Which of the following statement(s) is//are true or false?
`S_(1)` Complexes having `d^(0)` or `d^(10)` configuration of metal ions are always diamagnetic
`S_(2)` In organometallic compounds, carbon is bonded to metals directly
`S_(3)` In `Fe(CO)_(5)` the `Fe-C` bond possesses both `sigma` and `pi` characteristics
`S_(4)` Extra stability of metal carbonyls is explained by synergic bonding .

Options

A. `T T T T`
B. `FTFT`
C. `T T F F`
D. `F T T T`

Answer

To determine whether each statement is true or false, let's analyze them one by one.

### Step 1: Analyze Statement S1
**Statement S1**: Complexes having \(d^0\) or \(d^{10}\) configuration of metal ions are always diamagnetic.

- **Analysis**:
- A \(d^0\) configuration means there are no d electrons, hence no unpaired electrons, making it diamagnetic.
- A \(d^{10}\) configuration means all d orbitals are fully filled (2 electrons in each of the 5 d orbitals), which also results in no unpaired electrons, thus it is also diamagnetic.

- **Conclusion**: This statement is **True**.

### Step 2: Analyze Statement S2
**Statement S2**: In organometallic compounds, carbon is bonded to metals directly.

- **Analysis**:
- Organometallic compounds are defined as compounds containing a direct bond between carbon and a metal. This bond is typically a sigma bond.

- **Conclusion**: This statement is **True**.

### Step 3: Analyze Statement S3
**Statement S3**: In \(Fe(CO)_5\), the \(Fe-C\) bond possesses both sigma and pi characteristics.

- **Analysis**:
- In \(Fe(CO)_5\), the carbon monoxide (CO) acts as a ligand that donates a pair of electrons to the metal (sigma donation).
- Additionally, due to the electron-rich nature of the metal, back-donation occurs from the metal to the CO ligand, which involves pi bonding.

- **Conclusion**: This statement is **True**.

### Step 4: Analyze Statement S4
**Statement S4**: Extra stability of metal carbonyls is explained by synergic bonding.

- **Analysis**:
- Synergic bonding refers to the combined effect of sigma donation and pi back-donation in metal carbonyl complexes. This interaction increases the bond strength and stability of the complex.

- **Conclusion**: This statement is **True**.

### Final Conclusion
All statements S1, S2, S3, and S4 are **True**.

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