1841, "of or like the nucleus of a cell," from nucleus + -ar, probably by influence of French nucléaire. General sense of "central" is from 1912. In atomic physics, "of or belonging to the nucleus of an atom," from 1914; of weapons deriving their destructive power from nuclear reactions, by 1945.
Hence nuclear energy (1930), nuclear physics (1933), nuclear weapon (1947), nuclear war (1950; once in 1946 in reference to hypothetical attacks with nuclear rays). Nuclear winter was coined by U.S. atmospheric scientist Richard Turco but is first attested in article by Carl Sagan in "Parade" magazine, Oct. 30, 1983. Nuclear family, originally a sociologists' term, is first attested 1949 in "Social Structure," by American anthropologist G.P. Murdock (1897-1985).
The alternative adjective nucleal is recorded from 1840, probably from French. Also compare nucleic.