Homoleptic octahedral complexes of a metal ion M³⁺ with three monodentate ligands L₁, L₂ and L₃ absorb wavelengths in…

🧠 Absorbed Colour ↔ Energy ↔ Ligand Strength

For an octahedral complex, the absorbed wavelength corresponds to the $\mathrm{e_g \leftarrow t_{2g}}$ transition with energy $\Delta_o$. Stronger ligand → larger $\Delta_o$ → higher energy → shorter wavelength.

Wavelength order from spectrum (shortest → longest):

$\lambda_{blue}\,(\sim 450\,\mathrm{nm}) < \lambda_{green}\,(\sim 530\,\mathrm{nm}) < \lambda_{red}\,(\sim 670\,\mathrm{nm}).$

🗺️ Match Wavelength to Ligand

| Ligand | Absorbs | $\lambda$ | $\Delta_o$ | Strength | |---|---|---|---|---| | L₂ | blue | shortest | largest | strongest | | L₁ | green | middle | middle | middle | | L₃ | red | longest | smallest | weakest |

So $L_2 > L_1 > L_3$ in field strength.

⚡ The Inverse-Wavelength Mantra

Shorter wavelength absorbed → stronger ligand. Lock this. Many students reverse it because "blue" (high frequency) sounds energetic, but they then mismatch it with "weaker" — stay sharp.

⚠️ Absorbed vs Observed Colour

The complex appears the colour complementary to what it absorbs. So a complex absorbing red (L₃) appears green-blue, etc. This question asks about absorption, not appearance — keep them straight.

$\boxed{\text{Answer: (3) } L_2 > L_1 > L_3}$