This study investigates radiative proton capture reactions in light nuclei such as [⁹B- ⁷Li, - ⁷Be], which are crucial in stellar nucleosynthesis and energy production. The Woods-Saxon potential model was employed to describe nuclear interactions, and the Schrödinger equation was solved to determine bound and continuum state wave functions accurately. Astrophysical S-factors and reaction cross-sections were calculated at low energies characteristic of stellar environments, accounting for nuclear resonance effects that significantly enhance reaction probabilities. Radiative proton capture reactions, of the form A(p,γ)B, are fundamental processes in nuclear astrophysics. They are the primary mechanism for synthesizing elements in both hydrostatic and explosive stellar environments. he formation of ⁷Li and ⁷Be is a key outcome of the Big Bang. The reaction ³He(α,γ)⁷Be is the primary source of ⁷Be, which later decays to ⁷Li. Understanding the ⁷Be system is thus crucial for predicting the primordial lithium abundance. The theoretical results show strong agreement with experimental data, validating the model's reliability. These findings provide precise inputs for refining nuclear reaction rates in stellar evolution models, thereby improving predictions of elemental synthesis and energy generation in stars.