity, etc.. all show the same characteristic of twin quantum levels, immediately obvious at first glance at the paired curves for each quantum level. Shown below is the density vs atomic number graph, which makes it clear that all elements can be built up by nesting 4 paired structures.



Binding Energy Curve

This curve shows the nuclear binding energy vs mass (P+N) number. As one can see, the most stable nucleui are those shown at the peaks which are 2He4, 6C12, 8O16 and 28Fe56. Incidentally these are the most cosmic abundant elements. The heaviest most stable element is iron, element number 28, which also sets the divisor between fusion & fission elements. As you will see, in our model this element is achieved when quantum level 3 is fully completed and 'sealed'.

Nuclear Stability & Hybrid Tetrahedral fractal formation

Stable nuclei generally have the same number of protons and neutrons (or Z=N, where Z is the number of protons and N is the number of neutrons in the nucleus). This is more strictly observed for light nuclei with fewer than 20 protons (Z<=20) (see figure on the right). For heavier nuclei with more than 20 protons (Z>20), the nuclear structure takes over more complicated geometry with increasing number of protons. The most common combination of neutrons and protons for stable isotopes is an even number of protons and an even number of neutrons. In a chart of neutrons (N) vs. protons (Z) for stable isotopes, a region of stability (shown in white) can be drawn. The stability line shows that nuclei with Z<=20 have a balanced number of protons and neutrons, and thus indicate a highly symmetric structure. Spatial symmetry, obtained on completion of a quantum level is a possible driving force for structuring the electron configuration in such a way, and also the driving force for chemical reactions and molecular bonds. Atomic build up for Z=20 will follow the growth of shells {1s,2s},{2p,3s,3p,4s} or with the new model {1s, 1s'}, {2p 2s 2p' 2s'}. As you may follow in the below diagram, in our model, a 1s shell is a simple tetrahedron (2P+2N), the 1s' (conventional 2s) shell is then a bigger tetrahedron, which inscribes the first tetrahedron. The 2p (conventionally known to contain 6 electrons, 3 upspin and 3 downspin) is actually made up of 3 x 2s tetrahedrons, which together with the original 2s tetrasphere, will pack together into a hybrid tetrahedral formation, to be inscribed in a bigger spherical tetrahedron, which is the 2s shell (conventional 3s). This mechanism will repeat itself in exactly the same way for the opposite spin quantum level. 3s shell will take the place of 2s shown in the diagram, 3p that of 2p, and 4s that of 3s. This hybrid tetrahedron shell build up is no longer followed after shell 4s, where the octahedron will emerge, and that explains why the balance between protons and neutrons is lost for Z>20. Our model, also explains the 'staircase' plot shown in the graph. When Z satisfies the conditions for a complete tetrahedron to form, whether s type or p type, the atom recovers it stability. The last point where the proposed structure touches the stability line coincides to the completion of the pair of hybrid tetrahedrons of quantum level 2.



The fundamental hybrid tetrahedral structure

I am now going to explain the real origin of subshells s,p,d,f and also show that Zmax for shells g and h are somehow different than those defined for the conventional theoretic subshells. It is also shown that the empirical equation for the maximum number of electrons in level n = 2n2 just happens to give the correct answers only to the first four shells and such equation has no fundamentals. In fact the conventional equation implies that we can have an infinite number of subshells s,p,d,f,g,h,i.... whilst our proposed structure limits the shells to h, at which point the model can handle 412 atomic numbers. We will also go further to explain why nature abhors the existence of elements with Z>120.

At this point we no longer need Pauli's exclusion principle to explain subshells, since the limit of two opposite spin electrons per 'orbit' is built in the structure of the tetrahedron. In no electromagnetic standing wave structure could we ever have two vertices touching each other, so this principle is built inherently in our new definition for matter. In the preceeding sections I have explained that a tetrahedron, having 4 vertices, is equivalent to an atom having 2 Protons + 2 Neutrons. We also know that the number of electrons of such a stable atom will be equal to the number of protons. So for example, a tetrahedron structure we have 2 electrons. For each platonic, we can work out the number of electrons which is equal to half the number of vertices Z/2, as shown in the table below. Note that at each complete shell stage, that is a formation of a complete platonic shape, one of the spherical standing wave will always be a complete sphere formed by the previous higher energy levels. For higher atomic numbers, one of the vertices of each complete platonic shell will always be formed by a spherical platonic, which in turn can nest other spherical platonics within it. It's a fractal build up. For example, in the above diagram, you can see that the inscribed tetrahedron is made up of 4 spheres, three of which are 2p spheres and one 1s' sphere. So for the formation of a tetrahedron (4 vertices), you only need to have three extra spherical tetrahedrons. In general, you will always need the formation of n-1 new spheres which together with the existing complete spherical standing wave, will form the new platonic with n vertices. The quantum number dictates the energy level, seperated by s levels, so for example a 3s, a 3p or 3d subshell spheres will have the same quantum number. In the example shown, we see that although each of the 4 vertices of the tetrahedron looks electrically the same, one of them will result in a higher equivalent mass due to its internal structure. The higher the atomic number, the higher is such imbalance, which results in deviation of the nuclear stability line from the curve N=Z, as shown further above. Thus this model accounts for another experimental fact, which is otherwise unaccounted for in the conventional model. On the last column, Zavail shows the available electrons for each complete structure. Zavail= 2,10,18,36,54,86 and 118 represent all the noble gases, namely: Helium 2, Neon 10, Argon 18, Krypton 36, Xenon 54, Radon 86, and the still unknown ultimate element 118. Being complete platonic structures, these are the most inert elements to exist in nature.

Level
(Quantum number)
Lowest level PlatonicVerticesNo. of inscribed tetrahedronsNo. of tetrahedron vertices P+N=ZElectrons in subshell= Z/2ZsmaxZlmaxZmaxZavail
1 = s,s' Tetrahedron +4142 (s)2420
Tetrahedron -4142 (s)242
2 = (p,s)(p,s)' Dual Tetrahedron +43126 (p)8 161210
Dual Tetrahedron -43126 (p)82018
3 = (d,p,s)(d,p,s)' Octahedron +652010 (d)18 363836
Octahedron -652010 (d)185654
4 = (f,d,p,s)(f,d,p,s)' Cube +872814 (f)32 648886
Cube -872814 (f)32120118
5 = (g,f,d,p,s)(g,f,d,p,s)' Icosahedron +12114422 (g)54 108174172
Icosahedron -12114422 (g)54228226
6 = (h,g,f,d,p,s)(h,g,f,d,p,s)' Dodecahedron +20197638 (h)92 184320318
Dodecahedron -20197638 (h)92412410


Why 118 elements not 412 ?

In the above table we see, that we can model all known elements with the proposed fractal structure by just using the first four structures: Tetrahedron, Dual Tetra, Octahedron and Cube. The two 'extra' structures containing icosa & dodeca structures, which could result in a total of 410 elements, seem not to be applied in nature. Why? The answer is quite simple, and you may understand it better as you follow this section. I have hinted in various sections that our reality is just a 'projection' of a unified higher dimensional reality in our 3D vision of the universe. In simple words, those things that cannot be found in higher dimensions, are most probably unstable and usually abhored by nature. The tetrahedron, cube, and octahedron all occur naturally in crystal structures. These by no means exhaust the numbers of possible forms of crystals. However, neither the regular icosahedron nor the regular dodecahedron are amongst them! As we have discussed earlier during the introduction to platonics, the icosa & dodeca structures are limited to exist in 3D, whilst the first four, and ONLY the first four structures exist in all dimensions. The fact that no stable elements with Z>118 have ever been found in nature, is in itself a clear indication that atoms, of which the universe is known to be made of, exist as a projection of a higher dimension than 4. So our proposed model gets truncated to the 4th quantum level, and the shaded part of the chart is deleted.

previous home next