The word 一阵子 is formed by combining the concept of a single, specific unit (一) with the idea of a short burst or period of activity, often with a natural or abrupt quality, as evoked by 阵 (which can imply a gust of wind or a sudden spell of something). The suffix 子 is then added not to change the core meaning, but to soften it into a colloquial, vague measure of a brief, somewhat indefinite duration, transforming a more concrete notion of an "event" into the familiar sense of "a little while".