For tripositive ions of lanthanides, the ionic radius decreases with increasing atomic number because the electrons are being removed from the 4f orbitals, which have poor shielding. Gd\(^{3+}\), being closer to the middle of the lanthanide series, has the smallest size.
Thus, the correct answer is (E).
Considering Bohr’s atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of He+ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for Li++ ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of He+ ion for its ground state.
(D) the energy of He+ ion in its first excited state is same as that for Li++ ion in its ground state.