Among the statements (a)-(d), the incorrect ones are: (a) Octahedral Co(III) complexes with strong field ligands have…

🧠 Walk Each Statement

(a) Co(III) octahedral with strong-field ligands has very high magnetic moments.

• Co(III) is d⁶. Strong-field → LS → $t_{2g}^6 e_g^0$ → 0 unpaired → diamagnetic, $\mu = 0$.
• "Very high" is wrong → (a) is incorrect ✗.

(b) When $\Delta_o < P$, Co(III) octahedral is $t_{2g}^4 e_g^2$.

• HS d⁶ → $t_{2g}^4 e_g^2$ ✓ → (b) is correct.

(c) Wavelength absorbed by $[\mathrm{Co(en)_3}]^{3+}$ < that of $[\mathrm{CoF_6}]^{3-}$.

• en > F⁻ in spectrochemical series → Δ for $[\mathrm{Co(en)_3}]^{3+}$ > Δ for $[\mathrm{CoF_6}]^{3-}$ → smaller λ for en complex → (c) is correct ✓.

(d) If $\Delta_o = 18{,}000$ cm⁻¹, then $\Delta_t = 16{,}000$ cm⁻¹ for the same ligand.

• Standard relation: $\Delta_t = \frac{4}{9}\Delta_o = \frac{4}{9} \times 18{,}000 = 8{,}000$ cm⁻¹.
• 16,000 cm⁻¹ is wrong → (d) is incorrect ✗.

🗺️ Incorrect Statements: (a) and (d)

Match → option 1.

⚡ The $\Delta_t = \frac{4}{9}\Delta_o$ Rule

Same metal, same ligand, same M–L distance: tetrahedral splitting is exactly $\frac{4}{9}$ of octahedral. The factor comes from:

• Td has 4 ligands vs 6 in oct (factor $4/6 = 2/3$).
• Td orbitals don't point directly at ligands (factor $\sim 2/3$).
• Combined: $2/3 \times 2/3 = 4/9$.

⚠️ Strong-Field Co(III) Is Famously Diamagnetic

Statement (a) is the textbook trap. Co(III) with NH₃, CN⁻, en — all give 0 unpaired (LS d⁶). This is the standard "diamagnetic complex" example in JEE.

$\boxed{\text{Answer: (1) (a) and (d) only}}$