The pair in which both the species have the same magnetic moment (spin only) is :

Solution

Chemistry ma’am · 3 steps

Find each metal ion's d-electron count, then count unpaired electrons: same count means same moment.

1. What decides μ. The spin-only moment depends only on n, the number of unpaired electrons. So two species have the same moment exactly when they have the same n.

   μ = √n(n+2) BM

2. Count unpaired electrons. H₂O, Cl⁻ and OH⁻ are weak-field ligands, so these complexes are high spin. NH₃ with Fe²⁺ also stays high spin. Tetrahedral d⁷ always has 3 unpaired electrons.

   Option	First species	Second species	Same moment?
   (a)	Cr²⁺, d⁴: 4 unpaired	Co²⁺, d⁷ tetrahedral: 3 unpaired	No
   (b)	Co²⁺, d⁷ tetrahedral: 3 unpaired	Fe²⁺, d⁶ high spin: 4 unpaired	No
   (c)	Mn²⁺, d⁵ high spin: 5 unpaired	Cr²⁺, d⁴: 4 unpaired	No
   (d)	Cr²⁺, d⁴ high spin: 4 unpaired	Fe²⁺, d⁶ high spin: 4 unpaired	Yes, both √24 = 4.90 BM

3. So. Only in (d) do both ions have 4 unpaired electrons. [Cr(H₂O)₆]²⁺ and [Fe(H₂O)₆]²⁺ share the same spin-only moment, 4.90 BM.

The idea to keep. Spin-only moment depends only on the number of unpaired electrons. High-spin d⁴ and d⁶ both have 4 unpaired, so different ions can give the same moment.

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