According to vbt lone pair bond pair repulsion is greater than bond pair bond pair so axial sf bond fill more repulsion hence greater bond length

Introduction:
In SF4 (sulfur tetrafluoride), the axial S-F bond length is greater than the equatorial S-F bond length. This difference in bond lengths is due to the presence of a lone pair on sulfur. The lone pair affects the molecular geometry and bond angles in SF4, leading to the observed bond length discrepancy.

Explanation:

Molecular Geometry:
SF4 adopts a trigonal bipyramidal molecular geometry, with sulfur (S) at the center and four fluorine (F) atoms surrounding it. The geometry consists of three equatorial positions and two axial positions, as shown below:

F
|
F--S--F
|
F

Lone Pair Repulsion:
The sulfur atom in SF4 has an electron configuration of 1s2 2s2 2p6 3s2 3p4. This means that there are two lone pairs of electrons on sulfur, along with the four bonding electrons from the S-F bonds. The presence of these lone pairs affects the molecular geometry.

Electronic Repulsion:
The lone pairs of electrons repel other electron pairs (both bonding and lone pairs) in the molecule. This repulsion leads to a distortion in the molecular geometry, causing the equatorial S-F bond angles to be larger than the axial S-F bond angles.

Effect on Bond Lengths:
The repulsion between the lone pair and the bonding pairs affects the S-F bond lengths. The axial S-F bonds experience greater repulsion from the lone pair compared to the equatorial S-F bonds. As a result, the axial S-F bonds are pushed slightly farther away from the sulfur atom, leading to longer bond lengths.

Conclusion:
In SF4, the axial S-F bond length is greater than the equatorial S-F bond length due to the presence of a lone pair on sulfur. The lone pair repulsion affects the molecular geometry, resulting in longer axial bond lengths. Understanding the role of lone pairs and their impact on molecular geometry is crucial in predicting bond lengths and overall molecular structure.