Find the EAN value of cetral atom of ferrocene `[Fe(pi-C_(5)H_(5))_(2)]`

Explanation

To find the Effective Atomic Number (EAN) of the central atom in ferrocene \([Fe(\pi-C_5H_5)_2]\), we will follow these steps:

### Step 1: Identify the Atomic Number of the Central Metal Atom
The central metal atom in ferrocene is iron (Fe). The atomic number of iron is 26.

### Step 2: Determine the Electron Count from the Ligands
The ligands in ferrocene are cyclopentadienyl anions (\(C_5H_5^-\)). Each cyclopentadienyl anion donates 6 electrons. Since there are two cyclopentadienyl ligands, the total electron contribution from the ligands is:

\[ \text{Total electron count from ligands} = 6 \, \text{electrons} \times 2 = 12 \, \text{electrons} \]

### Step 3: Determine the Oxidation State of the Central Metal Atom
To find the oxidation state of iron in the complex, we can set up the following equation based on the overall charge of the complex:

Let the oxidation state of iron be \(x\). The charge of each cyclopentadienyl anion is -1, and there are two of them, contributing a total charge of -2. The overall charge of the complex is neutral (0). Therefore, we can write:

\[ x + 2(-1) = 0 \]

Solving for \(x\):

\[ x - 2 = 0 \implies x = +2 \]

### Step 4: Calculate the EAN
Now, we can use the formula for EAN:

\[ \text{EAN} = \text{Atomic number of central metal atom} + \text{Electron count from ligands} - \text{Oxidation state of the metal} \]

Substituting the values we found:

\[ \text{EAN} = 26 + 12 - 2 \]

Calculating this gives:

\[ \text{EAN} = 36 \]

### Conclusion
The Effective Atomic Number (EAN) of the central atom in ferrocene \([Fe(\pi-C_5H_5)_2]\) is 36.

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