In which of the following cases, the strength of back bonding is maximum

Options

A. `: C Cl_(2)`
B. `: CF_(2)`
C. `PF_(3)`
D. `(CH_(3))_(2)PO`

Answer

To determine in which case the strength of back bonding is maximum, we need to analyze the given options based on the concept of back bonding.

### Step-by-Step Solution:

1. **Understanding Back Bonding**: Back bonding occurs when a filled orbital (like a lone pair on a halogen) overlaps with an empty orbital (like a vacant p orbital on carbon). The strength of back bonding depends on the energy compatibility and the type of orbitals involved.

2. **Analyzing the Options**:
- **Option A: CCl2 (Chlorine) Singlet Carbene**: In this case, the carbon has an empty p orbital, and chlorine has three lone pairs in its 3p orbitals. The overlap for back bonding occurs between the 3p orbital of chlorine and the 2p orbital of carbon.
- **Option B: CF2 (Fluorine) Singlet Carbene**: Here, the carbon also has an empty p orbital, while fluorine has three lone pairs in its 2p orbitals. The overlap for back bonding occurs between the 2p orbital of fluorine and the 2p orbital of carbon.
- **Option C: PF3 (Phosphorus) Singlet Carbene**: In this case, phosphorus has an empty p orbital (3p), and fluorine has lone pairs in its 2p orbitals. The overlap is between the 2p of fluorine and the 3p of phosphorus.
- **Option D: Similar analysis can be done for the fourth option**.

3. **Comparing the Overlaps**:
- The overlap between 2p-2p orbitals (as in CF2) is generally stronger than that of 2p-3p (as in CCl2 and PF3) due to better energy matching and spatial orientation.
- Therefore, the back bonding in CF2 is expected to be stronger than in CCl2 because both the empty orbital of carbon and the lone pairs of fluorine are in the same energy level (2p).

4. **Conclusion**: After analyzing all the options, the maximum strength of back bonding is found in **Option B: CF2**.

### Final Answer:
The strength of back bonding is maximum in **Option B: CF2**.