nitrogen_ranking
plain-language theorem explainer
Nitrogen at atomic number 7 has electronegativity ranking 5/8 under the RS shell-closure model. Periodic trend analysts citing CH-008 predictions would reference the result. The proof simplifies the ranking definition to valence count over period length then evaluates the arithmetic for Z=7.
Claim. The ratio of valence electrons beyond the prior noble gas closure to the length of the current period for atomic number 7 equals $5/8$.
background
The Electronegativity module models rankings from phi-ladder scaling of shell structure. Electronegativity measures an atom's tendency to attract electrons and follows distance to next closure modulated by shell number, with the classical link to sqrt of ionization energy times electron affinity replaced by a closure-based proxy.
proof idea
The proof applies simplification to the ranking definition, valence electron count, period length, and closure functions. It then reduces the resulting numerical expression for Z=7.
why it matters
This result supplies a concrete instance for the ordering predictions listed in the CH-008 module section. It confirms ranking increase across the second period and supports the general claim that higher valence fraction yields higher ranking within a shell. The module lists five key predictions including fluorine at the top and noble gases at the bottom.
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