Among the following metal carbonyls the `C-O` bond order is lowest in .

Options

A. `[Mn(CO)_(6)]^(o+)`
B. `[Fe(CO)_(5)]`
C. `[Cr(CO)_(6)]`
D. `[V(CO)_(6)]^(Θ)`

Explanation

To determine which metal carbonyl has the lowest C-O bond order among the given options, we need to analyze the concept of backbonding and the electronic configurations of the metals involved.

### Step-by-Step Solution:

1. **Understanding Bond Order**:
- The bond order is defined as the number of bonds between two atoms. In the case of carbonyls (CO ligands), the bond order can be influenced by backbonding, where the metal donates electron density back to the π* (pi star) orbitals of CO.

2. **Identifying Backbonding**:
- Backbonding occurs when the metal donates electrons from its d orbitals to the empty π* orbitals of the CO ligand. The extent of backbonding is influenced by the number of d electrons present in the metal.

3. **Analyzing the Given Metal Carbonyls**:
- We need to analyze the oxidation states and electronic configurations of the metals in the carbonyl complexes:
- **Mn(CO)6^2-**: Manganese in +6 oxidation state has 5 d electrons (3d^5). Limited backbonding due to electron deficiency.
- **Fe(CO)5**: Iron in 0 oxidation state has 8 valence electrons (3d^6 4s^2). Good backbonding due to the presence of d electrons.
- **Cr(CO)6**: Chromium in 0 oxidation state has 6 valence electrons (3d^5 4s^1). Moderate backbonding.
- **V(CO)6^2-**: Vanadium in -2 oxidation state has 6 d electrons (3d^4 4s^2). Good backbonding.

4. **Comparing Backbonding**:
- The more d electrons a metal has, the stronger the backbonding and the lower the C-O bond order due to the increased π back-donation.
- In this case:
- Mn(CO)6^2- has the least backbonding due to its positive charge and fewer d electrons.
- Fe(CO)5 has the most effective backbonding due to its higher d electron count.
- Cr(CO)6 has moderate backbonding.
- V(CO)6^2- has good backbonding.

5. **Conclusion**:
- Since Mn(CO)6^2- has the least effective backbonding due to its electron deficiency, it will have the lowest C-O bond order among the given metal carbonyls.

### Final Answer:
The metal carbonyl with the lowest C-O bond order is **Mn(CO)6^2-**.