Regression Analysis for Better Understanding of Group I Elements

The compatibility of mathematical prediction and their agreement with the experimental data goes long way back in the history of science – most notably Physics. One of the important branches of mathematics is statistics and regression analysis is the vital element in this realm. The precise analysis and organizing of varying data have been possible due to the statistical calculations such as regression analysis. Through the intricate calculations of raw data using statistics, it has been easier for scientists to discover patterns and logical connection within the diverse range of data and information. Purpose: One of the important factors to distinguish the unique character of an element is its ionization energy or the energy required to make the electrons free from its atomic orbit or shell. Here, in this research, I have used the concept of Bohr’s atomic theory to determine the ionization energy of Hydrogen using mathematical analysis. Similarly, I have gathered the experimentally verified ionization energy data of other Group I alkali metals, and then I have used those data to establish logical connection between the elements using the mathematical concept of regression analysis. At last, I have shown how the ionization energy of Hydrogen varies greatly from the data obtained from the line of regression; Also, I have used the experimentally found regression equation to predict the ionization energy of the new hypothetical alkali metals having atomic number 119: which is yet to be experimentally verified. The main aim of this research was to show the mathematical relationship of the alkali metals and their compatibility with each other based on statistical analysis. Similarly, another purpose was to hypothetically establish the same coherent relationship between the alkali metals and unverified hypothetical element 119 using the underlying concept of statistics and mathematics. Statistical Methods: The atomic model of the, Danish physicist, Niels Bohr is used as a base model to calculate the ionization energy of Hydrogen; however, due to the limitation of the Bohr’s concept, the same method cannot be used to calculate the ionization energy of multiple electron system atoms. For this reason, experimentally verified ionization energy of alkali metals is taken as a raw data for the computational calculation of the line of regression and their corresponding equations. Keywords: Bohr’s atomic model, Regression analysis, Group I alkali metals, ionization energy (ground state level energy), Rydberg Constant, Planck Constant.