Which of the following complex ions has electrons that are symmetrically filled in both `t_(2g) and e_(g)` orbitals ?

Options

A. `[FeF_(6)]^(3-)`
B. `[Mn(CN)_(6)]^(4-)`
C. `[CoF_(6)]^(3-)`
D. `[Co(NH_(3))_(6)]^(2+)`

Answer

To determine which of the given complex ions has electrons that are symmetrically filled in both the \( t_{2g} \) and \( e_g \) orbitals, we will analyze the electronic configurations of the complexes provided in the options. The key is to understand how the d-orbitals split in an octahedral field and how to fill them based on the oxidation states and the nature of the ligands (weak or strong field).

### Step-by-Step Solution:

1. **Identify the Complexes**: We need to analyze the following complexes:
- \( \text{FeF}_6^{3-} \)
- \( \text{Mn(CN)}_6^{4-} \)
- \( \text{CoF}_6^{3-} \)
- \( \text{Co(NH}_3)_6^{2+} \)

2. **Determine the Oxidation States**:
- For \( \text{FeF}_6^{3-} \):
- Let oxidation state of Fe be \( x \).
- \( x + 6(-1) = -3 \) → \( x = +3 \)
- \( \text{Fe}^{3+} \) corresponds to \( 3d^5 \).
- For \( \text{Mn(CN)}_6^{4-} \):
- Let oxidation state of Mn be \( x \).
- \( x + 6(-1) = -4 \) → \( x = +2 \)
- \( \text{Mn}^{2+} \) corresponds to \( 3d^5 \).
- For \( \text{CoF}_6^{3-} \):
- Let oxidation state of Co be \( x \).
- \( x + 6(-1) = -3 \) → \( x = +3 \)
- \( \text{Co}^{3+} \) corresponds to \( 3d^6 \).
- For \( \text{Co(NH}_3)_6^{2+} \):
- Let oxidation state of Co be \( x \).
- \( x + 6(0) = +2 \) → \( x = +2 \)
- \( \text{Co}^{2+} \) corresponds to \( 3d^7 \).

3. **Determine the Electron Configuration**:
- **For \( \text{Fe}^{3+} (3d^5) \)**:
- Weak field ligand (F-) → High spin complex.
- Configuration: \( t_{2g}^3 e_g^2 \) (symmetrically filled).
- **For \( \text{Mn}^{2+} (3d^5) \)**:
- Strong field ligand (CN-) → Low spin complex.
- Configuration: \( t_{2g}^5 e_g^0 \) (unsymmetrically filled).
- **For \( \text{Co}^{3+} (3d^6) \)**:
- Weak field ligand (F-) → High spin complex.
- Configuration: \( t_{2g}^4 e_g^2 \) (unsymmetrically filled).
- **For \( \text{Co}^{2+} (3d^7) \)**:
- Strong field ligand (NH3) → Low spin complex.
- Configuration: \( t_{2g}^6 e_g^1 \) (unsymmetrically filled).

4. **Conclusion**:
- The only complex that has electrons symmetrically filled in both \( t_{2g} \) and \( e_g \) orbitals is \( \text{FeF}_6^{3-} \) with the configuration \( t_{2g}^3 e_g^2 \).

### Final Answer:
**The complex ion with symmetrically filled electrons in both \( t_{2g} \) and \( e_g \) orbitals is \( \text{FeF}_6^{3-} \).**