Which one of the following molecules will have unequal bond lengths ?

Options

A. `NF_3`
B. `BF_3`
C. `PF_5`
D. ` SF_6`

Explanation

To determine which molecule has unequal bond lengths, we will analyze the given options by calculating their steric numbers and hybridizations.

### Step 1: Identify the Molecules
We have the following molecules to analyze:
1. NaF3
2. BF3
3. PF5
4. SF6

### Step 2: Calculate Steric Numbers and Hybridization

#### Option 1: NaF3
- **Valence Electrons of Nitrogen (N)**: 5
- **Monovalent Atoms (F)**: 3
- **Steric Number Calculation**:
\[ \text{Steric Number} = \frac{(5 + 3)}{2} = \frac{8}{2} = 4 \]
- **Hybridization**: sp³
- **Geometry**: Tetrahedral
- **Bond Lengths**: All bond lengths are equal.

#### Option 2: BF3
- **Valence Electrons of Boron (B)**: 3
- **Monovalent Atoms (F)**: 3
- **Steric Number Calculation**:
\[ \text{Steric Number} = \frac{(3 + 3)}{2} = \frac{6}{2} = 3 \]
- **Hybridization**: sp²
- **Geometry**: Trigonal planar
- **Bond Lengths**: All bond lengths are equal.

#### Option 3: PF5
- **Valence Electrons of Phosphorus (P)**: 5
- **Monovalent Atoms (F)**: 5
- **Steric Number Calculation**:
\[ \text{Steric Number} = \frac{(5 + 5)}{2} = \frac{10}{2} = 5 \]
- **Hybridization**: sp³d
- **Geometry**: Trigonal bipyramidal
- **Bond Lengths**: Axial bond lengths are different from equatorial bond lengths (unequal bond lengths).

#### Option 4: SF6
- **Valence Electrons of Sulfur (S)**: 6
- **Monovalent Atoms (F)**: 6
- **Steric Number Calculation**:
\[ \text{Steric Number} = \frac{(6 + 6)}{2} = \frac{12}{2} = 6 \]
- **Hybridization**: sp³d²
- **Geometry**: Octahedral
- **Bond Lengths**: All bond lengths are equal.

### Step 3: Conclusion
From the analysis, we find that:
- NaF3, BF3, and SF6 have equal bond lengths.
- PF5 has unequal bond lengths due to its trigonal bipyramidal geometry.

Thus, the molecule with unequal bond lengths is **PF5**.