Chemistry Electronegativity Chlorine Gt Sodium

The chlorine-sodium ordering

Electronegativity is a chemical property that measures how strongly an atom attracts electrons in a bond. On the Pauling scale, chlorine (atomic number 17) is clearly more electronegative than sodium (atomic number 11), a fact familiar to any student of the periodic table. The Recognition Science library contains a theorem, named chlorine_gt_sodium, that reproduces this ordering using a simple arithmetic proxy rather than any measured data.

The proxy is defined in the library as a formula. For an element with atomic number Z, the electronegativity proxy (a stand-in value meant to track the real property) is the number of valence electrons divided by the length of the element's period. Oxygen, with 6 valence electrons in a period of length 8, gets a proxy value of 3/4. Fluorine, with 7 valence electrons in the same period, gets 7/8. The theorem chlorine_gt_sodium states that the proxy for chlorine (17) is greater than the proxy for sodium (11). Since chlorine has 7 valence electrons in period 3 and sodium has 1 valence electron in period 3, the values are 7/8 and 1/8, respectively, making the inequality immediate.

The theorem is proved by direct computation, using the definitions of the proxy, valence electron counts, and period lengths. It is a formal statement about the library's own definitions, not a claim about measured electronegativity values. The library does not assert that the proxy equals the true electronegativity of any element. It only shows that this particular simple formula produces the same ordering that chemists observe for these two elements.

In Recognition Science, this result is part of a broader pattern. The framework models electronegativity as depending on shell structure and distance to closure, meaning how close an atom is to completing its outer electron shell. The library proves similar ordering theorems for other pairs, such as fluorine greater than oxygen, nitrogen, carbon, and lithium, and cesium lower than fluorine. These are all statements about the proxy, not about the actual measured values from chemistry handbooks.

The practical consequence is narrow but real: a purely structural rule based on electron shell positions can reproduce a well-known chemical ordering. The theorem does not claim that the proxy is the true electronegativity, that it matches any particular scale like Pauling or Mulliken, or that it predicts any property beyond the ordering itself. It is a formal check that a simple model captures a known trend, nothing more.

/-- Chlorine (Z=17) has higher EN ranking than Sodium (Z=11). -/
theorem chlorine_gt_sodium : enRanking 17 > enRanking 11 := by
  simp only [enRanking, valenceElectrons, periodLength, prevClosure, nextClosure]
  norm_num

/-- Simplified EN ranking: valenceElectrons / periodLength.
    Higher valence fraction = higher EN (within same shell). -/
def enRanking (Z : ℕ) : ℝ :=
  if periodLength Z = 0 then 0
  else (valenceElectrons Z : ℝ) / (periodLength Z : ℝ)

/-- Oxygen (Z=8) has EN ranking 6/8 = 3/4. -/
theorem oxygen_ranking : enRanking 8 = 3/4 := by
  simp only [enRanking, valenceElectrons, periodLength, prevClosure, nextClosure]
  norm_num

/-- Fluorine (Z=9) has EN ranking 7/8. -/
theorem fluorine_ranking : enRanking 9 = 7/8 := by
  simp only [enRanking, valenceElectrons, periodLength, prevClosure, nextClosure]
  norm_num

What this page does not claim

The proxy is not a measurement of electronegativity and does not match any specific scale like Pauling or Mulliken. The theorem does not predict any property beyond the ordering itself, such as bond polarity or reaction energy. The framework does not claim that the proxy is the true physical mechanism of electronegativity, only a structural model.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/Electronegativity.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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