Radioactive decay — the exponential clock of matter

Sealed in-domain: after one half-life exactly half remains; after two, exactly one quarter (2^(−2) = 1/4, exact); carbon-14's decay constant is ln2/5730 years = 3.833×10⁻¹² per second: https://narrowhighway.com/s/8a5e89ab13bc499f39240c64360d90c34a65a291c91c73fcac4fc976131b17c5 . That constancy is the whole miracle of radiometric dating — a clock no chemistry, heat, or pressure can reset. The misconception "two half-lives means it's gone" seals BROKEN in-domain, with the remainder shown: https://narrowhighway.com/s/c3427196114ef0a0b5ed752c2233bdba9308f6ca78bbde70fe7364de2acaa6bb . The same exponential that discharges a capacitor empties a nucleus's odds — the bench's RC clock and the carbon clock are one curve wearing different constants. WHY each isotope has its particular half-life is measured, not derived — quantum tunnelling through a barrier only QCD could size.