The bond angles of `NH_3,NH_4^(+)and NH_2^(-)` are in the order

Options

A. `NH_2^(-)gtNH_3gtNH_4^(+)`
B. `NH_4^+gtNH_3gtNH_2^(-)`
C. `NH_3 gt NH_2^(-) gtNH_4^+`
D. `NH gt NH_4^+ gtNH_2^-`

Answer

To determine the bond angles of \( NH_3 \), \( NH_4^+ \), and \( NH_2^- \), we will analyze the hybridization and molecular geometry of each species step by step.

### Step 1: Analyze \( NH_4^+ \)
1. **Valence Electrons**: Nitrogen (N) has 5 valence electrons. In \( NH_4^+ \), one electron is removed due to the positive charge, leaving us with 4 valence electrons.
2. **Bond Pairs and Lone Pairs**: There are 4 hydrogen atoms bonded to nitrogen, resulting in 4 bond pairs and 0 lone pairs.
3. **Hybridization**: The hybridization can be determined using the formula:
\[ \text{Hybridization} = \text{Number of bond pairs} + \text{Number of lone pairs} = 4 + 0 = 4 \quad \Rightarrow \quad sp^3 \]
4. **Geometry and Bond Angle**: The geometry is tetrahedral, and the bond angle is approximately \( 109.5^\circ \).

### Step 2: Analyze \( NH_3 \)
1. **Valence Electrons**: In \( NH_3 \), nitrogen has 5 valence electrons and forms 3 bonds with hydrogen, leaving 1 lone pair.
2. **Bond Pairs and Lone Pairs**: There are 3 bond pairs and 1 lone pair.
3. **Hybridization**:
\[ \text{Hybridization} = 3 + 1 = 4 \quad \Rightarrow \quad sp^3 \]
4. **Geometry and Bond Angle**: The geometry is tetrahedral, but the presence of a lone pair alters the shape to trigonal pyramidal. The bond angle is slightly less than \( 109.5^\circ \) due to lone pair-bond pair repulsion, typically around \( 107^\circ \).

### Step 3: Analyze \( NH_2^- \)
1. **Valence Electrons**: In \( NH_2^- \), nitrogen has 5 valence electrons, forms 2 bonds with hydrogen, and has 2 lone pairs (due to the negative charge).
2. **Bond Pairs and Lone Pairs**: There are 2 bond pairs and 2 lone pairs.
3. **Hybridization**:
\[ \text{Hybridization} = 2 + 2 = 4 \quad \Rightarrow \quad sp^3 \]
4. **Geometry and Bond Angle**: The geometry is tetrahedral, but with 2 lone pairs, the shape is bent. The bond angle is less than that of \( NH_3 \), typically around \( 104.5^\circ \).

### Conclusion: Order of Bond Angles
Based on the analysis:
- \( NH_4^+ \) has the largest bond angle of \( 109.5^\circ \).
- \( NH_3 \) has a bond angle of approximately \( 107^\circ \).
- \( NH_2^- \) has the smallest bond angle of approximately \( 104.5^\circ \).

Thus, the order of bond angles is:
\[ NH_4^+ > NH_3 > NH_2^- \]