radioactive (adj.)

1590s, "cross-shaft, straight rod or bar," from Latin radius "staff, stake, rod; spoke of a wheel; ray of light, beam of light; radius of a circle," a word of unknown origin. Perhaps related to radix "root," but de Vaan finds that "unlikely." The classical plural is radii. 

The geometric sense of "straight line drawn from the center of a circle to the circumference" is recorded from 1650s. Meaning "circular area of defined distance around some place" is attested from 1853. As the name of the shorter of the two bones of the forearm from 1610s in English (the Latin word had been used thus by the Romans).

mid-14c., actif, active, "given to worldly activity" (opposed to contemplative or monastic), from Old French actif (12c.) and directly from Latin activus, from actus "a doing" (from PIE root *ag- "to drive, draw out or forth, move").

As "capable of acting" (opposed to passive), from late 14c. Meaning "energetic, lively" is from 1590s; that of "working, effective, in operation" (opposed to inactive) is from 1640s. The grammatical active voice is recorded from 1765; grammatical use of active, signifying performance and not endurance of an action, dates from mid-15c. (opposed to passive or reflexive).