Abstract: The decay of atomic nuclei, a process characterized by the transformation of nuclei through the emission of particles or the capture of electrons, is a phenomenon of immense scientific significance. Its exploration and accurate analysis hold the key to unraveling the intricate structure of unstable nuclei, gaining insights into neutrino energy spectra, and validating the underlying principles of decay theories. One of the scientific pursuit of decay lies in the meticulous calculation of the decay spectrum. The decay spectrum serves as a fundamental aspect in the understanding of nuclear decay process. Its comprehensive consideration is pivotal for advancing our knowledge across various domains, from probing the depths of unstable nuclei to extracting valuable information regarding neutrino energy spectra. Moreover, it plays a crucial role in the validation and refinement of existing decay theories, contributing to the continuous evolution of our understanding of nuclear physics. The indispensable part in computing the decay energy spectrum is intricately tied to the consideration of the decay branching ratio. This parameter, crucial for understanding the relative probabilities of different decay pathways, is typically obtained through sophisticated measurement techniques. Commonly, researchers employ the γ-γ coincidence method or directly measure with total absorption spectrometer method to obtain data on β decay products. These methods provide essential information that serves as the foundation for unraveling the complexities inherent in the decay process. Simultaneously, the calculation of the decay spectrum at the transition of a single energy level is based on the Fermi decay theory. Rooted in quantum mechanics, this theory offers a comprehensive framework for calculating the transition probabilities associated with nuclear decay. It enhances the accuracy of predicting the decay spectrum, enabling to develop a nuanced understanding of the underlying physics governing these processes. In the context of this paper, the empirical focus was on the decay of ⁹⁶Y, serving as a representative example. The experimental decay branching ratio data for ⁹⁶Y decay meticulously evaluated and from TAGS were discussed. To further refine the computed decay spectrum, shape factor correction was introduced. The addition of shape factor correction represented an adjustment, aimed at improving the alignment between theoretical predictions and experimental observations. This correction mechanism ensures that the computed energy spectrum not only adheres closely to the experiment data but also reflects the intricacies of the underlying decay processes. Beyond its specific implications for the decay of ⁹⁶Y, the necessity of fostering a deeper understanding of atomic decay processes and taking forbidden transitions into consideration was stressed.