EAN rule is followed by the complexes.
(i)`[Fe(pi-C_5H_5)_2]` (ii)`[Mn_2(CO)_10]` (iii)`[V(CO)_6]^(-)`

Options

A. only (i)
B. only (ii)
C. only (iii)
D. all

Explanation

To determine which of the given complexes follows the Effective Atomic Number (EAN) rule, we need to calculate the total number of valence electrons for each complex. The EAN rule states that a stable complex will have a total of 18 valence electrons.

### Step-by-Step Solution:

1. **Identify the Complexes:**
- (i) \([Fe(\pi-C_5H_5)_2]\)
- (ii) \([Mn_2(CO)_{10}]\)
- (iii) \([V(CO)_6]^-\)

2. **Calculate Valence Electrons for Each Complex:**

**(i) \([Fe(\pi-C_5H_5)_2]\):**
- Iron (Fe) has the electron configuration: \(3d^6 4s^2\), contributing a total of 8 valence electrons.
- Each \(\pi-C_5H_5\) (cyclopentadienyl) ligand donates 5 electrons. Since there are 2 such ligands, they contribute \(2 \times 5 = 10\) electrons.
- Total valence electrons = \(8 + 10 = 18\).

**(ii) \([Mn_2(CO)_{10}]\):**
- Manganese (Mn) has the electron configuration: \(3d^5 4s^2\), contributing 7 valence electrons per Mn atom. Since there are 2 Mn atoms, they contribute \(2 \times 7 = 14\) electrons.
- Each CO ligand donates 2 electrons. With 10 CO ligands, they contribute \(10 \times 2 = 20\) electrons.
- Additionally, there is a metal-metal bond between the two Mn atoms, contributing 2 electrons.
- Total valence electrons = \(14 + 20 + 2 = 36\). Since there are 2 Mn atoms, we can consider the contribution per Mn atom, which is \(36/2 = 18\).

**(iii) \([V(CO)_6]^-\):**
- Vanadium (V) has the electron configuration: \(3d^3 4s^2\), contributing a total of 5 valence electrons.
- Each CO ligand donates 2 electrons. With 6 CO ligands, they contribute \(6 \times 2 = 12\) electrons.
- The complex has a negative charge, which adds 1 electron.
- Total valence electrons = \(5 + 12 + 1 = 18\).

3. **Conclusion:**
- All three complexes \([Fe(\pi-C_5H_5)_2]\), \([Mn_2(CO)_{10}]\), and \([V(CO)_6]^-\) have a total of 18 valence electrons and thus follow the EAN rule.

### Final Answer:
All complexes follow the EAN rule.

---