How many of the given complexes follow E.A.N rule ?
(a) `[Fe(CO)_(5)]` (b) `[Co_(2)(CO)_(8)]` ( c) `[Fe(C_(5)H_(5))_(2)]` (d) `K_(3)[Fe(CN)_(6)]` ( e)`[Fe(NO)_(2)(CO)_(2)]` (f)`[CoF_(6)]^(4-)`

Explanation

To determine how many of the given complexes follow the Effective Atomic Number (EAN) rule, we will calculate the EAN for each complex step by step. The EAN is calculated using the formula:

\[ \text{EAN} = Z + E_L + O \]

Where:
- \( Z \) = Atomic number of the central metal atom
- \( E_L \) = Electron count from the ligands
- \( O \) = Oxidation state of the metal

Let's analyze each complex one by one.

### Step 1: Calculate EAN for each complex

**(a) \([Fe(CO)_{5}]\)**
- Atomic number of Fe = 26
- Oxidation state of Fe = 0 (since CO is a neutral ligand)
- Electron count from CO = 5 ligands × 2 electrons each = 10
- EAN = \( 26 + 10 + 0 = 36 \)
- 36 corresponds to the atomic number of Krypton (noble gas).
**Conclusion**: Follows EAN rule.

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**(b) \([Co_{2}(CO)_{8}]\)**
- Atomic number of Co = 27
- Oxidation state of Co = +1 (since there are two Co atoms sharing electrons, we consider the average oxidation state)
- Electron count from CO = 8 ligands × 2 electrons each = 16
- EAN = \( 27 + 16 + 1 = 44 \)
- 44 does not correspond to a noble gas.
**Conclusion**: Does not follow EAN rule.

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**(c) \([Fe(C_{5}H_{5})_{2}]\)**
- Atomic number of Fe = 26
- Oxidation state of Fe = 0 (since C5H5 is a neutral ligand)
- Electron count from C5H5 = 2 ligands × 6 electrons each = 12
- EAN = \( 26 + 12 + 0 = 38 \)
- 38 does not correspond to a noble gas.
**Conclusion**: Does not follow EAN rule.

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**(d) \(K_{3}[Fe(CN)_{6}]\)**
- Atomic number of Fe = 26
- Oxidation state of Fe = +3 (since K is +1 and CN is -1, the overall charge is neutral)
- Electron count from CN = 6 ligands × 2 electrons each = 12
- EAN = \( 26 + 12 - 3 = 35 \)
- 35 does not correspond to a noble gas.
**Conclusion**: Does not follow EAN rule.

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**(e) \([Fe(NO)_{2}(CO)_{2}]\)**
- Atomic number of Fe = 26
- Oxidation state of Fe = +2 (NO is a neutral ligand)
- Electron count from NO = 2 ligands × 2 electrons each = 4
- Electron count from CO = 2 ligands × 2 electrons each = 4
- EAN = \( 26 + 4 + 2 = 32 \)
- 32 does not correspond to a noble gas.
**Conclusion**: Does not follow EAN rule.

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**(f) \([CoF_{6}]^{4-}\)**
- Atomic number of Co = 27
- Oxidation state of Co = +4 (since F is -1 and there are 6 F ligands)
- Electron count from F = 6 ligands × 1 electron each = 6
- EAN = \( 27 + 6 - 4 = 29 \)
- 29 does not correspond to a noble gas.
**Conclusion**: Does not follow EAN rule.

### Final Summary
- Complexes that follow EAN rule: **(a)** \([Fe(CO)_{5}]\)
- Complexes that do not follow EAN rule: **(b)** \([Co_{2}(CO)_{8}]\), **(c)** \([Fe(C_{5}H_{5})_{2}]\), **(d)** \(K_{3}[Fe(CN)_{6}]\), **(e)** \([Fe(NO)_{2}(CO)_{2}]\), **(f)** \([CoF_{6}]^{4-}\)