AUDIO TRANSCRIPT OF MY ATTACHED VIDEO ON THE GEOMETRY OF THE PERIODIC LAW.

[Julio gutierrez samanez]

Colleagues, I send you this home video, which I made with the purpose of developing and deepening my ideas regarding the periodic law as a mathematical function, enriched with the ideas that René Vernon published, with a graph by Henry Bend, in which he shows with colors the properties of the elements and whose periodicities can be seen very clearly in the graph that I propose, the same one that I dedicate to our friend René Vernon.

(Excuse my translation with Google)

Julio.

 

VIDEO AUDIO TRANSCRIPTION

 

Today, April 12, as someone returning to the studies I have been doing on the Periodic System and the Periodic Table, I decided to develop something that was only in my thoughts. This table is based on other works such as those of Henry Bend and other characters that we have been discussing in our “list” of panel scholars. So I have decided to make this table, which is the one you are seeing, which is nothing more than the development of the previous one that I have here, where you can see a parabola whose formula is this one that we are seeing and that I have put here. It's still in pencil. Here is the parabola that I am going to follow with my fingers, it is the proportionality of the division of this continuous line that is the atomic number Z. which is a numerical sequence, of course, infinite; which is up to number 120 here.

 

So what I have found with this formula: four times the sum of n squared, is that there is a proportionality with which this line Z can be divided, which can be fractionated in proportions, according to the principal quantum number n; which, in turn, is the Binode number. (Bínodo called Dr. Oswaldo Baca Mendoza, a Peruvian scientist, the pair of symmetrical periods with the same number of elements).

 

The first pair would be this one, with elements s, four elements, two by two, in the first two small periods that are followed, according to my method. So here we can see a sequence, some volutes, a spiral that will develop in a sinusoidal, but increasing, shape.

So here we have these colors that they put, I think it was H. Bend, or else, our friend, to whom I dedicate this work, who is René Vernon, who lives in Australia, but he is from the United States.

 

So, here there is a kind of break, because that is where the parabolic curve is going to go; This whole part that I'm showing here passes on this side through the main quantum number, the number 2.

There you have a numerical sequence: Here there are four elements; here there are sixteen. They are the squares of even numbers: two squared, four; four squared, sixteen; six squared, 36, etc.

So, here we have, in this other part, 36 elements (18 plus 18). Then we have another quantity of 64 elements, (32 plus 32) up to 120.

This sequence gives us this series: 4, 20 56, 120... which are the ends of these sequences... Here we are seeing 56, we are seeing the number 20 and the number 4.

What we observe in this long table is that sequence and that way of dividing proportionally, under a mathematical function, by binodes or pairs of periods of chemical elements.

 

Then, what you see here in these colored squares, (which represent the elements), are the characteristics or chemical properties of the elements, which according to the Periodic Law: the chemical properties of the elements are functions of the number series atomic, Z.

And, since the atomic number, here, is an infinite horizontal line, these properties are going to repeat periodically, (I have used sinusoids or a growing solenoid, (I don't know what to call this shape...) And you can see how, every so often However, according to this mathematical function, there is this proportionality; that is, those same functions appear according to the growth of the secondary quantum numbers: s, p, d, f, etc.

 

So, this series is divided into that sequence: s, s, which are the first four elements; then: p s, p s, (also, it is the second binode, each period is p s, p s), then together they make this series. Then (in the third binode) p appears, with 10 elements that add up to a repetition of the previous series that was p s. So we are faced with a period: d, p, s, which is going to be duplicated here: d, p, s., then, this duplicate makes the third binode.

 

Likewise, in binode number four or main quantum number 4, the secondary quantum number f appears, with 14 elements and, then, the binode grows, it will be larger: 14 f elements, plus 10 d elements, (which there were already in the previous binode and are duplicating or reappearing) with 6 (elements) p, 2 (elements) s. So this sequence f, d, p, s, is going to be duplicated in the second part of this fourth binode, which is... (...Ugh!, I think I haven't recorded...it's not right, ha...ha, I have have to correct that).

 

That doubles and we have here: 14 f elements, 10 d elements, 6 p elements, and finally 2 s elements, which finally complete the 120 elements that are currently being studied. 119 and 120 are still in the process of study or work (research).

 

 

And all that is here organized with these sinusoidal sequences, it is the same thing that I have presented in my previous works, they are only a development of this graph that is in my first book from 2004 (https://www.meta-synthesis.com/ webbook/35_pt/pt_database.php?PT_id=1100) and the second from 2018 (must be 2012: https://www.academia.edu/104363278/PERIODIC_BINODIC_TABLE_as_mathematical_function)

  and it is developed in my works published on the international website www.meta-synthesis.com. in Dr. Mark Leach's Periodic Table Database. (https://www.meta-synthesis.com/webbook/35_pt/pt_database.php)

(Also in my scientific article published in Foundations of Chemistry, March 2020. (https://link.springer.com/article/10.1007/s10698-020-09359-3).

And in the video:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=946)

 

Well, that's what I wanted to show you friends and thank you very much.

 

Here is the home video that I put for your consideration

https://youtu.be/fqIaBRBQ34I?si=yCFVvkp2d2g0oDtR

[Rene]

Dear Pavel

in your 3D visual aid table you effectively show the f-block as follows:

+3 +4          +3 +2

57 58 59 60 61 62 63

La Ce Pr Nd Pm Sm Eu
Yb Tm Er Ho Dy Tb Gd

70 69 68 67 66 65 64

+2 +3          +4 +3

What you are showing is f1 to f7 and f14 to f8.

This does not work since the double periodicity in the f-block runs from f1 to f7, and then repeats as f8 to f14, as follows:

+3 +4          +3 +2

57 58 59 60 61 62 63

La Ce Pr Nd Pm Sm Eu

Gd Tb Dy Ho Er Tm Yb

64 65 66 67 68 69 70

+3 +4          +3 +2

The same problem occurs in the d- and p- blocks.

I see you have coloured He in the same way as the rest of the noble gases. That is a clever solution.

René

[Rene]

Dear Pavel

I have attached an image showing McCutcheon's folding periodic table of 1950.

The idea is clever but has the same drawback in that it seems to misrepresent the order of elements in the f-block, particularly in the way it reverses the sequence in the second half of the block from Yb to Gd instead of Gd to Yb, which is the correct increasing order of atomic numbers. The same problem occurs in the d-block.

Here’s what I mean:

+3 +4          +3 +2

57 58 59 60 61 62 63

La Ce Pr Nd Pm Sm Eu
Yb Tm Er Ho Dy Tb Gd

70 69 68 67 66 65 64

+2 +3          +4 +3

In your 3D table the same problem occurs in the p-block.

In this case the problem could be rectified, for example, by joining the left side of the right half of the f-block to the right side of the early f-block, and then folding the right half of the f-block under the left half of the f-block.

This adjustment allows both halves of the f-block to be visible and directly comparable when the table is fully opened. It would also preserve the structural integrity and pedagogical purpose of the folding design by keeping the entire f-block compact and easy to manipulate.

 It makes the periodic table more intuitive and user-friendly, particularly for educational purposes where visual representation significantly impacts learning.

If you were to make this modification to your 3D table you would retain the option of reading it anticlockwise, and clockwise, and also be able to fold out the second halves of the p-block, d-block, and f-block.

René