Step 1: Understanding the Concept:
Molecular geometry is defined by the VSEPR (Valence Shell Electron Pair Repulsion) theory.
The shape of a molecule depends on the total number of electron pairs (bonding pairs + lone pairs) surrounding the central atom, known as the Steric Number.
Lone pairs occupy more space than bond pairs, causing distortion in ideal shapes like octahedral or tetrahedral.
Step 2: Key Formula or Approach:
Steric Number \( (S.N.) = \frac{1}{2} [\text{Valence } e^- + \text{Monovalent atoms} - \text{Charge}] \).
Step 3: Detailed Explanation:
1. \( BrF_5 \): Bromine has 7 valence electrons. It bonds with 5 fluorine atoms.
\( S.N. = (7 + 5) / 2 = 6 \).
It has 5 bond pairs and 1 lone pair. This configuration leads to a Square Pyramidal shape. (Set I is correct).
2. \( XeF_6 \): Xenon has 8 valence electrons. It bonds with 6 fluorine atoms.
\( S.N. = (8 + 6) / 2 = 7 \).
It has 6 bond pairs and 1 lone pair. The lone pair distorts the regular octahedral symmetry, resulting in a Distorted Octahedral shape. (Set II is correct).
3. \( SF_4 \): Sulfur has 6 valence electrons. It bonds with 4 fluorine atoms.
\( S.N. = (6 + 4) / 2 = 5 \).
It has 4 bond pairs and 1 lone pair. This corresponds to a Seesaw shape, not square planar. (Set III is incorrect).
4. \( PbCl_2 \): Lead (Group 14) has 4 valence electrons. It bonds with 2 chlorine atoms and has 1 lone pair.
\( S.N. = 3 \). This results in a Bent (V-shaped) geometry, similar to \( SO_2 \), not linear. (Set IV is incorrect).
Therefore, only the first two sets correctly describe the molecular geometry.
Step 4: Final Answer:
Sets I and II are correctly matched.
This corresponds to Option (a).