the second group of radionuclides that exist naturally consists of [[radiogenic nuclide]]s such as (t = ), an isotope of [[radium]], which are formed by [[radioactive decay]]. they occur in the decay chains of primordial isotopes of uranium or thorium. some of these nuclides are very short-lived, such as [[isotopes of francium]]. there exist about 51 of these daughter nuclides that have half-lives too short to be primordial, and which exist in nature solely due to decay from longer lived radioactive primordial nuclides.