The nitrogen atom in `NH_(3), NH_(2)^(-)` and `NH_(4)^(+)` are all surrounded by eight electrons. When these species are arranged in increasing order of `H-N-H` bond angle, correct order is:

Options

A. `NH_(3), NH_(2)^(-), NH_(4)^(+)`
B. `NH_(4)^(+), NH_(2)^(-), NH_(3)`
C. `NH_(3), NH_(4)^(+), NH_(2)^(-)`
D. `NH_(2)^(-), NH_(3), NH_(4)^(+)`

Explanation

To determine the increasing order of the `H-N-H` bond angle in the species `NH3`, `NH2^(-)`, and `NH4^(+)`, we will analyze the molecular geometry and the influence of lone pairs on the bond angles.

### Step-by-Step Solution:

1. **Identify the Valence Electrons**:
- **NH3 (Ammonia)**: Nitrogen has 5 valence electrons, and each hydrogen has 1. Thus, NH3 has a total of 5 + 3(1) = 8 valence electrons.
- **NH2^(-) (Amide Ion)**: The nitrogen still has 5 valence electrons, but the negative charge adds 1 more, giving a total of 6 valence electrons. The total is 6 + 2(1) = 8 valence electrons.
- **NH4^(+) (Ammonium Ion)**: Here, nitrogen has 5 valence electrons, and the positive charge means we subtract 1, giving 4 valence electrons. The total is 4 + 4(1) = 8 valence electrons.

2. **Determine the Steric Number**:
- **NH3**: The steric number is 4 (3 bond pairs + 1 lone pair). The geometry is tetrahedral, but the shape is trigonal pyramidal due to the lone pair.
- **NH2^(-)**: The steric number is also 4 (2 bond pairs + 2 lone pairs). The geometry is tetrahedral, but the shape is bent due to the two lone pairs.
- **NH4^(+)**: The steric number is 4 (4 bond pairs + 0 lone pairs). The geometry and shape are both tetrahedral.

3. **Analyze the Bond Angles**:
- **NH3**: The ideal tetrahedral angle is 109.5°, but the presence of one lone pair reduces the bond angle due to lone pair-bond pair repulsion. The actual bond angle is approximately 107°.
- **NH2^(-)**: With two lone pairs, the bond angle is further reduced due to increased repulsion. The bond angle is approximately 104.5°.
- **NH4^(+)**: There are no lone pairs, so the bond angle remains close to the ideal tetrahedral angle of 109.5°.

4. **Arrange in Increasing Order of Bond Angle**:
- The increasing order of the `H-N-H` bond angle based on the analysis is:
- **NH2^(-)** < **NH3** < **NH4^(+)**
- Therefore, the correct order is:
- **NH2^(-) < NH3 < NH4^(+)**

### Final Answer:
The increasing order of `H-N-H` bond angle is:
**NH2^(-) < NH3 < NH4^(+)**