Short-lived radioisotopes are element selectively ionized by the resonance ionization laser ion source (RILIS) of the on-line isotope separator ISOLDE (CERN). The relative production of low- and high-spin isomers can be significantly changed when a narrow-bandwidth laser is used to scan through the atomic hyperfine structure. This allows the assignment of gamma ray transitions to the decay of the individual isomers. Moreover, the measurement of the hyperfine splitting provides a very sensitive method for the determination of magnetic moments of exotic isotopes. The technical developments are discussed for the example of copper.