ABSTRACT.

ADOMAH Periodic Table is based on the Left Step Periodic table that was introduced by Janet in 1928. It consists of four blocks (s, p, d and f) that correspond to the quantum numbers l = 0, 1, 2, 3. Blocks are separated from each other, shifted and reconnected via diagonal lines. ADOMAH Table allows direct reading of the quantum numbers 'n' and can be presented in horizontal or vertical formats. In vertical format ADOMAH Table has vertical columns that correspond to the quantum numbers n = 1, 2, ..., 8 and cascades n + l = 1, 2, ..., 8 (if diagonal lines are followed when moving form block to block). The cascades provide continuity with respect to the atomic number Z. Numbers on the bottom of the table represent either quantum number 'n', if columns are followed vertically, or 'n + l' if cascades are followed. This feature is very useful for determining the electronic configurations (see User Guide).

Quantum numbers ml and ms are addressed by placing elements in rectangular "boxes" with 1 x 1/2 proportions, so that any two such "boxes" make up a unit.

or Unit square used to establish proportions of spdf blocks to bring them in compliance with number of ml values corresponding to each block.

These seemingly cosmetic changes resulted in amazing discovery: quantum numbers n, l, ml and ms and their interrelation can be explained on the basis of a three dimensional geometric shape that is known as Regular Tetrahedron (see 3D Image).

The Whole Story

1. Introduction.

The quantum mechanics in its present state can not fully explain all intricacies of the Periodic System in part because the quantum numbers n, l, ml and ms , that describe electronic populations of the atoms, are not completely understood in terms of mathematics.

Attention of scientists has almost always concentrated on the contents of the Periodic Table, but its geometric form has generally been viewed as an outcome of the arrangement of the elements, or as a matter of preference. This article represents a serious attempt to analyze PT geometry based strictly on the set of the quantum numbers that define electronic configurations of the atoms (n, l, ml and ms) . It will be demonstrated here that analyzing PT geometry, on the basis of the objectivity that the quantum numbers represent, will help us to understand the basic mathematical idea that underlies them, as well as their interrelation.

The quantum numbers that define electronic shells and their relation to each other can be explained on the basis of the commonly known three dimensional shape. This geometric shape can be used as a visualization tool for the further exploration of not only the electronic shells, but also the atomic nuclei.

In order for us to begin serious discussion of the PT geometry, IUPAC Standard PT has to undergo three simple logical transformations that will bring it closer to the agreement with the quantum numbers.

Step 1. Transformation of the Standard PT to the Left Step Periodic Table.

a) First we have to identify and mark all distinctive parts of the Standard PT as s, p, d and f ;

b) assign angular momentum quantum numbers l = 0, 1, 2 and 3 to the corresponding sub shells s, p, d and f and move element He to its appropriate place in the s-block. (more discussion on this topic to follow).

e) and finally, move s-block to the right of p-block and move the footnote f-block to the left side of the table, so that the quantum numbers l are in correct order (3,2,1,0).

This PT formulation is known as the Left Step Periodic Table (LSPT) published by Janet in 1928.

Step 2. Correlating the primary quantum numbers with the rows.

Despite its orderly look, the LSPT has three draw backs: it does not allow direct reading of the quantum numbers 'n' (its rows represent n + l ); it does not have symmetry and it has disproportional length comparatively to its height.

First two deficiencies can be easily fixed by, separating the blocks from one another and by moving up each block by a number of units equal to the quantum number l, corresponding to each particular block.

Now the number of each row corresponds to the primary quantum number 'n' and each layer, or strata, corresponds to the sum of the quantum numbers n + l.

Coincidently, this operation has also addressed the question of the symmetry .

Step 3. Defining the correct proportions.

As it was noted above, PT proportions need to be addressed. At first it seems that this is just a matter of preference, or pure cosmetics, but, unlike its dimensions, proportions of the PT can be determined objectively. Lets define the meaning of each quantum number in terms of the PT geometry:

It should be noted that first three quantum numbers are integers, but the last one, the spin quantum number, is a fraction, that is one half. Given that each entry in the PT represents a single element, determined by one electron/proton pair, conclusion can be made that one dimension of each cell has to be objectively associated with the absolute value of the spin quantum number ms, that is 1/2. The other dimension shall be associated with the minimum value of the quantum number 'n' and shall be equal to unity.

Therefore, proportions of each cell of the geometrically correct Periodic Table have to be 1/2 : 1, not 1: 1 or so, as currently used by the Standard PT. That is, one unit square comprising two rectangular cells is used as a measure to proportion spdf blocks in order to reflect number of ml values corresponding to each block. or

Now, we can cut the length of each cell, each block and the total length of the PT in half and do it on the totally objective basis. (So much for cosmetics).

This PT formulation was discovered by the author of this article on February 13, 2006 and is known as The ADOMAH Periodic Table.