On the basis of VBT, find which is an inner orbital complex with O magnetic moment ?

Options

A. `[Mn(CN)_6]^(3-)`
B. `[Co(NH_3)_6]^(3+)`
C. `[Cr(H_2O)_6]^(3+)`
D. `[FeCI_6]^(4-)`

Answer

To determine which complex is an inner orbital complex with zero magnetic moment based on Valence Bond Theory (VBT), we can analyze the given complexes one by one.

### Step-by-Step Solution:

1. **Identify the Complexes**: We will analyze the following complexes:
- [Mn(CN)6]³⁻
- [Co(NH3)6]³⁺
- [Cr(H2O)6]³⁺
- [FeCl6]²⁻

2. **Analyze [Mn(CN)6]³⁻**:
- Manganese in this complex has a +3 oxidation state.
- The electron configuration of Mn is [Ar] 3d⁵. For Mn³⁺, it will be [Ar] 3d⁴.
- CN⁻ is a strong field ligand, which will cause pairing of electrons.
- The configuration will be d²sp³ (using inner d-orbitals).
- However, there are unpaired electrons (4 electrons), so the magnetic moment is not zero.

3. **Analyze [Co(NH3)6]³⁺**:
- Cobalt in this complex has a +3 oxidation state.
- The electron configuration of Co is [Ar] 3d⁷. For Co³⁺, it will be [Ar] 3d⁶.
- NH₃ is a strong field ligand, leading to pairing of electrons.
- The configuration will be d²sp³ (using inner d-orbitals).
- All electrons are paired, so the magnetic moment is zero. This is a candidate for the answer.

4. **Analyze [Cr(H2O)6]³⁺**:
- Chromium in this complex has a +3 oxidation state.
- The electron configuration of Cr is [Ar] 3d⁵. For Cr³⁺, it will be [Ar] 3d³.
- H₂O is a weak field ligand, which does not cause pairing.
- The configuration will be d²sp³ (using inner d-orbitals).
- There are unpaired electrons (3 electrons), so the magnetic moment is not zero.

5. **Analyze [FeCl6]²⁻**:
- Iron in this complex has a +2 oxidation state.
- The electron configuration of Fe is [Ar] 3d⁶. For Fe²⁺, it will be [Ar] 3d⁶.
- Cl⁻ is a weak field ligand, which does not cause pairing.
- The configuration will be sp³d² (using outer d-orbitals).
- There are unpaired electrons (6 electrons), so the magnetic moment is not zero.

### Conclusion:
The only complex that is an inner orbital complex with zero magnetic moment is **[Co(NH3)6]³⁺**.