The molecular geometry of $$SF_6$$ is octahedral. What is the geometry of $$SF_4$$ (including lone pair(s) of electrons, if any)?

We begin by counting the total number of valence electrons around the central atom sulphur in $$SF_4$$.

Atomic sulphur lies in Group 16, so it provides $$6$$ valence electrons. Each fluorine atom lies in Group 17 and contributes $$7$$ valence electrons. Because there are four fluorine atoms, the contribution from fluorine is $$4 \times 7 = 28$$ electrons.

Adding these values we obtain the total number of valence electrons present in one $$SF_4$$ molecule:

$$6 + 28 = 34 \text{ electrons}$$

Next, we distribute these electrons to form single S-F bonds. A single covalent bond contains two electrons. With four S-F bonds we must allocate

$$4 \times 2 = 8 \text{ electrons}$$

Subtracting these from the total gives the electrons that are still unassigned:

$$34 - 8 = 26 \text{ electrons}$$

Every fluorine atom requires an octet. Each already owns two bonding electrons, so each fluorine still needs $$6$$ more. For all four fluorine atoms this means

$$4 \times 6 = 24 \text{ electrons}$$

Placing those $$24$$ electrons as lone pairs on fluorine leaves

$$26 - 24 = 2 \text{ electrons}$$

These two electrons remain with sulphur as one lone pair. Thus around the central sulphur we have

• $$4$$ bonding pairs (one along each S-F bond)
• $$1$$ lone pair.

The sum of bonding pairs and lone pairs is called the steric number. Therefore

$$\text{Steric number} = 4 + 1 = 5$$

VSEPR (Valence-Shell Electron-Pair Repulsion) theory states: "An arrangement of $$5$$ electron pairs around a central atom adopts a trigonal-bipyramidal electron-pair geometry to minimize repulsions."

Hence the electron-pair geometry of $$SF_4$$, which explicitly includes the lone pair, is trigonal bipyramidal.

(If one talks only about the positions of the atoms and ignores the lone pair, the molecular shape is a see-saw, but that choice is not offered in the options.)

So, the geometry requested in the problem—"including lone pair(s) of electrons"—is trigonal bipyramidal.

Hence, the correct answer is Option 2.