Absorption of visible light by a transition metal complex is generally due to d−d transitions. This requires the central metal ion to have an incompletely filled d-subshell (d1 to d9 configuration).
Let's check the electronic configurations of the central metal ions in the given complexes:
(A) In [Sc(H2O)3(NH3)3]3+, the oxidation state of Sc is +3. The electronic configuration of Sc3+ (Z=21) is [Ar]3d0. Since it has no d-electrons, no d−d transition can occur.
(B) In [Ti(en)2(NH3)2]4+, the oxidation state of Ti is +4. The electronic configuration of Ti4+ (Z=22) is [Ar]3d0. It also has no d-electrons, so no d−d transition is possible.
(C) In [\text{Cr(\text{NH}_3)}_6]^{3+}, the oxidation state of Cr is +3. The electronic configuration of Cr3+ (Z=24) is [Ar]3d3. It has three unpaired d-electrons (t2g3eg0), making it capable of undergoing d−d transitions and absorbing visible light.
(D) In [Zn(NH3)6]2+, the oxidation state of Zn is +2. The electronic configuration of Zn2+ (Z=30) is [Ar]3d10. Since the d-subshell is completely filled, there are no empty d-orbitals available for electrons to transition into, meaning d−d transitions are not possible.
Therefore, [\text{Cr(\text{NH}_3)}_6]^{3+} is the only complex expected to absorb visible light.