To solve this question, we must identify the \( p \)-block elements \( X \) and \( Y \) that form fluorides of the type \( EF_3 \), and understand the difference in their hybridization based on their Lewis acid or base behavior.
- First, understand the nature of \( XF_3 \) which acts as a Lewis acid. A Lewis acid has an empty orbital to accept electrons. In \( p \)-block elements, this behavior is typically seen in elements like Boron. For example, \( \text{BF}_3 \) is a well-known Lewis acid because Boron has an empty \( p \)-orbital.
- The hybridization of Boron in \( \text{BF}_3 \) is \(sp^2\) because it forms three bonds with fluorine and has no lone pairs, leading to a trigonal planar geometry.
- Now, consider \( YF_3 \) as a Lewis base. A Lewis base has lone pairs of electrons to donate. In the context of the \( p \)-block, a typical example would be Nitrogen, which forms \( \text{NF}_3 \). Nitrogen in \( \text{NF}_3 \) has a lone pair of electrons.
- The hybridization here is \(sp^3\), since Nitrogen forms three bonds with Fluorine and has one lone pair, resulting in a tetrahedral electron geometry.
- Therefore, the hybridizations of the central atoms in \( XF_3 \) and \( YF_3 \) are \(sp^2\) and \(sp^3\), respectively.
Based on the analysis above, the correct answer is: \(sp^2\) and \(sp^3\).
The hybridizations are determined by the number of bonds, lone pairs, and the resulting electron pair geometry of the molecular structures:
- Lewis Acid (like Boron): Needs empty orbitals, thus giving rise to an \(sp^2\) hybridization due to three bonds and no lone pairs.
- Lewis Base (like Nitrogen): Possesses lone pairs, hence \(sp^3\) hybridization with three bonds and one lone pair.