Question

The correct pair in which both the complex ions show the ground state electronic degeneracy is

• A. [TiF$_6$]$^{2-}$ and [Ti(H$_2$O)$_6$]$^{2+}$
• B. [Fe(CN)$_6$]$^{4-}$ and [Mn(CN)$_6$]$^{3-}$
• C. [Ti(H$_2$O)$_6$]$^{2+}$ and [Mn(CN)$_6$]$^{3-}$
• D. [Fe(CN)$_6$]$^{4-}$ and [TiF$_6$]$^{2-}$

Hint:

Electronic degeneracy occurs when d-orbitals are partially filled (not $d^0$ or $d^{10}$)Always check oxidation state and ligand field strength

Answer 1

The Correct Option is C

Step 1: Understand electronic degeneracy.
Ground state electronic degeneracy occurs when electrons occupy degenerate orbitals asymmetrically (partially filled $t_{2g}$ or $e_g$ levels)This leads to unequal occupancy and hence degeneracy

Step 2: Analyze [TiF$_6$]$^{2-}$.
Oxidation state of Ti:
\[ x + 6(-1) = -2 \Rightarrow x = +4 \]
Ti$^{4+}$ has electronic configuration $d^0$No electrons in d-orbitals $\Rightarrow$ no degeneracy

Step 3: Re-evaluate carefully.
Actually, Ti$^{2+}$ (in [Ti(H$_2$O)$_6$]$^{2+}$) has $d^2$ configuration

Step 4: Analyze [Ti(H$_2$O)$_6$]$^{2+}$.
Ti$^{2+}$: $d^2$ configurationIn octahedral field:
\[ t_{2g}^2 e_g^0 \]
Electrons occupy degenerate $t_{2g}$ orbitals $\Rightarrow$ degeneracy present

Step 5: Correct evaluation of [TiF$_6$]$^{2-}$.
F$^-$ is a weak field ligand, so Ti is actually in +4 oxidation state → $d^0$ → no degeneracy
Thus option (A) seems incorrect at first glance, so we check other options

Step 6: Analyze [Mn(CN)$_6$]$^{3-}$.
Oxidation state of Mn:
\[ x + 6(-1) = -3 \Rightarrow x = +3 \]
Mn$^{3+}$ is $d^4$CN$^-$ is strong field → low spin configuration:
\[ t_{2g}^4 e_g^0 \]
This leads to paired electrons but still degeneracy exists in $t_{2g}$ set

Step 7: Final conclusion.
The only pair where both show degeneracy is
\[ \boxed{\text{[Ti(H}_2\text{O)}_6]^{2+} \text{ and [Mn(CN)}_6]^{3-}} \]
Thus, correct answer is option (C)