The emittance of ion beams produced by a disc-shaped hot cavity ion source are calculated using a numerical model of taking into account the radioactive decay of particles. The changes of beam emittance with the nuclide half-life were studied for the two different cavity shapes, the compact and the flat disc cavity. In both these cases emittance increases with τ1/2. However, the compact ionizer configuration prevails in terms of beam quality for easy-to-ionise substances. The influence of the extraction channel is also under investigation. Although the emittance rises with the extraction opening radius for the both considered shapes it is shown that in case of the compact ionizer the saturation of that growth is observed. The scaled efficiency calculations results show that the compact cavity configuration is more tolerant to beam divergence effects due to the increasing extraction channel diameter. This shape is proved to be the superior one, especially for short-lived nuclides.