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

Options

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

Explanation

To determine which metal carbonyl has the lowest C-O bond order among the given options, we will analyze the electronic configurations and the extent of back-bonding in each case. The bond order of the C-O bond in metal carbonyls is influenced by the extent of back-bonding from the metal d-orbitals to the π* orbitals of CO.

### Step-by-Step Solution:

1. **Identify the Metal and its Oxidation State:**
- For each metal carbonyl, identify the metal and determine its oxidation state based on the overall charge of the complex.

2. **Determine the Electronic Configuration of the Metal:**
- Write the electronic configuration of the metal in its oxidation state. Consider the d and s orbitals.

3. **Assess the Effective Electronic Configuration in Presence of CO:**
- When CO acts as a ligand, it can participate in back-bonding. The effective electronic configuration of the metal will change due to this interaction.

4. **Count the Lone Pairs Available for Back-Bonding:**
- Determine how many lone pairs of electrons from the metal can be used for back-bonding with the vacant π* orbitals of CO. More lone pairs typically lead to greater back-bonding and a higher bond order.

5. **Analyze Each Option:**
- For each metal carbonyl, analyze the extent of back-bonding and how it affects the C-O bond order.
- The more effective back-bonding occurs, the higher the bond order of the C-O bond.

6. **Conclusion:**
- Compare the bond orders derived from the analysis of back-bonding for each metal carbonyl. The one with the least effective back-bonding will have the lowest C-O bond order.

### Application to the Given Options:

- **Option 1: Mn(CO)6^+**
- Oxidation state: +1
- Electronic configuration: 3d^6 4s^0
- Back-bonding: Moderate

- **Option 2: Fe(CO)5**
- Oxidation state: 0
- Electronic configuration: 3d^8
- Back-bonding: Strong

- **Option 3: Cr(CO)6**
- Oxidation state: 0
- Electronic configuration: 3d^6
- Back-bonding: Moderate

- **Option 4: V(CO)6^-**
- Oxidation state: -1
- Electronic configuration: 3d^6
- Back-bonding: Moderate

### Final Answer:
Based on the analysis, the metal carbonyl with the lowest C-O bond order is **Fe(CO)5 (Option 2)**, as it has the maximum back-bonding leading to the lowest bond order.