You are correct that, in general, the radius of an atom decreases as the atomic number increases. This trend is observed in the periodic table and is known as the periodic trend of atomic size or atomic radius.
However, when it comes to the study of lanthanide and actinide elements, a different phenomenon called "lanthanide contraction" and "actinide contraction" is observed. Lanthanide contraction refers to the gradual decrease in the size of atoms or ions as you move across the lanthanide series (elements with atomic numbers 57 to 71) in the periodic table. Similarly, actinide contraction refers to the decrease in size observed across the actinide series (elements with atomic numbers 89 to 103).
The reason for lanthanide and actinide contractions can be attributed to the unique electronic configurations of these elements. Lanthanides and actinides have partially filled 4f and 5f electron subshells, respectively. These subshells shield the outermost electrons from the increasing nuclear charge less effectively than the 3d and 4d subshells in the transition metals.
As a result, the increased effective nuclear charge (Zeff) experienced by the outermost electrons in the lanthanide and actinide elements leads to a stronger attraction between the nucleus and the outer electrons. This stronger attraction causes a contraction in the atomic and ionic radii of these elements compared to what would be expected based solely on the periodic trend of atomic size.
The study of lanthanide and actinide contraction is important in various fields, including chemistry and materials science. Understanding the size variations in these elements helps in predicting and explaining their chemical behavior, complexation properties, and physical properties. Additionally, it has implications in the design and synthesis of materials and compounds that incorporate these elements.