Structure of \(XeO_2F_2\) as per VSEPR theory is:

See-Saw

The correct answer is option 3. See-Saw.

Let us go through a detailed explanation of the structure of \( \text{XeO}_2\text{F}_2 \) using VSEPR (Valence Shell Electron Pair Repulsion) theory.

Xenon is a noble gas from group 18, so it has 8 valence electrons. In \( \text{XeO}_2\text{F}_2 \), xenon is bonded to 2 oxygen atoms and 2 fluorine atoms:

The bonds to oxygen are typically double bonds (because oxygen prefers to form two bonds).

The bonds to fluorine are single bond (fluorine always forms single bonds).

Out of the 8 valence electrons on xenon:

4 electrons are used in bonding (2 electrons for each of the 2 double bonds with oxygen).

2 more electrons are used to form single bonds with the 2 fluorine atoms (1 electron for each fluorine bond).

This leaves 2 electrons or  1 lone pair on the xenon atom.

Total electron pairs around Xenon

4 bonding pairs (2 double bonds with oxygen + 2 single bonds with fluorine) and 1 lone pair.

Thus, the xenon atom in \( \text{XeO}_2\text{F}_2 \) has a total of 5 electron pairs (4 bonding pairs + 1 lone pair) around it.

According to VSEPR theory, 5 electron pairs around a central atom adopt a trigonal bipyramidal arrangement to minimize repulsion. In a trigonal bipyramidal arrangement:

The lone pair will prefer to occupy one of the equatorial positions because lone pairs experience less repulsion in the equatorial plane than in the axial positions.

The fluorine atoms (which form single bonds) will also occupy the equatorial position because single bonds tend to experience more repulsion than double bonds.

The two oxygen atoms, which form double bonds, will occupy the axial positions.

After placing the lone pair and the fluorine atoms in the equatorial positions, the remaining bonding pairs (the double bonds to oxygen) will be in the axial positions. The presence of a lone pair in one of the equatorial positions distorts the geometry from ideal trigonal bipyramidal to a see-saw shape.

The geometry around xenon is based on a trigonal bipyramidal arrangement of electron pairs. However, due to the presence of the lone pair, the molecular shape becomes see-saw.

The shape of \( \text{XeO}_2\text{F}_2 \) is see-saW, as determined by VSEPR theory.