In which of the following species the angle around the central atom is exactly equal to `109^(@)28` ?

Options

A. `SF_(4)`
B. `:NH_(3)`
C. `NH_(4) ^(+)`
D. None of the above

Explanation

To determine which species has a bond angle around the central atom equal to exactly 109° 28', we will analyze the given species one by one.

### Step 1: Analyze SF4 (Sulfur Tetrafluoride)
- **Valence Electrons**: Sulfur (S) has 6 valence electrons. Each fluorine (F) contributes 1 electron. Thus, the total number of valence electrons = 6 (from S) + 4 (from 4 F) = 10 electrons.
- **Lewis Structure**: Sulfur forms 4 single bonds with fluorine and has 1 lone pair.
- **Steric Number**: The steric number is calculated as the number of sigma bonds + number of lone pairs = 4 (sigma bonds) + 1 (lone pair) = 5.
- **Hybridization**: With a steric number of 5, the hybridization is sp³d.
- **Bond Angle**: The bond angle in SF4 is approximately 101.6°, which is not equal to 109° 28'.

### Step 2: Analyze NH3 (Ammonia)
- **Valence Electrons**: Nitrogen (N) has 5 valence electrons. Each hydrogen (H) contributes 1 electron. Thus, the total number of valence electrons = 5 (from N) + 3 (from 3 H) = 8 electrons.
- **Lewis Structure**: Nitrogen forms 3 single bonds with hydrogen and has 1 lone pair.
- **Steric Number**: The steric number is 3 (sigma bonds) + 1 (lone pair) = 4.
- **Hybridization**: With a steric number of 4, the hybridization is sp³.
- **Bond Angle**: The ideal bond angle for sp³ hybridization is 109° 28', but due to lone pair-bond pair repulsion, the actual bond angle is reduced to approximately 107°.

### Step 3: Analyze NH4+ (Ammonium Ion)
- **Valence Electrons**: Nitrogen (N) has 5 valence electrons. The positive charge indicates that it has lost one electron. Thus, it has 4 valence electrons now (5 - 1 = 4).
- **Lewis Structure**: Nitrogen forms 4 single bonds with hydrogen and has no lone pairs.
- **Steric Number**: The steric number is 4 (sigma bonds) + 0 (lone pairs) = 4.
- **Hybridization**: With a steric number of 4, the hybridization is sp³.
- **Bond Angle**: Since there are no lone pairs to cause repulsion, the bond angle remains at the ideal value of 109° 28'.

### Conclusion
The species that has a bond angle around the central atom equal to exactly 109° 28' is **NH4+ (Ammonium Ion)**.

**Final Answer**: C. NH4+