"carbon-14," a radioactive isotope of carbon, 1940, from radio-, combining form of radioactive, + carbon. Radio-carbon dating is attested from 1949 (the carbon-14 in organic matter decays at a known rate from the time of death).
1898, of an atomic nucleus, "capable of spontaneous nuclear decay releasing ionizing emissions," from French radio-actif, coined by Pierre and Marie Curie from radio-, combining form of Latin radius "ray" (see radius) + actif "active" (see active). Of processes, etc., "involving or produced by radioactivity," by 1903.
non-metallic element occurring naturally as diamond, graphite, or charcoal, 1789, coined 1787 in French by Lavoisier as charbone, from Latin carbonem (nominative carbo) "a coal, glowing coal; charcoal," from PIE root *ker- (3) "heat, fire."
Carbon 14, long-lived radioactive isotope used in dating organic deposits, is from 1936. Carbon-dating (using carbon 14) is recorded from 1958. Carbon cycle is attested from 1912; carbon footprint was in use by 2001. Carbon-paper "paper faced with carbon, used between two sheets for reproduction on the lower of what is drawn or written on the upper" is from 1855, earlier it was carbonic paper (1850).
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Harper, D. (n.d.). Etymology of radio-carbon. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/radio-carbon