The correct order of ionic radii of \(Y^{3+}, La^{3+}, Eu^{3+}\) and \(Lu^{3+}\) is:

\(Y^{3+} < Lu^{3+} < Eu^{3+} < La^{3+}\)

The correct answer is (4), \(Y^{3+} < Lu^{3+} < Eu^{3+} < La^{3+}\)

The ionic radii of the lanthanide ions decrease as the atomic number increases. This is due to the lanthanide contraction, which is a decrease in the size of the lanthanide ions due to the increasing nuclear charge.

Yttrium is not a lanthanide element, but it has similar chemical properties. The ionic radius of Y3+ is slightly larger than the ionic radii of the lanthanide ions.

Therefore, the order of the ionic radii of \(Y^{3+}, La^{3+}, Eu^{3+},\) and \(Lu^{3+}\) is:\(Y^{3+} < Lu^{3+} < Eu^{3+} < La^{3+}\)