Lanthanoid which has the smallest size in \( +3 \) state is:
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In the lanthanide series, as the atomic number increases, the electrons are added to the \( 4f \) subshell, which does not shield the nucleus effectively, leading to a decrease in atomic and ionic size. This is known as the lanthanide contraction.
In the lanthanide series, the ionic size of lanthanoids decreases as we move from \( Ce^{3+} \) to \( Lu^{3+} \) because the effective nuclear charge increases with the increasing atomic number while the electron shielding remains nearly constant.
Lanthanum and Lutetium have the smallest ionic radii in the \( +3 \) oxidation state. Lutetium (\( Lu^{3+} \)) has the smallest ionic radius because of the f block contraction, where the size of the atoms decreases as the atomic number increases from \( La^{3+} \) to \( Lu^{3+} \).
Final Answer: Option (d) \( Lu \).