What is the geometrical shape of `XeO_3`

Options

A. Planar triangular
B. trigonal pyramidal
C. square planar
D. Tetrahedral

Explanation

To determine the geometrical shape of \( \text{XeO}_3 \), we can follow these steps:

### Step 1: Identify the central atom
The central atom in \( \text{XeO}_3 \) is xenon (Xe).

### Step 2: Count the valence electrons
Xenon is in group 18 of the periodic table and has 8 valence electrons. Each oxygen atom (there are three) contributes 6 valence electrons. Therefore, the total number of valence electrons is:
\[ 8 \, (\text{from Xe}) + 3 \times 6 \, (\text{from O}) = 8 + 18 = 26 \, \text{valence electrons} \]

### Step 3: Draw the Lewis structure
In the Lewis structure of \( \text{XeO}_3 \), xenon will form double bonds with each of the three oxygen atoms. This utilizes 6 electrons (2 for each double bond), leaving us with:
\[ 26 - 6 = 20 \, \text{electrons} \]
Since each oxygen atom is bonded to xenon, we can place lone pairs on the oxygen atoms to satisfy their octet. Each oxygen will have 4 electrons (2 lone pairs) after forming the double bond, which uses up:
\[ 3 \times 4 = 12 \, \text{electrons} \]
This leaves us with:
\[ 20 - 12 = 8 \, \text{electrons} \]
These remaining 8 electrons will be placed as lone pairs on the xenon atom, which will have 2 lone pairs.

### Step 4: Determine the molecular geometry
With 3 double bonds to oxygen and 2 lone pairs on xenon, we can use VSEPR theory to determine the molecular geometry. The presence of lone pairs affects the shape. The arrangement of the electron pairs (3 bonding pairs and 2 lone pairs) around the xenon atom will adopt a trigonal bipyramidal arrangement, but due to the presence of the lone pairs, the actual shape is trigonal pyramidal.

### Conclusion
The geometrical shape of \( \text{XeO}_3 \) is **trigonal pyramidal**.

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