Mathematical Structure of the Periodic System Table

Mathematical structure of the Periodic System Table

Dipl.ing. Aco Z. Muradjan

Abstract:

The Periodic Table with a new double numerical structure, presented here is attempt to find table form which will in some new way represent the periodicity and symmetry of the Elements, with the Periodic System as base. Also this tetrahedral laminar table structure maybe will became a base for developing a new shell structure of atomic nucleus.

This new rearrangement of the chemical element is based on mathematical formula which result is simple, length of the periods.

Keywords: Periodic System, Table, Law, mirror, new, form, electron configuration, shell, period Introduction

The form or the shape of the Periodic Table, which base is The Periodic System of the Elements is subject of many researches works all over the world. The fact that there is hundred and more different form or shapes of the Periodic Table signify that the final shape of the Table isn’t rich yet.

As is well known the length of periods in present standard Periodic Table haven’t mathematical basis. The quantum mechanical explanation of this seven period’s table is based on shell model with four quantum numbers n, l, ms and s and aufbau principle (Madelung rule) based on n and l quantum numbers.

The maximum number of electrons in periods is N = 2n2 (N = 2, 8, 18, 32,), where “n” is principal quantum number. But seven period’s table has different order 2, 8, 8, 18, 18, 32, which doesn’t correspond to this formula, which also indicates that something is wrong with this period order.

New model

With some rearrangements of the order of the periods and elements in periods, which order corresponds to reality or electronic configuration, different order will be get (N = 2, 2, 8, 8, 18, 18, 32, 32). Here each period has own mirrored structure.

Strict model or table which explain physical and chemical properties of the element based on their atomic number, electron configuration and above order is presented by French scientist Charles Janet in 1929,

and also similar table, but with new modified notation scheme of today accepted numeration of periods and groups, presented in Muradjan’s Periodic Table from 2001. Here are added new marks for shells with capital letters from K to R, new quantum number for shells ns and spdf notation scheme for blocks.

2 The length of the shells (periods) in this table is also given with the formula N = Ns = 2n (2, 8,

18, 32,), where Ns is length of the shells. The length of the same doubled mirrored shells 2 (periods), or dyads according Janet is expressed with formula Nd = 4*n (4, 16, 36, 64,).

2 Here, this simple formula Nd = 4 n is taken as base for new rearrangement of the elements.

First number group I - 1+4+9+16

Second number group II - 1+4+9+16

Third number group III - 1+4+9+16

Fourth number group IV - 1+4+9+16

The Table which expresses this order only with numbers, same as the atomic numbers in periodic table is given below.

And same table with chemical element’s notation.

With a new rearrangement of these groups the next tetrahedral laminar structure or form of the Periodic Table will be get.

There are four groups of the elements with 30 elements each.

I - Hydrogen group

II - Helium group

III - Lithium goup and

IV – Berilium group

The aufbau principle for this table shape is lemninscate build up principle.

If the notation scheme from Muradjan’s Periodic Table will be applied on above Table the next form will be get.

Every element from one group from this table can be symmetrical pictured in all other three groups, up or down, left or wright, or diagonaly. For chemical or physical properties left - wright symmetry has preferred position. But for atomic nucleus structure all symmetry are possible. The color and numeration on table above is presented as doubled “spdf” scheme. This scheme is shown on picture below.

Left-right step “spdf” scheme

This scheme presented with chemical elements in groups will show that the mirrored structure of the Periodic Table (the table below) is based on left - wright symmetry.

Conclusion

The Nature is full of different form and shapes. The laws that describe this are based on several basic principles. One of them is symmetry. Up and down, left - right, back and forward, pair odd, particle antiparticle, parity or mirror symmetry and so on, are samples of symmetry.

Periodic System with his graphical presentation, the Periodic Table, is example where mathematical aspects and symmetry are fully included. The present seven periods Periodic Table form hasn’t such symmetry. Here presented natural mathematical aspects of Periodic Table structure must be taken as base for revision this hundred and more year old Periodic Table shape.

Katz, G. An Eight-Period Table for the 21st Century, Chem. Educator 2001, 6, pp324- 332. Restrepo, G.; Pachón, L. Mathematical aspects of the periodic law. Found. Chem. 2007, 9, 189- 214. THE PERIODIC LAW IN MATHEMATICAL FORM – Reino Hakala, department of Chemistry, Syracuse University N.Y. November 1950 - Abstract

Mazurs, E. G. Graphic Representations of the Periodic System During One Hundred Years; University of Alabama Press: Tuscaloosa, 1974.

Eric R. Scerri, “The Periodic Table: Its Story and its Significance”, Oxford University Press, N.Y., 2007 http://www.meta-synthesis.com/webbook/35_pt/JanetIII.jpg http://www40.brinkster.com/maks47/ http://www.meta-synthesis.com/webbook/35_pt/Muradjan_pt2.gif