[Co(NH₃)₆]³⁺ and [CoF₆]³⁻ are respectively known as :

Solution

Chemistry ma’am · 3 steps

Same Co³⁺, same d⁶: the ligand decides whether those six electrons pair up or spread out.

1. Find the metal. In both complexes cobalt is +3: x + 6(0) = +3 and x + 6(-1) = -3. So Co³⁺ is [Ar] 3d⁶ each time.
2. Strong or weak. NH₃ is a strong-field ligand for Co³⁺, so the splitting Δₒ is larger than the pairing energy and all six electrons pair in t_(2g). F⁻ is a weak-field ligand, so the electrons spread out as t_(2g)⁴ e_g² before pairing.

   Complex	d⁶ arrangement	Unpaired electrons	Hybridisation	Known as
   [Co(NH₃)₆]³⁺	t_(2g)⁶ e_g⁰	0	d²sp³ (inner orbital)	spin paired, low spin
   [CoF₆]³⁻	t_(2g)⁴ e_g²	4	sp³d² (outer orbital)	spin free, high spin

3. So. [Co(NH₃)₆]³⁺ is spin paired and [CoF₆]³⁻ is spin free, which is option (b).

The idea to keep. For Co³⁺ (d⁶), a strong-field ligand gives a spin-paired, inner-orbital (d²sp³) complex. A weak-field ligand like F⁻ gives a spin-free, outer-orbital (sp³d²) one.

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