1. Identify the species involved

The elements given are lanthanoids:

• $Ce$ = Cerium
• $Sm$ = Samarium
• $Tb$ = Terbium
• $Lu$ = Lutetium

2. Use the concept of lanthanoid contraction

Across the lanthanoid series, as atomic number increases, the ionic radii of the common ions decrease gradually.

This happens because electrons are added to the $4f$ subshell, and $4f$ electrons shield the nuclear charge poorly. Hence, the effective nuclear charge increases from left to right, pulling the electrons closer.

This phenomenon is called lanthanoid contraction.

3. Apply it to the given elements

The order of these elements in the lanthanoid series is: $Ce < Sm < Tb < Lu$ (increasing atomic number)

Therefore, their ionic radius decreases in the same direction: $Ce > Sm > Tb > Lu$

4. Match with the options

• A: $Ce > Sm > Tb > Lu$ ✅
• B: $Lu > Tb > Sm > Ce$ ❌ reverse order
• C: $Tb > Lu > Sm > Ce$ ❌ incorrect
• D: $Sm > Tb > Lu > Ce$ ❌ $Ce$ should be the largest

5. Final answer

The correct order of ionic radius is: $Ce > Sm > Tb > Lu$ So, the correct option is A.