To determine the correct statement, we need to analyze the structure and basicity of ${(SiH3)3N}$ and ${(CH3)3N}$. Let's go through the concepts step by step:
- **Structure of ${(CH3)3N}:**
- Trimethylamine, ${(CH3)3N}$, has a pyramidal shape due to the sp3 hybridization of the nitrogen atom. The lone pair on the nitrogen creates a tetrahedral electron-pair geometry, but the molecular shape is pyramidal.
- **Structure of ${(SiH3)3N}:**
- In contrast, trisilylamine, ${(SiH3)3N}$, tends to be planar. The larger size of silicon compared to carbon, and its lower ability to participate in effective hyperconjugation or back-bonding with nitrogen, leads to a planar structure where the lone pair is delocalized over the Si-N-Si bonds.
- **Basicity Comparison:**
- Basicity is often related to the availability of the lone pair of electrons that can be donated. In ${(CH3)3N}$, the lone pair is more localized and available for donation, making it a stronger base.
- In ${(SiH3)3N}$, the lone pair on nitrogen is less available because of delocalization over the Si-N-Si bonds, making it less basic than trimethylamine.
Based on the structural and electronic considerations above, the correct statement is: \({(SiH3)3N}\) is planar and less basic than \({(CH3)3N}\).
**Conclusion:**
The option "\({(SiH3)3N}\) is planar and less basic than \({(CH3)3N}\)" is correct because of the delocalization of the lone pair in the planar structure of ${(SiH3)3N}$, reducing its basicity compared to the pyramidal and more localized lone pair in ${(CH3)3N}$.