Find the number of species having bond angle less than `109^(@)28'`
`NH_(3),PH_(3),SiH_(4),NH_(4)^(+),PF_(3),NH_(2)^(-),SO_(3),NO_(2)^(+),"CCl"_(4),H_(2)O,H_(2)S,SO_(4)^(2-)`

Explanation

To find the number of species having a bond angle less than \(109^\circ 28'\), we will analyze each species given in the question step by step.

### Step 1: Analyze NH₃ (Ammonia)
- **Valence Electrons**: Nitrogen has 5, and each hydrogen has 1. Total = \(5 + 3 \times 1 = 8\).
- **Bond Pairs**: 3 (N-H bonds).
- **Lone Pairs**: 1 (on nitrogen).
- **Steric Number**: 4 (3 bond pairs + 1 lone pair).
- **Hybridization**: sp³.
- **Geometry**: Tetrahedral, but shape is pyramidal due to lone pair.
- **Bond Angle**: Approximately \(107^\circ\) (less than \(109^\circ 28'\)).

**Conclusion**: NH₃ has a bond angle less than \(109^\circ 28'\).

### Step 2: Analyze PH₃ (Phosphine)
- **Valence Electrons**: Phosphorus has 5, and each hydrogen has 1. Total = \(5 + 3 \times 1 = 8\).
- **Bond Pairs**: 3 (P-H bonds).
- **Lone Pairs**: 1 (on phosphorus).
- **Steric Number**: 4.
- **Hybridization**: sp³, but lone pair is non-directional.
- **Bond Angle**: Approximately \(90^\circ\) (less than \(109^\circ 28'\)).

**Conclusion**: PH₃ has a bond angle less than \(109^\circ 28'\).

### Step 3: Analyze SiH₄ (Silane)
- **Valence Electrons**: Silicon has 4, and each hydrogen has 1. Total = \(4 + 4 \times 1 = 8\).
- **Bond Pairs**: 4 (Si-H bonds).
- **Lone Pairs**: 0.
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: \(109^\circ 28'\) (not less).

**Conclusion**: SiH₄ does not have a bond angle less than \(109^\circ 28'\).

### Step 4: Analyze NH₄⁺ (Ammonium Ion)
- **Valence Electrons**: Nitrogen has 5, and each hydrogen has 1. Total = \(5 + 4 \times 1 - 1 = 8\) (due to positive charge).
- **Bond Pairs**: 4 (N-H bonds).
- **Lone Pairs**: 0.
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: \(109^\circ 28'\) (not less).

**Conclusion**: NH₄⁺ does not have a bond angle less than \(109^\circ 28'\).

### Step 5: Analyze PF₃ (Phosphorus Trifluoride)
- **Valence Electrons**: Phosphorus has 5, and each fluorine has 7. Total = \(5 + 3 \times 7 = 26\).
- **Bond Pairs**: 3 (P-F bonds).
- **Lone Pairs**: 1 (on phosphorus).
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: Less than \(109^\circ 28'\) due to lone pair repulsion (approximately \(102^\circ\)).

**Conclusion**: PF₃ has a bond angle less than \(109^\circ 28'\).

### Step 6: Analyze NH₂⁻ (Amide Ion)
- **Valence Electrons**: Nitrogen has 5, and each hydrogen has 1. Total = \(5 + 2 \times 1 + 1 = 8\) (due to negative charge).
- **Bond Pairs**: 2 (N-H bonds).
- **Lone Pairs**: 2 (on nitrogen).
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: Approximately \(105^\circ\) (less than \(109^\circ 28'\)).

**Conclusion**: NH₂⁻ has a bond angle less than \(109^\circ 28'\).

### Step 7: Analyze SO₃ (Sulfur Trioxide)
- **Valence Electrons**: Sulfur has 6, and each oxygen has 6. Total = \(6 + 3 \times 6 = 24\).
- **Bond Pairs**: 3 (S=O bonds).
- **Lone Pairs**: 0.
- **Steric Number**: 3.
- **Hybridization**: sp².
- **Bond Angle**: \(120^\circ\) (not less).

**Conclusion**: SO₃ does not have a bond angle less than \(109^\circ 28'\).

### Step 8: Analyze NO₂⁺ (Nitronium Ion)
- **Valence Electrons**: Nitrogen has 5, and each oxygen has 6. Total = \(5 + 2 \times 6 - 1 = 16\) (due to positive charge).
- **Bond Pairs**: 2 (N=O bonds).
- **Lone Pairs**: 0.
- **Steric Number**: 2.
- **Hybridization**: sp.
- **Bond Angle**: \(180^\circ\) (not less).

**Conclusion**: NO₂⁺ does not have a bond angle less than \(109^\circ 28'\).

### Step 9: Analyze CCl₄ (Carbon Tetrachloride)
- **Valence Electrons**: Carbon has 4, and each chlorine has 7. Total = \(4 + 4 \times 7 = 32\).
- **Bond Pairs**: 4 (C-Cl bonds).
- **Lone Pairs**: 0.
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: \(109^\circ 28'\) (not less).

**Conclusion**: CCl₄ does not have a bond angle less than \(109^\circ 28'\).

### Step 10: Analyze H₂O (Water)
- **Valence Electrons**: Oxygen has 6, and each hydrogen has 1. Total = \(6 + 2 \times 1 = 8\).
- **Bond Pairs**: 2 (O-H bonds).
- **Lone Pairs**: 2 (on oxygen).
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: Approximately \(104.5^\circ\) (less than \(109^\circ 28'\)).

**Conclusion**: H₂O has a bond angle less than \(109^\circ 28'\).

### Step 11: Analyze H₂S (Hydrogen Sulfide)
- **Valence Electrons**: Sulfur has 6, and each hydrogen has 1. Total = \(6 + 2 \times 1 = 8\).
- **Bond Pairs**: 2 (S-H bonds).
- **Lone Pairs**: 2 (on sulfur).
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: Approximately \(92^\circ\) (less than \(109^\circ 28'\)).

**Conclusion**: H₂S has a bond angle less than \(109^\circ 28'\).

### Step 12: Analyze SO₄²⁻ (Sulfate Ion)
- **Valence Electrons**: Sulfur has 6, and each oxygen has 6. Total = \(6 + 4 \times 6 + 2 = 32\) (due to 2 negative charges).
- **Bond Pairs**: 4 (S=O bonds).
- **Lone Pairs**: 0.
- **Steric Number**: 4.
- **Hybridization**: sp³.
- **Bond Angle**: \(109^\circ 28'\) (not less).

**Conclusion**: SO₄²⁻ does not have a bond angle less than \(109^\circ 28'\).

### Final Count of Species with Bond Angle Less than \(109^\circ 28'\)
- The species with bond angles less than \(109^\circ 28'\) are:
- NH₃
- PH₃
- PF₃
- NH₂⁻
- H₂O
- H₂S

**Total Species**: 6