Which one of the following does not have a pyramidal shape?

To determine which compound does not have a pyramidal shape, we need to recall that pyramidal geometry typically occurs when a central atom has three bonding pairs and one lone pair of electrons, resulting in a trigonal pyramidal structure. This is common for group 15 elements like nitrogen and phosphorus. However, the presence of back-bonding or other effects can alter the geometry.

Let's analyze each option:

Option A: (CH$$_3$$)$$_3$$N (trimethylamine). The nitrogen atom has three methyl groups and one lone pair. Nitrogen uses sp$$^3$$ hybridization, forming a tetrahedral electron geometry with the lone pair occupying one position, leading to a pyramidal shape. This is similar to ammonia (NH$$_3$$). Thus, it is pyramidal.

Option B: (SiH$$_3$$)$$_3$$N (trisilylamine). The central nitrogen atom has three SiH$$_3$$ groups and one lone pair. Silicon has vacant d-orbitals, allowing nitrogen's lone pair to engage in p$$_\pi$$-d$$_\pi$$ back-bonding. This delocalizes the lone pair, reducing its repulsion and causing the molecule to adopt a planar (trigonal planar) geometry instead of pyramidal. Experimental evidence confirms trisilylamine is planar due to this back-bonding.

Option C: P(CH$$_3$$)$$_3$$ (trimethylphosphine). The phosphorus atom has three methyl groups and one lone pair. Phosphorus uses sp$$^3$$ hybridization, and since carbon lacks low-lying d-orbitals for significant back-bonding, the lone pair remains localized, resulting in a pyramidal shape.

Option D: P(SiH$$_3$$)$$_3$$ (trisilylphosphine). The phosphorus atom has three SiH$$_3$$ groups and one lone pair. Although silicon has vacant d-orbitals, phosphorus's larger atomic size (3p orbitals) leads to weaker p$$_\pi$$-d$$_\pi$$ overlap compared to nitrogen. Thus, back-bonding is insufficient to cause planarity, and the molecule retains a pyramidal shape.

Therefore, (SiH$$_3$$)$$_3$$N (option B) is the compound that does not have a pyramidal shape due to back-bonding-induced planarity.

Hence, the correct answer is Option B.