The `pi` acceptor ligands are those which possess vacant `pi-` orbitals in addition to the lone pairs of electrons
Which of the following complex ion has lowest `M-C` bond length?
(a) `[V(CO)_(6)]^(o+)`
(b) `[Mn(CO)_(6)]^(o+)`
(c ) `Ni(CO)_(4)`
(d) `Fe(CO)_(5)` .

Answer

To determine which complex ion has the lowest M-C bond length among the given options, we need to analyze the nature of the ligands and the metal centers in each complex. The key concept here is synergic bonding, which involves the donation of electron pairs from the ligand to the metal and the acceptance of electrons back into the ligand's antibonding orbitals.

### Step-by-Step Solution:

1. **Identify the Complexes**:
- (a) \([V(CO)_{6}]^{+}\)
- (b) \([Mn(CO)_{6}]^{+}\)
- (c) \([Ni(CO)_{4}]\)
- (d) \([Fe(CO)_{5}]\)

2. **Understand the Role of CO as a Ligand**:
- Carbon monoxide (CO) is a strong field ligand and acts as a \(\pi\)-acceptor. It can donate a lone pair of electrons to the metal and also accept back electrons from the metal into its antibonding \(\pi^*\) orbitals.

3. **Analyze the Charge on the Metal Ions**:
- For (a) and (b), both vanadium and manganese have a +1 oxidation state. A positive charge on the metal decreases its ability to donate electrons to the ligands, thus reducing synergic bonding.
- For (c) nickel is neutral, and for (d) iron is also neutral. Neutral metal centers can engage in more effective synergic bonding.

4. **Compare the Number of Electrons**:
- Nickel (atomic number 28) has more electrons than iron (atomic number 26). More electrons can lead to greater overlap with the ligand's orbitals, enhancing synergic bonding.

5. **Evaluate the Synergic Bonding**:
- The complexes with neutral metal centers (\([Ni(CO)_{4}]\) and \([Fe(CO)_{5}]\)) will have stronger synergic bonding compared to those with positive charges (\([V(CO)_{6}]^{+}\) and \([Mn(CO)_{6}]^{+}\)).
- Among the neutral complexes, \([Ni(CO)_{4}]\) will exhibit more synergic bonding due to the higher electron count compared to \([Fe(CO)_{5}]\).

6. **Determine Bond Strength and Length**:
- Since bond order is inversely proportional to bond length, a higher bond order (due to stronger synergic bonding) will result in a shorter bond length.
- Therefore, \([Ni(CO)_{4}]\) will have the highest bond order and consequently the lowest M-C bond length.

### Conclusion:
The complex ion with the lowest M-C bond length is \([Ni(CO)_{4}]\).