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Summary form only given. We have performed a study of quantum jumps in single magnesium ions held in a Penning trap. This system is unusual in that quantum jumps may be observed using only a single laser frequency which serves to laser cool the ion (providing fluorescence for detection), shelve the ion in a metastable state (via an off-resonant Raman transition) and also to repump the ion from the metastable state back into the cooling cycle (again via a Raman transition). Single /sup 24/Mg/sup +/ ions have been studied in a Penning trap before but we have predicted and now observed a number of interesting effects that occur only in /sup 25/Mg/sup +/. We have also trapped single ions of /sup 26/Mg/sup +/ and confirmed that their quantum jump behaviour is similar to that of /sup 24/Mg/sup +/ as expected. The novel features in the behaviour of /sup 25/Mg/sup +/ are due to the presence of hyperfine structure in this ion.