Although the advent of ionization energies predated Slater’s rule, there was unawareness of the utilitarian value of the former for the computation of effective nuclear charge (ENC for short) until recently and in this research. The study aimed to derive another equation in which the average ionization energies of hydrogen and any other multi-electron atom are independent variables. The objective was to answer the question in the literature that states, "Are Slater’s Rules the Best Approach for Calculating Effective Nuclear Charge for Undergraduates?" (Moore & Birnbaum, 2014) and compare the graphical portrayal of chemical periodicity between outcomes using data generated using Slater's rules for some elements and data generated in this research. By exploring theoretical and computational methods and the data in the literature, the study showed that ENC (1.34458-3.32446) for the first 30 elements computed using the 2021 CODATA fine structure constant (FSC, for short) was higher than those (1.34402-3.32309) without it; however, the equation containing the computed FSC using e^2/2_0hc and other equations gave the same value of ENC. The use of Slater’s result (atomic radii) for the computation of ENC (1.29859-5.06996) and average ionization energy, IE (553.21-2108.13 kJ), gave higher values than other methods. All plots using Slater’s values of ENC and IE versus atomic number (Z) did not show chemical periodicity (greater linearity), unlike the use of other values (less linearity or lower R^2). The new equation was derived, and with earlier equations, ENC can be accurately computed; they should therefore be part of the school curriculum at all levels without ceasing to teach Slater’s rule, which is not the best approach. A future study should include 30 other elements of the periodic table.