Select the correct statement.

Options

A. `BF_(3) and NH_(3)` have same dipole moment
B. Dipole moment of `NH_(3)` is smaller than that of `BF_(3)`
C. `BF_(3)` molecule has a planar structure, while the `NH_(3)` molecule is tetrahedral
D. The nitrogen atom has unshared pair of electrons, while the boron atom has a free (vacant) valence orbital.

Explanation

To solve the question of selecting the correct statement regarding BF3 and NH3, we will analyze the properties of both molecules step by step.

### Step 1: Analyze BF3
1. **Valence Electrons**: Boron (B) has 3 valence electrons and each Fluorine (F) has 7 valence electrons.
2. **Bonding**: Boron forms three bonds with three Fluorine atoms using its three valence electrons.
3. **Lone Pairs**: There are no lone pairs on Boron in BF3.
4. **Steric Number**: The steric number is 3 (3 bond pairs, 0 lone pairs).
5. **Hybridization**: The hybridization of BF3 is sp².
6. **Molecular Geometry**: The geometry is trigonal planar.
7. **Dipole Moment**: Due to the symmetry of the molecule, the dipole moments of the B-F bonds cancel out, resulting in a net dipole moment of zero.

### Step 2: Analyze NH3
1. **Valence Electrons**: Nitrogen (N) has 5 valence electrons and each Hydrogen (H) has 1 valence electron.
2. **Bonding**: Nitrogen forms three bonds with three Hydrogen atoms using three of its valence electrons.
3. **Lone Pairs**: There is one lone pair on Nitrogen.
4. **Steric Number**: The steric number is 4 (3 bond pairs, 1 lone pair).
5. **Hybridization**: The hybridization of NH3 is sp³.
6. **Molecular Geometry**: The geometry is tetrahedral, but the shape is trigonal pyramidal due to the lone pair.
7. **Dipole Moment**: The dipole moment is directed from the Hydrogen atoms towards the Nitrogen atom due to the electronegativity difference, resulting in a net dipole moment of approximately 1.46 D.

### Step 3: Evaluate the Statements
1. **Statement 1**: "BF3 and NH3 have the same dipole moment." - **Incorrect** (BF3 has a dipole moment of 0, NH3 has a dipole moment of 1.46 D).
2. **Statement 2**: "The dipole moment of NH3 is smaller than that of BF3." - **Incorrect** (NH3 has a dipole moment of 1.46 D, while BF3 has 0 D).
3. **Statement 3**: "BF3 molecule has a planar structure." - **Correct** (BF3 is trigonal planar).
4. **Statement 4**: "NH3 molecule is tetrahedral." - **Incorrect** (NH3 is trigonal pyramidal due to the lone pair).
5. **Statement 5**: "The nitrogen atom has an unshared pair of electrons, while the boron atom has a free valence orbital." - **Correct** (Nitrogen has a lone pair, and Boron has a free valence orbital).

### Conclusion
The correct statements are:
- "BF3 molecule has a planar structure."
- "The nitrogen atom has an unshared pair of electrons, while the boron atom has a free valence orbital."

### Final Answer
The correct statement is: "BF3 molecule has a planar structure."