1. The 2x2-series behind the periodic
First to establishis the fact that a an elementary
number chain 2x2 , (x = 5 - 0) lies behind the periodic
system and electron configurations in atomic shells. That is to
say a version of the same kind as the
dimension model described in part Physics.
Whole shells and number of electrons in the orbitals
from the number chain 2x2
(x = 5-0), "theoretically":
Orbital "x" here regarded as decomposed
in what has been called the "P"-and "Q"-shells".
*Through the displacement of d- and f-orbitals to
next shell, we get the real number series for whole shells:
The 2x2 -series may also be derived as a chain of energy,
as Force times Distance in the dimension chain of our model. We
have defined higher dimension degree (d-degree) in relation to a
lower one as a binding force, the lower one as potential with number
value ("E") = sum of the outer poles (or partial structures):
A dimension chain:
Counting on 5 orbitals,, although the 5th (x) not realized, the
theoretical maximum of Z becomes 110 Z, sum of the 2x2-chain.
As in the dimension model, we may regard higher
numbers transformed into lower ones. The whole series of elements
may be regarded as developed through one and the same dimension
chain, with secondary development in each step giving a level chain:
(This implies the aspect of "half-step" displacements
of the type "border to interval", which in these papers
has been suggested as an elementary definition of a quantum jump.)
With numbers for the 2x2-chain as "borders":
We get number of electrons theoretically in orbitals s, p, d,
In reality a full second f-orbital of U is replaced by 4 s, 6 p,
1 d, 3 f electrons.
E-numbers and orbitals - sp(d)-hybridization:
Another way to derive the orbital numbers could be to interpret
them as sums of outer poles in lower degrees, in agreement with
the general postulates in our dimension model: higher d-degrees
polarized to outer poles in the lower d-degree.
This interpretation may give aspects on sp(d)-hybridizations in
d-degree step (3)-2-1:
Such hybridizations, regarded as a superposed level, could indicate
that in the underlying scheme the whole shell numbers may precede
their differentiation into different orbitals.
*(As to this derivation of orbital numbers, see also paragraph
There is still a third way to get the 2x<2-chain from
a simple number chain 5-4-3-2-1-0 which could be mentioned here.
It concerns transformations between number-base systems (nb-x).
(Such transformations give number relations in the genetic code.
See pdf-files on "The Genetic Code" on the menu bar.)
Assuming the elementary number chain x 10 represents
d-degrees connected with declining number-base systems we have:
2. Lower steps or degrees in the number chain as debranched
from higher steps:
With respect to the orbital forms the s-orbital represents the
innermost orbital, the least polarized one but simultaneously the
last step in number of electrons in the chain. We could here apply
the loop model of a dimension chain, where debranched d-degrees
from higher d-degree steps meet "the other way around":
A sketch with question marks for the development of the f-orbitals:
The periodic system should be possible to regard from the double
aspect of polarizations and synthesis, where the direction of polarization
or disintegration on some underlying level is followed by the synthezising
direction (inwards) on a superposed level.
In this sense Uranium (the heaviest atom in Nature)
as a potential mass on a field level could be thought of as an equal
primary element as H, D, or He (1, 2, 4 A). (Cf. perhaps the atomic
radius of He and Fr (87 Z): both = 2,7 Å.)
Counterdirection "from outside" may be interpreted as
a condition for development of the higher orbitals. The filling
up of d-orbitals "demands" such counterdirection from
outside, expressed as s-electrons of the next higher shell further
out, and filling up of the f-orbital demands both s- and p-electrons
in still another shell further out.
Regarding a secondary centre in step 3-2
Pd, 46 Z = ½ x max. Z in Nature, is the only element where
the d-orbital is "naked", the outmost one, without any
s-electron further out. It could represent a centre in the 3-2-step,
the step of the d-orbital number 10, where counterdirections meet,
perhaps a virtual way to level developments? Or a channel in to
the nucleus? Compare the geometrically sensitive experiments with
Pd for cold fusion?
Compare too that Z-numbers about 46 has been identified
as one kind of border in the periodic system (between fusion and
fission forces? (Gamow). See figures 07-2, 09-4.
forms: Dimensional aspects on the geometries.
Quantum numbers n,
l, m, ms.