Concept:
The shape of molecules can be predicted using the VSEPR theory (Valence Shell Electron Pair Repulsion Theory).
According to VSEPR theory:
• Electron pairs around the central atom repel each other.
• The electron pairs arrange themselves in such a way that repulsion becomes minimum.
• Both bond pairs and lone pairs contribute toward repulsion.
The order of repulsion is:
\[
\text{Lone pair - Lone pair} > \text{Lone pair - Bond pair} > \text{Bond pair - Bond pair}
\]
Thus, the presence of lone pairs changes the molecular geometry significantly.
Step 1: Find the valence electrons of sulfur.
Sulfur belongs to Group 16.
Therefore, sulfur has:
\[
6 \text{ valence electrons}
\]
Fluorine belongs to Group 17 and contributes one bond each.
In \( \mathrm{SF_4} \):
• Sulfur forms four S--F bonds.
• Four electrons are used in bonding.
Remaining electrons on sulfur:
\[
6 - 4 = 2
\]
These two electrons form:
\[
1 \text{ lone pair}
\]
Step 2: Determine the total electron domains.
Around sulfur:
• \(4\) bond pairs
• \(1\) lone pair
Total electron domains:
\[
4 + 1 = 5
\]
According to VSEPR theory, five electron domains correspond to:
\[
\boxed{\text{Trigonal bipyramidal electron geometry}}
\]
Step 3: Understand the placement of the lone pair.
In trigonal bipyramidal geometry:
• There are two axial positions.
• There are three equatorial positions.
A lone pair prefers the equatorial position because:
• Equatorial position experiences fewer repulsions.
• Axial positions have three \(90^\circ\) interactions.
• Equatorial positions have only two \(90^\circ\) interactions.
Thus, the lone pair occupies an equatorial position.
Step 4: Determine the molecular shape.
After placing one lone pair in trigonal bipyramidal arrangement, the remaining four fluorine atoms form a distorted geometry called:
\[
\boxed{\text{Seesaw shape}}
\]
The molecule resembles the shape of a seesaw due to unequal distribution of atoms around sulfur.
Step 5: Verify the remaining options.
• Tetrahedral: Requires four bond pairs and no lone pair. Hence incorrect.
• Square planar: Usually arises from octahedral geometry with two lone pairs. Hence incorrect.
• Trigonal bipyramidal: This is the electron pair geometry, not the molecular geometry because one position is occupied by a lone pair.
Therefore, only seesaw is correct.
Final Conclusion:
The molecular geometry of \( \mathrm{SF_4} \) is:
\[
\boxed{\text{Seesaw}}
\]
Hence, the correct answer is:
\[
\boxed{(2)}
\]