In this paper, we systematically studied half-lives of the different decay modes using various theoretical models such as the unified fission model (UFM) and the effective liquid drop model. Beta-decay half-lives were evaluated using semi-empirical formulae available in the literature. We compared half-lives of all the studied decay modes and identified shorter half-lives among the same in [Formula: see text]Ac nuclei. We investigated the actinium series which is similar to the thorium series. Among these decay series, alpha-emitting isotopes show great promise for cancer treatment because of their short path length and high-energy transfer of radiation. Furthermore, we predicted the decay chains of the actinium isotopes. All the decay series of actinium ends with the formation of stable nuclei or with longer half-lives. The predicted decay series and new isotopes during the decay process are helpful in the field of medicine and radiotherapy.