To determine the number of lone pairs on the central atom (Xe) in XeF₂ and XeF₄, we can use the VSEPR theory or a simple formula involving valence electrons.

The number of lone pairs on the central atom can be calculated using the formula:

Number of lone pairs = (Total valence electrons of central atom - Number of electrons used in bonding) / 2

Alternatively, we can determine the steric number (SN = number of bond pairs + number of lone pairs) and then deduce the number of lone pairs.

For XeF₂:

• Xenon (Xe) is a noble gas, so it has 8 valence electrons.
• Fluorine (F) is monovalent, forming one single bond.
• Number of electrons used in bonding = 2 (for two F atoms).
• Number of lone pairs = (8 - 2) / 2 = 6 / 2 = 3.
• Alternatively, the steric number for XeF₂ is 5 (2 bond pairs + 3 lone pairs), corresponding to a trigonal bipyramidal electron geometry and linear molecular geometry.

For XeF₄:

• Xenon (Xe) has 8 valence electrons.
• Number of electrons used in bonding = 4 (for four F atoms).
• Number of lone pairs = (8 - 4) / 2 = 4 / 2 = 2.
• Alternatively, the steric number for XeF₄ is 6 (4 bond pairs + 2 lone pairs), corresponding to an octahedral electron geometry and square planar molecular geometry.

Thus, the number of lone pairs on Xe in XeF₂ and XeF₄ are 3 and 2, respectively.

• A) 2, 3: Incorrect. XeF₂ has 3 lone pairs, not 2.
• B) 1, 2: Incorrect. XeF₂ has 3 lone pairs, not 1.
• C) 2, 1: Incorrect. XeF₂ has 3 lone pairs, not 2, and XeF₄ has 2 lone pairs, not 1.
• D) 3, 2: Correct, as calculated above.

Correct Answer: (D)