Chemistry Atomic Radii Oganesson Full Shell

The closed shell of oganesson

Oganesson is the heaviest known element, with atomic number 118, sitting at the end of period 7 on the periodic table. Its valence shell, the outermost electron shell that participates in chemical bonding, is full. In the standard periodic table, each period ends with a noble gas whose valence shell is complete: helium at period 1, neon at 10, argon at 18, and so on. Oganesson, as the last element of its period, follows this pattern. The Recognition Science framework's machine-checked library of formal theorems contains a declaration named oganesson_full_shell that proves this fact in its own terms. The theorem states that the number of valence electrons for element 118 equals the length of its period, a definition that matches the classical picture of a closed shell.

In the framework's model of atomic radii, each element gets a shell number based on its period, and a radius proxy scales with the golden ratio raised to that shell number. A screening factor reduces this base radius according to how many valence electrons the element has. For a full shell, the screening factor takes a specific value, and the framework proves this for all the noble gases, from helium through radon to oganesson. The theorem for oganesson is one of a series that also covers neon, argon, krypton, xenon, and radon. These declarations are not measurements of physical radii; they are formal statements about the framework's definitions of shell number, period length, and valence electron count.

What the declaration does not claim is any empirical value for oganesson's atomic radius. The framework's radius proxy is a model, a definitional choice, not a measured quantity. The theorem establishes a consistency between the framework's internal definitions and the known periodic structure, but it does not predict a specific radius in picometers or any physical measurement. The framework's own documentation notes that noble gases have local maxima in their periods but are special due to their closed shells, and the theorem confirms the shell is closed in the framework's arithmetic. The comparison between the framework's radius proxy and measured atomic radii from chemistry is an empirical check, not a theorem, and the framework does not claim to have measured oganesson's radius.

theorem oganesson_full_shell : valenceElectrons 118 = periodLength 118 := by native_decide

theorem neon_full_shell : valenceElectrons 10 = periodLength 10 := by native_decide

theorem argon_full_shell : valenceElectrons 18 = periodLength 18 := by native_decide

theorem krypton_full_shell : valenceElectrons 36 = periodLength 36 := by native_decide

theorem xenon_full_shell : valenceElectrons 54 = periodLength 54 := by native_decide

theorem radon_full_shell : valenceElectrons 86 = periodLength 86 := by native_decide

/-- Atomic radius proxy: combines shell and screening effects.
    radius = shellRadius * screeningFactor -/
def radiusProxy (Z : ℕ) : ℝ :=
  shellRadiusProxy Z * screeningFactor Z

What this page does not claim

The declaration does not predict a numerical value for oganesson's atomic radius in any physical unit. The theorem does not establish that the framework's model matches any experimental measurement of atomic radii. The declaration does not claim that oganesson behaves chemically like a typical noble gas in practice.

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/AtomicRadii.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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