Determine the Atomic Number That Maximizes the Binding Energy Per Nucleon Using an Algebraic Approach

The semi-empirical mass formula, or the liquid drop model, is a common method used to estimate nuclear binding energy. Based on this model, the most stable nuclide can be identified by determining the atomic number that maximizes the binding energy per nucleon (BEN) using calculus. However, using calculus here may not be appropriate since the independent variable, atomic number A, is always an integer and thus BEN, expressed as a function of A, is not differentiable. In the present work, I will present an algebra-based approach to find the atomic number that yields the maximal BEN. It involves applying the AM-GM inequality creatively and methodically.