{"id": "card_n_cfb57dd6b005", "kind": "note", "title": "Radioactive decay — the exponential clock of matter", "body": "Sealed in-domain: after one half-life exactly half remains; after two, exactly one\nquarter (2^(−2) = 1/4, exact); carbon-14's decay constant is ln2/5730 years = 3.833×10⁻¹²\nper second: https://narrowhighway.com/s/8a5e89ab13bc499f39240c64360d90c34a65a291c91c73fcac4fc976131b17c5 . That constancy is the whole miracle of radiometric dating — a clock no\nchemistry, heat, or pressure can reset. The misconception \"two half-lives means it's gone\"\nseals BROKEN in-domain, with the remainder shown: https://narrowhighway.com/s/c3427196114ef0a0b5ed752c2233bdba9308f6ca78bbde70fe7364de2acaa6bb . The same exponential that\ndischarges a capacitor empties a nucleus's odds — the bench's RC clock and the carbon clock\nare one curve wearing different constants. WHY each isotope has its particular half-life is\nmeasured, not derived — quantum tunnelling through a barrier only QCD could size.", "source": {"label": "Concordance assay — 2026-07-09", "url": "https://narrowhighway.com/s/8a5e89ab13bc499f39240c64360d90c34a65a291c91c73fcac4fc976131b17c5", "ref": "nuclear_dig", "authority_tier": "engine_derived"}, "shelf": "science", "box": "nuclear", "bands": ["radioactive decay", "half-life", "carbon-14", "radiometric dating", "decay constant", "exponential", "c14 dating"], "connections": [], "author": "engine", "created_at": "2026-07-10T01:19:38.918200+00:00", "updated_at": "2026-07-10T01:19:38.918200+00:00", "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "metrics": {"paperclips_count": 0, "helpful_count": 0, "not_helpful_count": 0, "cite_count": 0, "walks_through_count": 0, "flagged_count": 0}, "source_hash": "d221817f3fc7bd7f91139de26854378c877c3add5ddedd5866a321cd724883b2"}