Decay chains of

This study investigates the decay chains of 233Th and 234Th isotopes, emphasizing their nuclear stability and transformation pathways. Thorium isotopes, integral to environmental and health concerns, undergo diverse radioactive decay modes: proton decay, alpha decay, beta decay (β+ and β−), and spontaneous fission. Using the effective liquid drop model and semi-empirical formulas, the half-lives of these decay modes were calculated. Results reveal that alpha and beta decays dominate the decay chains of both isotopes, with their pathways involving multiple transformations to achieve nuclear stability. For 233Th, the decay sequence progresses through β−-decay into 233Pa, followed by additional β−-decay to 233U. This nucleus undergoes successive alpha decays, ultimately stabilizing as 205Tl. Similarly, 234Th decays through β−-decay to 234Pa and then 234U, which transitions through alpha decay sequences, stabilizing as 206Pb. The calculated half-lives span from milliseconds to years, correlating with energy release and nuclear characteristics. The study highlights the critical role of alpha and beta decays in thorium's stability pathways, providing a detailed understanding of their decay behaviors. These insights contribute significantly to nuclear physics, environmental safety, and radiometric dating applications.