The Mystery of the Periodic Table

The mystery of the Periodic Table PT is the arrangement into a rectangular grid with elements/atoms listed with increasing atomic number into rows of length 2, 8, 8, 18, 18, 32, 32..., signifying number of electrons with twice repeated periods according to $2n^2$ with $n=1,2,3,4.$ Basic questions are: 

1. Why periods of length 2, 8, 18, 32?
2. Why the factor 2 in $2n^2$?
3. Why repetition of periods 8, 8 et cet?
4. What is the meaning of filled shells with 2, 8, 18 and 32 electrons defining the periods? 

The answer by text book Standard Quantum Mechanics StdQM is that electrons arrange around atomic kernels in s, p, d and f orbitals with 1, 3, 5 and 7 electrons as spherical harmonics, and that s+p orbitals give a filled shell with 4 electrons, s+p+d orbitals give a filled shell with 9 electrons, s+p+d+f orbitals fill a shell with 16 electrons, which is viewed to be an answer to 1. An answer to the factor 2 is given by introducing a 4th quantum number as spin in an ad hoc fashion. Questions 3 and 4 have complex answers, if any.

StdQM seeks to explain chemical properties of atoms in the PT as the result of formality of spherical harmonics.

RealQM is an alternative to StdQM which gives completely different answers to 1-4. Electrons in RealQM have non-overlapping supports and meet at a common boundary with continuity of charge density.

• RealQM starts (after Hydrogen with one electron) with Helium with 2 electrons each occupying a half-space and meeting at a common plane containing the kernel together forming a 1st shell. 
• Lithium with 3 electrons has 2 electrons in a Helium-configuration and the third electron in an outer 2nd shell. 
• Beryllium with 4 electrons has a shell structure with 2 electrons in 1st shell and 2nd shell split into 2 half-shells.  
• Boron with 5 electrons has 2 electrons in 1st shell and 2nd shell split into 3 electrons. 
• The 2nd shell is filled with 8 electrons, which comes from splitting each 2nd half-shell into $2\times 2=4$ electrons and gives Neon with atomic number 10.
• The 3rd shell is filled with 18 electrons which comes from splitting each 3rd half-shell into $3\times 3=9$ electrons. 

RealQM explains PT as the result of a geometric packing problem. RealQM invites to an exploration of chemical properties of atoms resulting from electron packing. RealQM opens to a rich structure of subshells. 

Comment by chatGPT:

🔎 Summary of the post’s main argument

• The post asks why the Periodic Table is arranged in “periods” (rows) of length 2, 8, 18, 32… — i.e. following the sequence $2n^2$ for $n=1,2,3,\dots$. claesjohnson.blogspot.com

• According to standard quantum mechanics (StdQM), the explanation involves electron orbitals (s, p, d, f …) and quantum numbers (including “spin”) — giving filled shells that reflect the period lengths. claesjohnson.blogspot.com

• Johnson claims this is an ad hoc, formal explanation — in his view unsatisfying or incomplete — and instead promotes an alternative he calls RealQM. claesjohnson.blogspot.com

• In RealQM, electrons “have non-overlapping supports” and “meet at a common boundary” with continuous charge density. Johnson argues that under this model the periodicities arise from a geometric “packing problem,” rather than spherical-harmonic orbitals. claesjohnson.blogspot.com

👍 What is interesting / worth discussing

1. Challenging orthodoxy. The article embodies a classic scientific-philosophical stance: questioning accepted theory, highlighting what may be “formalism without physical insight.” That sort of critical inquiry can sometimes lead to deeper understanding or new perspectives. It’s healthy for science to revisit foundational assumptions — especially in complex domains like quantum mechanics.

2. Simplicity and intuition. The idea of a geometric/packing-based model for electron shells is intuitively attractive: structure emerging from “space-filling” constraints has a kind of classical appeal. For readers uncomfortable with purely mathematical abstractions (wavefunctions, Hilbert-space, probability amplitudes), a more “visualizable” model can feel more concrete.

3. Encouraging deeper questions. By raising “why this pattern?” instead of “because quantum mechanics says so,” the post encourages reflection on why the standard model is accepted — what is explanatory vs. what is computational convenience. That attitude often underpins conceptual advances.

🤔 What is problematic or questionable

1. Lack of established support. The proposed RealQM does not — at least in this post — come with detailed quantitative evidence (e.g., calculated energy levels, spectral lines, chemical behavior) matching observed atomic physics. The standard quantum model is supported by a vast body of empirical evidence (spectra, chemical periodicity, atomic interactions) — any alternative needs equally strong backing.

2. Orbital theory’s empirical success. The standard explanation using orbitals, quantum numbers including spin, and the mathematics of wavefunctions has proven extremely successful: it predicts atomic spectra, chemical behavior, ionization energies, etc. Any alternative must reproduce all of that, not just the period lengths.

3. Risk of oversimplification. The “geometric packing” picture may offer intuition, but nature at the atomic scale doesn’t behave like classical rigid balls — quantum mechanics shows that electrons are delocalized, subject to the uncertainty principle, and have wave-like properties. A model based purely on classical geometry risks missing essential quantum phenomena.

4. Ad-hoc replacement. Introducing non-overlapping “supports” and partitioned “half-shells” seems itself an assumption that needs justification. Without physical derivation (from fundamental equations) the new model risks being as arbitrary as the one it critiques.

🧠 Broader reflections: What the debate tells us about scientific theories

• The periodic table — simple and familiar to chemists and physicists — encodes deep quantum-mechanical truths. The fact that there is a straightforward pattern (2, 8, 18, 32…) is part of why quantum theory was such a breakthrough. Understanding why the pattern emerges fosters better insight into what the theory means.

• However, successful theories are not judged solely by offering “intuitive pictures,” but by their predictive and explanatory power. Theories must match data, across many phenomena (spectra, chemical reactivity, bonding, etc.).

• Creative, critical proposals — like RealQM — can inspire reexamination of foundations; but they must eventually confront the full weight of empirical evidence.

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