Indian Journal of Industrial and Applied Mathematics

Rare earth elements are pivotal in various industries, including electronics, defence, renewable energy, and automotive sectors. The extraction and processing of rare earths are essential for modern technological advancements. This article explores the challenges in optimising extraction processes, reducing costs, and addressing environmental risks associated with rare earth mining. Emphasis is placed on sustainable practices and innovative solutions to ensure the responsible utilisation of these critical resources. We have also included in our study some inherent properties of the first inner transition elements to discuss some controversial results, with reference to reactivity and the nucleophilic and electrophilic character based upon inconsistencies in their electronegativity values. The discussion about electronegativities, in particular for the chemical elements of the first internal transition elements, is of paramount importance in helping the understanding of a number of relevant issues in basic and applied processes. This research review tackles the substantial issue regarding electronegativity as an essential key scientific discussion to make a breakthrough, so we will introduce substantial improvements in the next article to be made public for many readers interests to advance the state of the art in this broad area.