To determine the geometry of electron pairs around the central atom, we first need to find the steric number (SN) of the central atom. The steric number is the sum of the number of bond pairs and lone pairs around the central atom.

Step 1: Determine the number of valence electrons of the central atom.
The central atom is Iodine (I). Iodine is in Group 17, so it has 7 valence electrons.

Step 2: Determine the number of electrons contributed by surrounding atoms.
There are 5 Fluorine (F) atoms. Each F atom contributes 1 electron for bonding. So, 5 F atoms contribute $5\times 1=5$ electrons.

Step 3: Calculate the total number of electrons involved in bonding and lone pairs.
Total electrons = Valence electrons of I + Electrons from F atoms = $7+5=12$ electrons.

Step 4: Calculate the number of electron pairs.
Number of electron pairs = Total electrons / 2 = $12/2=6$ electron pairs.

Step 5: Determine the number of bond pairs and lone pairs.
Number of bond pairs = Number of surrounding atoms = 5 (for 5 F atoms).
Number of lone pairs = Total electron pairs - Number of bond pairs = $6-5=1$ lone pair.

Step 6: Determine the geometry of electron pairs.
The steric number (SN) = Number of bond pairs + Number of lone pairs = $5+1=6$.
According to VSEPR theory, if the steric number is 6, the geometry of electron pairs is Octahedral.

Option Analysis:

• A) Octahedral: This is correct. With 6 electron pairs (5 bond pairs and 1 lone pair), the electron pair geometry is octahedral.
• B) Trigonal bipyramidal: This geometry corresponds to a steric number of 5.
• C) Square pyramidal: This is the molecular geometry of ${\mathrm{IF}}_5$, not the electron pair geometry. The molecular geometry is derived from the electron pair geometry by considering only the positions of the atoms.
• D) Pentagonal planar: This geometry is rare and typically associated with a steric number of 7 (e.g., ${\mathrm{IF}}_7$ has pentagonal bipyramidal electron geometry).

Correct Answer: (A)