Chemistry Ionic Bond Alkali Valence One

The alkali valence fact

An alkali metal is any element in the first column of the periodic table: lithium, sodium, potassium, rubidium, cesium, and francium. Their defining chemical property is that each has exactly one electron in its outermost shell, the valence electron that participates in bonding. This single electron explains why the alkali metals are so reactive: losing it leaves a stable, noble-gas-like cation with a full outer shell. The fact is standard textbook chemistry, known since the periodic table was organized in the 1860s by Dmitri Mendeleev and others.

The Recognition Science framework's machine-checked library of formal theorems includes a declaration named alkali_valence_one. It states that every element in the list [3, 11, 19, 37, 55, 87], which is the framework's representation of the alkali metals by atomic number, has exactly one valence electron. The proof is computational: the declaration checks each element in the list and confirms the count. This is a formal restatement of the classical fact, not a new chemical claim. The framework models the periodic table's first column with this list and then proves the one-valence-electron property for each member.

The declaration is part of a larger framework that tries to derive chemical behavior from a small set of axioms about recognition cost. In that framework, the alkali metals' single valence electron pairs with the halogens' need for one more electron to complete a shell. A separate theorem, alkali_halogen_stable_1_1, combines the alkali valence fact with the halogen distance-to-closure fact to show that a 1:1 alkali-halogen compound is stable in the framework's sense. This is the framework's way of encoding why sodium chloride forms as NaCl rather than Na2Cl.

What the declaration does not claim is important. It does not derive the existence of alkali metals from first principles; the list of atomic numbers is an input, not an output. It does not prove that the ionization energy is low, though that is a separate assumption in the framework. It does not establish the Madelung constant or lattice energy values, which are defined elsewhere as proxies. The declaration is a narrow, verified fact about a list of elements, useful as a building block but not a standalone theory of ionic bonding.

/-- Helper: all alkali metals have valence 1. -/
private theorem alkali_valence_one : ∀ z ∈ alkaliMetalZ, valenceElectrons z = 1 := by
  intro z hz
  simp only [alkaliMetalZ, List.mem_cons, List.mem_nil_iff, or_false] at hz
  rcases hz with rfl | rfl | rfl | rfl | rfl | rfl <;> native_decide

/-- Ion pair stability: alkali + halogen forms stable 1:1 compound.
    Alkali metals have 1 valence electron, halogens are 1 electron from closure. -/
theorem alkali_halogen_stable_1_1 (Z_alkali Z_halogen : ℕ)
    (h_alkali : isAlkaliMetal Z_alkali) (h_halogen : isHalogen Z_halogen) :
    valenceElectrons Z_alkali = 1 ∧ distToNextClosure Z_halogen = 1 := by
  exact ⟨alkali_valence_one Z_alkali h_alkali, halogen_dist_one Z_halogen h_halogen⟩

What this page does not claim

The declaration does not derive the existence or properties of alkali metals from first principles; the atomic number list is an input. The declaration does not prove that alkali metals have low ionization energy, which is a separate framework assumption. The declaration does not establish Madelung constants or lattice energy values, which are defined separately as proxies.

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

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