In the linear `I_3^(-)` (triiodide ion), the central iodine atom contains

Options

A. (a) no unshared pair of electrons
B. (b) four unshared pairs of electrons
C. (c) three unshared pair of electrons
D. (d) two unpaired electrons

Explanation

To determine how many lone pairs of electrons the central iodine atom in the linear triiodide ion (I₃⁻) contains, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Valence Electrons of Iodine:**
- Iodine (I) is in Group 17 of the periodic table and has 7 valence electrons.

2. **Account for the Negative Charge:**
- The triiodide ion (I₃⁻) has an extra electron due to the negative charge. Therefore, the total number of valence electrons in I₃⁻ is:
\[ 3 \times 7 \text{ (from three iodine atoms)} + 1 \text{ (from the negative charge)} = 22 \text{ valence electrons} \]

3. **Draw the Lewis Structure:**
- In the Lewis structure of I₃⁻, the central iodine atom is bonded to two iodine atoms. Each bond uses 2 electrons, so:
\[ 2 \text{ bonds} \times 2 \text{ electrons/bond} = 4 \text{ electrons used for bonding} \]
- Subtracting these from the total valence electrons gives:
\[ 22 - 4 = 18 \text{ electrons remaining} \]

4. **Distribute Remaining Electrons as Lone Pairs:**
- The remaining 18 electrons are placed around the central iodine atom and the two terminal iodine atoms. Each terminal iodine atom will have 3 lone pairs (6 electrons), using up:
\[ 2 \text{ terminal I} \times 6 \text{ electrons} = 12 \text{ electrons} \]
- This leaves:
\[ 18 - 12 = 6 \text{ electrons} \]
- The central iodine atom will have these 6 electrons as 3 lone pairs.

5. **Determine the Hybridization:**
- The central iodine atom has 2 bond pairs (from the two I-I bonds) and 3 lone pairs. The total number of electron pairs is:
\[ 2 \text{ bond pairs} + 3 \text{ lone pairs} = 5 \text{ electron pairs} \]
- The hybridization corresponding to 5 electron pairs is \( sp^3d \).

6. **Conclusion:**
- Therefore, the central iodine atom in the I₃⁻ ion contains **three lone pairs of electrons**.

### Final Answer:
The central iodine atom in the linear I₃⁻ ion contains **three lone pairs of electrons**.