Among following molecule `N-Si` bond length is shortest:

Options

A. `N(SiH_(3))_(3)`
B. `NH(SiH_(3))_(2)`
C. `NH_(2)(SiH_(3))`
D. All have equal `N-Si` bond length

Explanation

To determine which molecule has the shortest N-Si bond length among the given options, we can analyze the structures and the concept of backbonding.

### Step-by-Step Solution:

1. **Identify the Molecules**: The three molecules given are:
- (A) N(SiH3)3
- (B) NH(SiH3)2
- (C) NH2(SiH3)

2. **Understand Backbonding**: Backbonding occurs when there is a donation of electron density from a filled orbital of one atom (in this case, nitrogen) to an empty orbital of another atom (silicon). This interaction can affect bond lengths.

3. **Analyze Each Molecule**:
- In **(A) N(SiH3)3**, nitrogen is bonded to three SiH3 groups. The backbonding is distributed among three SiH3 groups, which means the extent of backbonding is less effective for each individual N-Si bond.
- In **(B) NH(SiH3)2**, nitrogen is bonded to two SiH3 groups. The backbonding is shared between two SiH3 groups, leading to a stronger interaction compared to (A).
- In **(C) NH2(SiH3)**, nitrogen is bonded to only one SiH3 group. This means that the backbonding is concentrated on a single N-Si bond, resulting in a stronger bond and thus a shorter bond length.

4. **Compare Bond Lengths**:
- The bond length of N-Si in (A) is the longest due to the distribution of backbonding across three groups.
- The bond length of N-Si in (B) is shorter than in (A) but longer than in (C) due to the distribution across two groups.
- The bond length of N-Si in (C) is the shortest because the backbonding is fully utilized in a single bond.

5. **Conclusion**: Therefore, the N-Si bond length is shortest in **(C) NH2(SiH3)**.

### Final Answer:
The N-Si bond length is shortest in **NH2(SiH3)**.

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