The correct order of ionic radii for the given ions is:

Solution

1. Lanthanoid contraction refers to the steady decrease in ionic radii as the atomic number increases from $\text{La}$ to $\text{Lu}$.
2. The atomic numbers are $\text{Pm}(61)$, $\text{Sm}(62)$, $\text{Eu}(63)$, and $\text{Gd}(64)$.
3. As the atomic number increases, the effective nuclear charge increases, pulling the electrons closer to the nucleus.
4. Therefore, the ionic radii follow the order ${\text{Gd}}^{3+}<{\text{Eu}}^{3+}<{\text{Sm}}^{3+}<{\text{Pm}}^{3+}$.
5. Hence the answer is (B).