Origins
Nuclear power is, at its etymological core, nut power. The word comes from nucleus, Latin for 'kernel' or 'inner part', a diminutive of nux — 'nut'. A nucleus is a little nut: the hard centre inside.
The word's scientific career began in 1704, when Edmond Halley used nucleus to describe the solid centre of a comet. In 1831, Robert Brown borrowed it for the central body he observed inside plant cells. In 1844, Michael Faraday applied it to the central part of an atom. Each step moved the little nut deeper into the heart of matter.
The discovery of nuclear fission in 1938 changed the word permanently. When Otto Hahn and Fritz Strassmann split a uranium nucleus, the energy released was millions of times greater than any chemical reaction. The humble nut-word became the most feared term in geopolitics.
Later History
The nuclear family — parents and children only, no extended relatives — predates the atomic sense. It was first used in 1925 to describe the core unit of family structure, the kernel around which wider kinship is arranged.
The common mispronunciation 'nucular' (rhyming with 'particular') is attested since the 1940s and was used by multiple US presidents, most notably Dwight Eisenhower and George W. Bush. Linguists note it follows a natural English pattern of inserting a vowel for easier pronunciation, the same process that gives some speakers 'athalete' for athlete.