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. Step 1: Identify the geometry of each complex. The splitting pattern of d orbitals depends on the geometry of the complex. For example, octahedral complexes split d orbitals differently than square planar or tetrahedral complexes.
2. Step 2: Recall the d orbital splitting in an octahedral field: the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals (collectively called \(e_g\) orbitals) are higher in energy than the \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals (called \(t_{2g}\) orbitals).
3. Step 3: Recall the d orbital splitting in a square planar field: the \(d_{x^2-y^2}\) orbital is the highest in energy, but the \(d_{z^2}\) orbital energy is lowered compared to octahedral geometry, often becoming lower than some other d orbitals.
4. Step 4: Recall the d orbital splitting in a tetrahedral field: the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals (called \(e\) orbitals in tetrahedral symmetry) are lower in energy than the \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals (called \(t_2\) orbitals), which is the opposite of the octahedral case.
5. Step 5: Analyze the given complexes: [Co(en)\(_3\)]\(^{3+}\) is octahedral, [Ni(CN)\(_4\)]\(^{2-}\) is square planar, [Zn(H\(_2\)O)\(_4\)]\(^{2+}\) is tetrahedral, and [AuCl\(_2\)]\(^{-}\) is linear. Therefore, the complex where \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals are lower than the other three d orbitals is the tetrahedral complex [Zn(H\(_2\)O)\(_4\)]\(^{2+}\).