Simplified absorption spectra of three complexes ((i), (ii) and (iii)) of Mn⁺ ion are provided below; their λₘₐₓ values are marked as A, B and C respectively. The correct match between the complexes and their λₘₐₓ values is
(i) [M(NCS)₆] (–6 + n)
(ii) [MF₆] (–6 + n)
(iii) [M(NH₃)₆]ⁿ⁺

Solution

Chemistry ma’am · 3 steps

Rank the ligands by field strength first, then flip the order: a bigger split means a shorter λmax.

1. Same metal ion. All three complexes are octahedral with the same metal ion, so only the ligand changes the splitting Δₒ. In the spectrochemical series, F⁻ < NCS⁻ (N-bonded) < NH₃.
2. Energy versus wavelength. The d–d absorption energy equals Δₒ, and energy is inversely proportional to wavelength. So the strongest-field ligand absorbs at the shortest wavelength.

   Δₒ = hc/λₘₐₓ ⇒ λₘₐₓ ∝ 1/Δₒ

   Complex	Ligand strength	Δₒ	λₘₐₓ
   (iii) [M(NH₃)₆]ⁿ⁺	strongest	largest	shortest, A
   (i) [M(NCS)₆]	middle	middle	middle, B
   (ii) [MF₆]	weakest	smallest	longest, C

3. So. The match is A-(iii), B-(i), C-(ii), which is option (d).

The idea to keep. Stronger ligand gives a larger Δₒ, which means higher absorption energy and a shorter λₘₐₓ. Always invert the spectrochemical order when the graph shows wavelength.

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