3-Dimensional Natural Fractions, Electronegativity and Bond Lengths.

[elas]

1. Current knowledge of electronegativity is given on:

 

<http://www.meta-synthesis.com/webbook/36_eneg/electroneg.html>

 

Where the most popular values are described in the following manner:

 

Pauling's empirical electronegativity scale is derived from thermochemical bond-energy data

 

2. Details of 2-dimensional fractions found in composite fermion theory are describe by Jainendra K Jain in his book 'Composite Fermions'.

 

3. For current bonding theories see especially(especially bond lengths):

http://en.wikipedia.org/wiki/Chemical_bond#Electrons_in_chemical_bonds

 

4. On a the forum found at:

http://www.scienceforums.net/forum/showthread.php?t=32854&page=2

Will be found the arguments for 3-dimnensional fractions constructed using the Electron Bonding Energies of atoms.

 

Table 1 is taken from an earlier submission (4) concerning Composite fermion fractions where the fractions are 'approximations' (Jain). Table 2 shows that the vortex width is approximately 1/2 of the longitudinal axis width.

 

 

Table 1

 

Table 2

The next stage is to show that in the 3-dimensdional frame of particles and atoms it is again the particle fraction that determines the atomic bond length; but first it is necessary to determine the cause of particle bonding.

 

 

Electronegativity

 

Of the three tables of electronegativity listed by Emsley, two have some similarity as shown in Fig, 1

 

 

 

Fig.1

 

Pauling and Allred electronegativity values are derived from chemical bonding; where the use of more than one atom fails to describe the action within each individual atom.

 

Action within single atoms can de deduced using the EBE fractions that is:

EBE of s2 (shell) electrons divided by the EBE of s1 (nuclear) electrons. (Fig.2 )

 

Fig.2

 

The fractions either side of atomic No. 10 increase in opposite directions. In Table 3 the fractions to the left of atomic No.10 are extended (shown highlighted) by following Laughlin's example of using an ansatz.

 

Table 3

The 2s shell electron approximate fractions (predicted and actual) are shown in Fig.3

 

Fig.3

 

Without S2 electrons, the two nuclear electrons do not form fractions.

The single S2 electron of element 1 does not wrap around the nucleus, it bonds in meson style, therefore the high electronegativity value of element 1 does not equate with a high bonding value.

From elements 2 to 9 (inclusive) the gap between electrons narrows increasing the Casimir force (vacuum bonding) until the gap closes at element 10.

From element 11 to element 92 the S2 electrons are subject to compression (vortex) bonding.

Element 9 (Fluorine [shown in yellow in Fig.3 and red in Fig.4]) has the greatest Casimir force and is, for that reason; the most corrosive of all the elements.

Fig.4 shows elements 1 to 15 electronegativity in greater detail.

 

Fig.4

 

Bond lengths.

 

Note: A conversion factor of 8.551 converts (decimal) fractions to pm.

Bond lengths are found by adding together the s2 EBE fractions for each element of the bonding pair (Table 4). Fig. 5A shows the results in graph form.

Fig. 5B shows the percentage variation between Pauling's empirical values and EBE fraction values. Because the variation is large, Fig. 5C is produced to show the variation between two widely accepted values for bond lengths, one by Pauling and one by Sanderson. Comparing B with C it will be seen that the EBE fractions differ from Pauling by roughly one half of the difference between Sanderson and Pauling (note difference in scale).

Table 2 provides the data for Fig. 5A

 

 

Fig.5

 

Table 4

 

Atomic electrons are compressed on the atomic radius in the fractional sequence 1/5, 1/6, 1/7, 1/8, 1/9 etc. In FQHE Laughlin found the sequence 1/5, 1/7, 1/9 etc. Laughlin did not find fractions with an even denominator for the reasons given in my earlier submission (4). But it is shown that the fractions found in the 2-dimensional frame of FQHE experiments are the same as the fractions found in the 3-dimensional (atomic) frame.

It is also shown that atomic pair bond length is the sum of the s2 electron fractions of each member of the pair.

 

Postscript 13 Dec 2008

To the above can be added the table below, it shows how in molecules an increasing number of particles resists compression; In FQHE experiments a similar effect is achieved by increasing the magnetic pressure (hence the approximate fractions).

Col. g is a measure of the reduction in the width of the so-called '2-dimensional' band.

Edited December 13, 2008 by elas
multiple post merged