The molecule in which hybrid MOs involve only one d-orbital of the central atom is :

Solution

Chemistry ma’am · 3 steps

Six hybrid orbitals always need two d orbitals, so look for the species that uses only four.

1. Count the d orbitals. One s and three p orbitals give at most 4 hybrids. Each hybrid beyond 4 needs one d orbital, so 6 hybrids need two d orbitals. That rules out every octahedral arrangement.

   Species	Electron pairs on centre	Hybridisation	d orbitals used
   XeF₄	4 bond pairs + 2 lone pairs = 6	sp³d², square planar	2
   [Ni(CN)₄]²⁻	4 ligand pairs	dsp², square planar	1
   [CrF₆]³⁻	6 ligand pairs	d²sp³, octahedral	2
   BrF₅	5 bond pairs + 1 lone pair = 6	sp³d², square pyramidal	2

2. Why Ni uses dsp2. Ni²⁺ is 3d⁸. Strong-field CN⁻ pairs up these 8 electrons into four 3d orbitals, leaving one 3d orbital empty. That one 3d, the 4s and two 4p orbitals mix to give four dsp² hybrids.
3. So. Only [Ni(CN)₄]²⁻ uses a single d orbital, so the answer is (b).

The idea to keep. Count the hybrid orbitals first. 4 hybrids can use 0 or 1 d orbital (sp³ or dsp²), 5 hybrids use 1, and 6 hybrids always use 2, whether written sp³d² or d²sp³.

Answer from the NTA final answer key. Solution by PrepWiser.