The new relationship between the Periodic Table’s shape and the Quantum

Mechanics postulates

Research paper

Abstract

As is well known the year 2019 as the International Year of the Periodic System Table was declared. Moreover,

there are 150 years from the Mendeleev’s formulation of the Periodic System, Periodic Table or Law. In the year (2016), in

addition, the rest of the all known 118 elements with their names and symbols were defined. Also with the quantum

mechanics’ postulates and principles, the physical and chemical properties of the elements, which vary periodically by their

atomic structure, with their place in the Periodic Table were related. It looks like that all questions concerning Periodic Table

are solved, with the exception of some, so told, unimportant or no so relevant things. Besides this small number of

exceptions, one big the most important thing, regarding the relationship between Quantum Mechanics and Periodic Table's

shape is excluded, and ignored from the scientific community for nearly 100 years, or from the of the quantum mechanics

birth. This is the duality of all rows (periods) in the Periodic Table. Each of these doubled periods is with the same "spd or f"

structure and these doubled periods were named as Dyads (French – Dyades). This new possibility in the Periodic Table

on the reflection or the mirror symmetry is based. This information is so important that will change the qualification of the

main or principal quantum number if it, in the new modified quantum number’s set will be applied.

Keywords: Periodic Table, quantum mechanics, periods, notation, quantum numbers, reflection symmetry, dyads

Introduction

With the plan, nothing to change in the present Periodic Table's notation, at this point a new quantum number “nd”,

for the dyads, presently is added. Moreover, with the purpose not additionally to minimize the role of a chemical and

physical characteristic of the all chemical elements in the Periodic Table's groups and periods order, here is given attention,

first of all, to the fact that the most significant role for such grouping has doubling-up of all periods. This new quantum

number is added for the reason that whit this number the importance of the duality of the rows (periods), in the Periodic

Table is especially emphasized and the link between Periodic Table’s shape and Quantum Mechanics, for the first time,

can be really established. This new quantum number has a very significant role. Whit this new quantum number the region

of the action of the azimuthal and orbital quantum numbers is very well defined. This new quantum numbers “nd” for the

dyads has the role of the present principal or main quantum number. The numbering of the periods in the Dyads is almost

the same as their current numbering and marks, a little bit changed, but with similar meaning.

Symmetry

Almost all objects, processes, or systems in Physics, the same as in Nature, on some sort of symmetry are based.

If any object, process, or system posses’ symmetry than these objects, processes or systems for any kind of change or

transformation are invariant. In mathematics, the most known symmetries, through geometric transformations, are reflection

symmetry, rotation symmetry, and scaling.

For the question, does the two-dimensional Periodic Table have any kind of symmetry, the answer is yes? The Periodic

Table as a two-dimensional figure has reflection symmetry and axis as symmetry or mirror line. The base for this statement

is a fact that all rows or periods in Periodic Table are doubled or paired.

If the "Lemniscates” build up principle will be applied for ordering and grouping for all chemical elements in the Periodic

Table than the next figure will be obtained.

At first, on the image below, the graphically, this “Lemniscates” build-up principle is present.

The two-dimensional Periodic Table's shape with the reflection symmetry on the next image is shown.

This two-dimensional figure of the Periodic Table, shown on this way, has reflection symmetry with the symmetry or mirror

axis line. All chemical elements from the left side of the symmetry or mirror line have on the identical right place, the

element - pair, which is in the most cases with the similar physical or chemical properties made. In addition, both chemical

elements have a similar “spdf” notation.

This Periodic Table figure is base for the creation of the tabular presentation of all chemical elements in the table with

vertical groups and horizontal doubled rows or periods. Such table shape, for the first time, in the year 1929, by the French

scientist Charles Janet was proposed.

Here below is presented the Periodic Table with the same shape, but fulfilled with the newly discovered chemical elements

and with the new modified periods and group notation. The double rows or periods which are as Dyads marked to go on

from one to four and dyad number “nd”. The order of periods in the dyads in this Periodic Table’s shape, from the current

numbering of the periods, is a little bit different. Instead the seven periods from K to Q, now there are the eight periods,

from K to R. The period numbers with the same sign “n” is marked. The group numbering is from 1 to 32. A such number

of dyads is proposed because is very difficult when something new is suggested, this new suggestion from wide auditorium

easily to be accepted. (In some of my previous articles different numbering for dyads and periods were proposed).

The Periodic System Table with the new modified numbering of the groups and the periods

Quantum numbers and the Periodic Table

The current quantum number’s set

According to present modern quantum theory, the next four quantum numbers values are needed to specify the

distribution of electrons of an atom in atomic orbitals (n, l, ml, and ms). With these quantum numbers, each orbital is

defined uniquely. First three numbers came from Schrodinger’s wave equitation and the fourth number came from the Pauli

Exclusion Principle. The exclusion principle states that, in general, no two electrons can occupy exactly the same quantum

state.

- The principal quantum number n describes the size of the orbital and expresses the quantization of energy En.

- The orbital quantum number describes the shape of the orbital and expresses the quantized values of the total

angular momentum of the electron in an atom, and has values:

- The angular momentum of an electron is a vector quantity and describes the orientation in space of a particular

orbital. Choosing only discrete directions, as, for example, the -axis, then the “z“ component of angular

momentum, named Lz to take only certain discrete values: Lz = ml, where the integer “ml” is the magnetic

quantum number.

- The orientation in space of a particular electron is defined with an intrinsic angular momentum, called spin. This

angular momentum is determinate by vector S with z-component Sz = m, where ms is the spin quantum number which can take only two values along the z-axis.

The quantum numbers may get the following values:

- Principal quantum number n from 1 to n

- Orbital quantum number l from 0 to n-1

- Magnetic quantum number ml from - l, … 0, … + l

- Spin quantum number ms from -1/2 to +1/2

The orbital quantum number with the azimuthal quantum number through the next relation is connected:

I = n - 1, (n equal or smaller than n)

The new proposed and the modified quantum number's set

So what is so important about the newly added quantum number for the dyads “nd” and why the role of this

number is so significant?

First of all the shape of the Periodic Table must be investigated as a table consisting of two similar separated tables which

are with reflection symmetry and with similar “spdf” notation signed. Each table has the same principal quantum number

“nd” for both periods in same dyads. Both tables look like they are with the positive or negative sign, which sign, with some

sort of isospin, can be interrelated and marked.

They can be viewed also as tables with left and right orientation, positive and negative charge, and so on, like many things

in Nature.

Because the Periodic Table in such way is presented, with the new quantum number “nd”, the region of action of the

azimuthal quantum number “n" or orbital quantum number "l" now can be differently defined, for each table separately, but

with the same value?

The difference between the periods, in the same quantum number “nd”, with the present quantum number “n” is marked,

from one to eight, or from K to R, according the new modified quantum number’s set.

This quantum number “n” has the same role as before and presents the periods in which electrons are positioned. The

current quantum number “n” in the same dyad presents the difference in the energies in both periods. Such energies with

the different distance (radius) from the central nucleus are related.

For the new quantum number's set the next values are proposed:

- Dyad quantum number nd from 1 to nd

- Period quantum number n from 1 to n (n = 2*nd - 1 to 2*nd)

- Orbital quantum number l from nd - 1 to 0

- Magnetic quantum number ml from - l, … 0, … + l

- Spin quantum number ms from -1/2 and +1/2

Here the main difference with present or current quantum numbers notation, as is said before, is that the azimuthal or the

orbital quantum numbers are not anymore with the quantum number “n” connected or interrelated, but with the new

quantum number “nd”. The orbital quantum number has the same formula l = n -1, (n equal or smaller than nd). When this

new quantum number is used in the quantum mechanical clarification of the electron configuration of all elements in the

Periodic Table, then many of known irregularities toward correlations between Quantum mechanics and Periodic Table’s

shape can be solved. With this modification, the rights "spdf" order can be very easily obtained, without any additional

principles or rules. This is evident in the image below where the new quantum number’s set is in a table applied.

Note: The column sub-shell symbol instead (n-l) should be marked as “n” - (1s, 2s, 3p, 3s, 4p, 4s, 5d, 5p, 5s, 6d, 6p, 6s, 7f,

7d, 7p, 7s, 8f, 8d, 8p, 8s), but because of current spectroscopic quantum number’s notation (n-l) is used. (1s, 2s, 2p, 3s, 3p, 4s,

3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s).

Conclusion

With this new table shape, which is with the quantum number’s set correlated, including the new quantum number

for the dyads “nd”, the relationship between Quantum Mechanics’ postulates and Periodic Table’s shape is maybe

realized? Also, the heaver elements, larger than elements with the number 120, can be in such Periodic Table’s shape

easily included. Such Periodic Table shape, as left step table named, in present time exists, which by French scientist

Charles Janet, almost a hundred years ago, was proposed. But, until now there is no any suggestion for the dyads

significance in the relation between quantum mechanics’ postulates and the Periodic Table. Besides the role of the

chemical and physical characteristic for the all chemical elements, in the classification of the Periodic Table's groups and

periods order, it looks that the duality of all periods in the Periodic Table is most important, consider quantum mechanics.

Note: Once more, because of the importance of the work consider Periodic Tables' shape, presented by Charles Janet, he

deserves the chemical element with the number 120, to be named as Janetium. For the question does the element with the

number 120 exists, the answer must be yes. Why, because hi, like Mendeleev, predict with his table’s shape, such element.

References

- Mathematical structure for the Periodic System Table –http://gsjournal.net/Science-Journals/ResearchPapers-

Chemistry/Download/5094

- New pt notation - http://gsjournal.net/Science-Journals/ResearchPapers-QuantumTheory/PartlicePhysics/Download/5755

- From telluric helix to telluric remix Philip J. Stewart https://www.researchgate.net/publication/331285671

- Eric Scerri - Can quantum ideas explain chemistry's greatest icon

- The evolution of the Physicist's Picture of Nature Scientific American 208 (5) (1963) - http://www-history.mcs.st-andrews.ac.uk/Quotations/Dirac.html

- Nomenclature of Inorganic Chemistry, Recommendations 1990, Blackwell Scientific Publications, 1990. Edited by G J Leigh. [ISBN 0-632-02319-8; 0-632-02494-1 (pbk)].

- http://old.iupac.org/publications/books/rbook/Red_Book_2005.pdf

- http://www.meta-synthesis.com/webbook/35_pt/JanetIII.jpg

- http://www.brinkster/maks47

- http://www.meta-synthesis.com/webbook/35_pt/Muradjan_pt2.gif

- E FLUCK - New notations in the periodic table http://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf

- Katz, G. The Periodic Table: An Eight-Period Table for the 21st Century. Chem. Educator 2001, 6, pp 324–332.

http://depa.fquim.unam.mx/amyd/archivero/The_Periodic_Table_An_Eight_Period_Table_For_The_21st_Centrury_5008.pdf

- Henry Bent-New Ideas in Chemistry from Fresh Energy for the Periodic Law (2006).

- Scerri, E., the Past and Future of the Periodic Table. American Scientist, January-February 2008, 96, pp 52–58

- Stewart, P. J. A New Image of the Periodic Table. Education in Chemistry, November 2004, 41, pp 156–158.

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

- Campbell, J.A. (1989). Let us make the table periodic. Journal of Chemical Education. (66) 9, 739-40.

- van Spronsen, J. W. The Periodic System of Chemical Elements; Elsevier: Amsterdam/New York, 969.

- Bent, H. A. Construction and Uses of the Left-step Tabular Expression of the Periodic Law monograph), Pittsburgh PA., 2000,p 44.

- Tarantola-Periodic Table of the Elements(Janet form) http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Mendeleev/

- Dr. Neubert’s - Double-Shell periodic System of the Elements (PSE) http://www.neubert.net/PSETable.html

- Ostrovsky, V. 2001. What and how physics contributes to understanding the periodic law. Foundations of Chemistry 3:145-182.

25.04.2019

©Aco Z. Muradjan, maks06@gmail.com

Appendix: The tables with the new quantum number's set for the all Elements in the Periodic Tables (from 1 to-56 and

from 57 to 120) below are presented: