Mathematical Pattern Analysis of the Periodic Table to Predict the Stability of Superheavy Elements and Location of the Island of Stability.

This study presents a hybrid approach combining empirical data analysis and the semi empirical mass formula (SEMF) to investigate nuclear stability and predict properties of superheavy elements. Using data up to Oganesson, polynomial regression was applied to model trends in neutron number, relative atomic mass, neutron to proton ratio and binding energy per nucleon. To provide a physical basis for these trends, the SEMF was incorporated, accounting for key nuclear interactions such as volume effects, Coulomb repulsion and neutron-proton asymmetry. The combined model enables estimation of optimal nuclear configurations in the superheavy region. The results predict a local maximum in stability around atomic number Z ≈ 120 dan neutron number N ≈ 184, corresponding to a neutron to proton ratio of approximately 1.5. this region aligns with the theoretically proposed island of stability, where superheavy nuclei may exhibit relatively enhanced stability. These findings demonstrate that integrating empirical modelling with nuclear theory provides a practical framework for exploring the limits of the periodic table and guiding future experimental investigations.