Calculate the EAN of central atom in the following complexes
`(a) [Fe(CO)_(2)(NO)_(2)] " " (b) [Fe(C_(5)H_(5))_(2)]`

Explanation

To calculate the Effective Atomic Number (EAN) of the central atom in the given complexes, we will follow a systematic approach.

### Step-by-Step Solution:

#### (a) For the complex \([Fe(CO)_{2}(NO)_{2}]\):

1. **Identify the central metal atom and its atomic number**:
- The central metal atom is Iron (Fe).
- The atomic number of Iron (Fe) is 26.

2. **Determine the oxidation state of Iron in the complex**:
- Let the oxidation state of Iron be \( x \).
- Carbonyl (CO) is a neutral ligand, so it contributes 0 to the oxidation state.
- Nitrosyl (NO) is a cationic ligand with a +1 charge.
- The equation for the oxidation state can be set up as:
\[ x + 0 + 1 \times 2 = 0 \]
- This simplifies to:
\[ x + 2 = 0 \implies x = -2 \]

3. **Count the number of lone pair donating sites**:
- Each CO contributes 1 lone pair, and there are 2 CO ligands: \( 2 \times 1 = 2 \).
- Each NO contributes 1 lone pair, and there are 2 NO ligands: \( 2 \times 1 = 2 \).
- Total lone pair donating sites = \( 2 + 2 = 4 \).

4. **Calculate the EAN**:
- Using the formula for EAN:
\[ \text{EAN} = \text{Atomic number of central metal} - \text{Oxidation state} + (\text{Number of lone pair donating sites} \times 2) \]
- Substituting the values:
\[ \text{EAN} = 26 - (-2) + (4 \times 2) = 26 + 2 + 8 = 36 \]

#### (b) For the complex \([Fe(C_{5}H_{5})_{2}]\):

1. **Identify the central metal atom and its atomic number**:
- The central metal atom is Iron (Fe).
- The atomic number of Iron (Fe) is 26.

2. **Determine the oxidation state of Iron in the complex**:
- Let the oxidation state of Iron be \( x \).
- Cyclopentadienyl (C\(_5\)H\(_5\)) is an anionic ligand with a -1 charge.
- The equation for the oxidation state can be set up as:
\[ x + (-1) \times 2 = 0 \]
- This simplifies to:
\[ x - 2 = 0 \implies x = +2 \]

3. **Count the number of lone pair donating sites**:
- Each C\(_5\)H\(_5\) contributes 5 electrons (or 5/2 = 2.5 pairs), but since we consider only whole pairs, we take it as 5 electron pairs from 2 C\(_5\)H\(_5\) ligands:
\[ 2 \times 5 = 10 \text{ electrons} \implies 5 \text{ lone pairs} \]

4. **Calculate the EAN**:
- Using the formula for EAN:
\[ \text{EAN} = \text{Atomic number of central metal} - \text{Oxidation state} + (\text{Number of lone pair donating sites} \times 2) \]
- Substituting the values:
\[ \text{EAN} = 26 - 2 + (5 \times 2) = 26 - 2 + 10 = 34 \]

### Final Results:
- **EAN of \([Fe(CO)_{2}(NO)_{2}]\)** = 36
- **EAN of \([Fe(C_{5}H_{5})_{2}]\)** = 34