Observe the following complex ions Identify the option in which the unpaired electrons in the complex ions are in correct increasing order
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The key to determining the number of unpaired electrons in an octahedral complex is the Spectrochemical Series, which dictates whether the complex is High Spin (Weak Field Ligand, small $\Delta_o$, electrons go to $e_g$) or Low Spin (Strong Field Ligand, large $\Delta_o$, electrons pair up in $t_{2g}$).
Step 1: Determine the oxidation state and $d$-electron configuration for the metal ion in each complex.
\begin{tabular}{|l|c|c|c|c|}
\hline
Complex & Metal O.S. & Metal Ion & d-Config & Ligand Type
\hline
A: $[\text{Mn}(\text{CN})_6]^{3-}$ & $\text{Mn} \to +3$ & $\text{Mn}^{3+}$ & $d^4$ & Strong Field ($\text{CN}^-$)
B: $[\text{Fe}(\text{CN})_6]^{3-}$ & $\text{Fe} \to +3$ & $\text{Fe}^{3+}$ & $d^5$ & Strong Field ($\text{CN}^-$)
C: $[\text{CoF}_6]^{3-}$ & $\text{Co} \to +3$ & $\text{Co}^{3+}$ & $d^6$ & Weak Field ($\text{F}^-$)
D: $[\text{Co}(\text{C}_2\text{O}_4)_3]^{3-}$ & $\text{Co} \to +3$ & $\text{Co}^{3+}$ & $d^6$ & Strong Field ($\text{C}_2\text{O}_4^{2-}$)
\hline
\end{tabular}
Oxalate ($\text{C}_2\text{O}_4^{2-}$) is typically considered a strong field ligand for $3d$ series metals in high oxidation states like $\text{Co}^{3+}$, leading to low spin complexes.
Step 2: Apply Crystal Field Theory (CFT) to find the number of unpaired electrons ($n$).
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Complex & d-Config & Ligand Type & Spin State & $\mathbf{t_{2g}}$ $\mathbf{e_g}$ & n
\hline
A: $[\text{Mn}(\text{CN})_6]^{3-}$ & $d^4$ & Strong Field & Low Spin & $t_{2g}^4 e_g^0$ & 2
B: $[\text{Fe}(\text{CN})_6]^{3-}$ & $d^5$ & Strong Field & Low Spin & $t_{2g}^5 e_g^0$ & 1
C: $[\text{CoF}_6]^{3-}$ & $d^6$ & Weak Field & High Spin & $t_{2g}^4 e_g^2$ & 4
D: $[\text{Co}(\text{C}_2\text{O}_4)_3]^{3-}$ & $d^6$ & Strong Field & Low Spin & $t_{2g}^6 e_g^0$ & 0
\hline
\end{tabular}
Step 3: Determine the correct order of increasing unpaired electrons.
The number of unpaired electrons is:
D ($n=0$)<B ($n=1$)<A ($n=2$)<C ($n=4$).
The increasing order is D, B, A, C.
Step 4: Conclude the final correct option.
The order D<B<A<C corresponds to option (D).
