Why scientists care
Atomic radius is not a single directly measurable hard boundary; several operational definitions are used, such as covalent, metallic and van der Waals radii.
The definition must be stated before comparing values. Periodic trends are useful, but different radius definitions should not be mixed.
A concrete example
A sodium atom is larger than a chlorine atom in the same period because effective nuclear attraction increases across the row.
Try to notice
Science becomes memorable when a definition is connected to something measurable or observable.