Find the difference in EAN of the complexes :
`[Ti(sigma-C_(5)H_(5))_(2)(pi-C_(5)H_(5))_(2)]" and "[Cr(C_(6)H_(6))_(2)]`

Options

A. 2
B. 4
C. zero
D. 3

Explanation

To find the difference in Effective Atomic Number (EAN) of the complexes \([Ti(\sigma-C_5H_5)_2(\pi-C_5H_5)_2]\) and \([Cr(C_6H_6)_2]\), we will follow these steps:

### Step 1: Determine the EAN of the first complex \([Ti(\sigma-C_5H_5)_2(\pi-C_5H_5)_2]\).

1. **Identify the central metal atom and its atomic number**:
- The central metal atom is Titanium (Ti), which has an atomic number of 22.

2. **Determine the oxidation state of Titanium**:
- In this complex, both \(\sigma-C_5H_5\) and \(\pi-C_5H_5\) are neutral ligands. Therefore, the oxidation state of Titanium is 0.

3. **Calculate the total electron contribution from the ligands**:
- Each \(\sigma-C_5H_5\) donates 2 electrons, and there are 2 of them: \(2 \times 2 = 4\) electrons.
- Each \(\pi-C_5H_5\) donates 6 electrons, and there are 2 of them: \(2 \times 6 = 12\) electrons.
- Total electron contribution from ligands = \(4 + 12 = 16\) electrons.

4. **Calculate the EAN**:
\[ \text{EAN} = \text{Atomic Number of Ti} + \text{Total Electron Count from Ligands} + \text{Oxidation State} \]
\[ \text{EAN} = 22 + 16 + 0 = 38 \]

### Step 2: Determine the EAN of the second complex \([Cr(C_6H_6)_2]\).

1. **Identify the central metal atom and its atomic number**:
- The central metal atom is Chromium (Cr), which has an atomic number of 24.

2. **Determine the oxidation state of Chromium**:
- Benzene (\(C_6H_6\)) is also a neutral ligand. Therefore, the oxidation state of Chromium is 0.

3. **Calculate the total electron contribution from the ligands**:
- Each \(C_6H_6\) donates 6 electrons, and there are 2 of them: \(2 \times 6 = 12\) electrons.

4. **Calculate the EAN**:
\[ \text{EAN} = \text{Atomic Number of Cr} + \text{Total Electron Count from Ligands} + \text{Oxidation State} \]
\[ \text{EAN} = 24 + 12 + 0 = 36 \]

### Step 3: Calculate the difference in EAN between the two complexes.

\[ \text{Difference in EAN} = \text{EAN of } [Ti(\sigma-C_5H_5)_2(\pi-C_5H_5)_2] - \text{EAN of } [Cr(C_6H_6)_2] \]
\[ \text{Difference in EAN} = 38 - 36 = 2 \]

### Final Answer:
The difference in EAN of the complexes \([Ti(\sigma-C_5H_5)_2(\pi-C_5H_5)_2]\) and \([Cr(C_6H_6)_2]\) is **2**.

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