Rydberg (1914), and Janet (1928) and Mazurs (1957)

[Rene]

The recent discussion about the binodic PT prompted me to look closer at Rydberg's article of 1913 in which he proposed the 4n^2 formula for the lengths of periods. My source is the 1914 French translation.

His attached PT shows four horizontal groups, as he called them: G1, G2, G3 and G4, perhaps riffing on Werner’s four double periods. Werner, in 1905, had earlier published a 33-column table, with four double periods of lengths 3, 3, 8, 8, 18, 18, 33, 33: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=64

In Rydberg’s table, the number of elements in each of his "groups" is 4, 16, 36, 64 i.e. 4n^2. He adds:

"The groups are not only divided into two halves, but, as the number of elements of a group suggests, they are further divided into four fractions, each containing p^2 elements. In the first four groups these fractions contain 1, 4, 9 and 16 elements; we will call them the quadrants of a group." (1914, p. 605).

Since he knew that the series helium to chlorine (G1) showed double periodicity (2 x 8), and that argon to iodine (G3) did the same (2 x 18) he had hypothesised that hydrogen must also be part of a series showing double periodicity (2 x 2). Rydberg therefore proposed counting the electron as element 0 and adding coronium and nebulium between H and He. Aside from H, the numbering of the elements differed from the true atomic numbers by two, since He is 4, Li is 5, and so on.

On the electron, Rydberg (1914, pp. 603–604) wrote, "Electrons, as I have indicated in my brochure [1906] 'Electron, the first element', present all the properties which characterize atoms."

In this brochure he explained that:

"During the course of many years of research into the properties of basic materials, of which various individual sections, e.g. on spectra, have already been published, I recently arrived at results which appear to be of such general interest that I did not want to postpone their publication until the whole work was completed. Since the variety of scientific problems involved made it difficult to choose between the specialised journals, I have chosen the present form in order to provisionally communicate the most important of the results obtained so far...

We claim that they [electrons] are atoms because they behave like atoms in the following relationships:

1. Electrons are independently existing parts of matter. 

2. The electrons, no matter where they come from, are always equal to each other. 

3. The electrons are permanent and cannot be divided or destroyed by known means.

4. The electrons have mass. 

5. The electrons occur partly free, partly in compounds with atoms or atomic complexes.

6. The electrons can combine with atoms and atomic complexes and be expelled from these compounds.

7. The bonds between electrons and atoms vary in their stability depending on the nature of the atoms.

8. The connections of electrons with atoms can be broken down by increasing the temperature.

9. The electrons move like the molecules of a gas." (1906, pp. 1, 17–18) 

Bizarrely, the lack of acceptance of Rydberg’s system was attributed by Hakala (1952, p. 582) to seeming evidence against a second rare-earth series in the seventh period (the eighth in Rydberg’s table), citing Soddy (1916, p. 254).

Janet, in 1928, subsequently included two periods of length two but by that time coronium and nebulium had fallen out of fashion so his first two periods had to be H-He, and Li-Be, a decision which was to haunt the reception of his table. https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=152

Mazurs (1957, p. 132) misleadingly redrew a spiral form of Rydberg’s table, in which the first four elements were instead the electron, neutron, H and He: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=973

I say "misleadingly" since Rydberg died in 1919, and the neutron wasn't discovered until 1932.

René

• Hakala RW 1952, Letters, Journal of Chemical Education, vol 29, no. 6, pp. 581–582, https://doi.org/10.1021/ed029p581.2
• Mazurs EG 1957, Types of Graphic Representation of the Periodic System of Chemical Elements, La Grange, Illinois
• Rydberg JR 1906, Elektron: Der erste Grundstoff, Håkan Olsson Buchdruckeri, Lund
• — 1913, Untersuchungen über das System der Grundstoffe, Lunds Univ. Årsskrift, (Acta Univers, Lundensis, vol. 9, no. 18, pp. 1–41
• — 1914, Recherches sur le système des éléments, Journal de Chimie Physique, vol. 12, pp. 585–639, https://doi.org/10.1051/jcp/1914120585
• Soddy F 1916, Radioactivity, Annual Reports on the Progress of Chemistry, vol. 13, pp. 245–272, https://doi.org/10.1039/ar9161300245

[Julio gutierrez samanez]

Muy bien René, siempre tú, exhaustivo, puntilloso e investigador. Nos has Ilustrado sobre el tema. Lo que no sé es si Janet (1929) que conocía el trabajo de Rydberg (1914) ya usó los números cuánticos azimutales, como la razón o fundamento de la periodicidad de los períodos dobles: s, s; ps, ps; dps, dps;.. Baca Mendoza (1953)  y sobre todo en (1965) en su obra de edición póstuma (qué hice publicar con Mark Leach) , pues el falleció en 1962, ya lo considera; aunque sus bínodos no comienzan con los nuevos azimutales (pero señala por ejemplo, la permanencia de orbitales s, después de los orbitales d, etc.
Algo que ninguno de ellos mostró es la función binódica  4n^2  graficada como parábola cuadrática ni mucho menos como: Z= 4 (sumatoria n^2). Aquí no se necesita ni neutrones ni electrones, mucho menos coronio ni nebulio. Solo comprender que el primer bínodo está conformado por elementos s y los siguientes dobles periodos comienzan con los nuevos azimutales. Sin necesidad de tríadas, octavas ni reglas de Mádelung. Simplemente, aceptar que el número cuántico principal. (o número del bínodo) Funciona para dos períodos pares o simétricos y no solo para un periodo. Esto no equivale a demoler la tabla periódica sino a recomponer sus partes colocando todo a su verdadero lugar. Mucho mejor separando los períodos iniciales de sus complementarios en los bínodos como hice en mi Genoma de la Materia que publicó Mark el 2018, lo que evidencia la  necesidad de un quinto número cuántico. Para evitar flagrancia contra el principio de Pauli:
00/00;
11111100/11111100;
222222222211111100/ 222222222211111100, etc.
Saludos
Julio

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[Jess Tauber]

Rene writes above, following Rydberg:  "The groups are not only divided into two halves, but, as the number of elements of a group suggests, they are further divided into four fractions, each containing p^2 elements. In the first four groups these fractions contain 1, 4, 9 and 16 elements; we will call them the quadrants of a group." (1914, p. 605).

Curious how we keep seeing numbers related to the Pascal Triangle (and its 'generalized' variants) in atomic math. Remember that in my discussion of the nuclear model, under the simple harmonic oscillator and for spherical nuclei, we have 'total shell energies' whose DIFFERENCES are all 3x simple square integers, in sequence. Multiplying shell occupancies by their energy levels (in terms of h-bar omega units) gives the following sequence: 1s=2x1.5=3; 1p=6x2.5=15; 1d2s=12x3.5=42; 1f2p=20x4.5=90; 1g2d3s=30x5.5=165; 1h2f3p=42x6.5=273; 1i2g3d4s=56x7.5=420; 1j2h3f4p=72x8.5=612. Starting from a default level of 0x0.5, differences between these total shell energies are: 3, 12, 27, 48,75, 108, 147, 192... successively, which turn out to all be 3x 1, 4, 9, 16, 25, 36, 49, 64...

I guess the question is WHY the harmonic oscillator, again and again, delivers results that can be rationalized by simple number theoretical models, combinatorics of the Pascal Triangle and its generalized variants, once you've broken these systems down into their component parts?

Jess Tauber