Determine Molecular Structure of Xenon Trioxide

To determine the molecular structure of xenon trioxide ($\text{XeO}_3$), we can apply the Valence Shell Electron Pair Repulsion (VSEPR) theory and hybridization concepts:

1. Valence Electrons of the Central Atom:
   Xenon ($\text{Xe}$) is a noble gas belonging to Group 18 and has $8$ valence electrons in its outermost shell.

2. Bonding with Oxygen Atoms:
   Each oxygen atom requires $2$ electrons to form a double bond (consisting of $1$ $\sigma$-bond and $1$ $\pi$-bond) with Xenon.
   For $3$ oxygen atoms, the number of valence electrons from Xenon involved in bonding is:
   $3 \times 2 = 6 \text{ electrons}$

3. Lone Pairs on Central Atom:
   The remaining valence electrons on Xenon form a lone pair:
   $\text{Remaining electrons} = 8 - 6 = 2 \text{ electrons } (1 \text{ lone pair})$

4. Steric Number and Hybridization:
   The steric number ($Z$) is given by the sum of the number of $\sigma$-bonds and lone pairs around the central Xenon atom:
   $\text{Steric Number} = \text{Number of } \sigma\text{-bonds} + \text{Number of lone pairs} = 3 + 1 = 4$

   A steric number of $4$ corresponds to $sp^3$ hybridization with a tetrahedral electron-pair geometry.

5. Molecular Geometry (Shape):
   With $3$ bonding positions and $1$ lone pair occupying the corners of the tetrahedron, the lone pair-bond pair repulsion distorts the shape, resulting in a trigonal pyramidal (or pyramidal) molecular structure.

Thus, the correct structure of $\text{XeO}_3$ is pyramidal.

Correct Option: (C) pyramidal