For which of the following complexes, the energies of the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals will be lower than the other three d orbitals?

• A. [Co(en)₃]³⁺
• B. [Ni(CN)₄]^2–
• C. [Zn(H₂O)₄]²⁺
• D. [AuCl₂]^–

Answer: (C)

Verified step by step guidance

1. Identify the geometry of each complex. The geometry affects the splitting of the d orbitals. For example, [Co(en)3]3+ is octahedral, [Ni(CN)4]2– is square planar, [Zn(H2O)4]2+ is tetrahedral, and [AuCl2]– is linear.
2. Understand the concept of crystal field splitting. In octahedral complexes, the dx2−y2 and dz2 orbitals are higher in energy compared to the other three d orbitals (dxy, dxz, dyz). In tetrahedral complexes, the opposite is true; the dx2−y2 and dz2 orbitals are lower in energy.
3. Analyze the electronic configuration of the metal ions in each complex. This helps in understanding how the d orbitals are filled and which orbitals are affected by the ligand field.
4. Consider the ligand field strength. Strong field ligands like CN- in [Ni(CN)4]2– can cause significant splitting of the d orbitals, affecting their relative energies.
5. Determine which complex has a geometry that results in the dx2−y2 and dz2 orbitals being lower in energy. Based on the geometry and ligand field strength, [Zn(H2O)4]2+ is tetrahedral, where the dx2−y2 and dz2 orbitals are lower in energy compared to the other three d orbitals.