Out of `N_(2) O , SO_(2), I_(3)^(+), I_(3)^(-), H_(2)O, NO_(2)^(-) and N_(3)^(-)`
the linear species are

Options

A. `NO_(2)^(-), I_(3)^(+), H_(2)O`
B. `N_(2)O,I_(3)^(-), N_(3)^(-)`
C. `N_(2)O, I_(3)^(-), N_(3)^(-)`
D. `N^(3-),I_(3)^(+), SO_(2)`

Explanation

To determine which of the given species are linear, we will analyze each compound using the concept of steric number and molecular geometry.

### Step 1: Understand the concept of steric number
The steric number is calculated using the formula:
\[ \text{Steric Number} = \frac{( \text{Number of valence electrons of central atom} + \text{Number of monovalent atoms} - \text{Charge})}{2} \]
A linear molecular geometry typically corresponds to a steric number of 2 or 5.

### Step 2: Analyze each compound

1. **N₂O (Nitrous oxide)**
- Valence electrons: N (5) + N (5) + O (6) = 16
- Central atom: N (one of the nitrogen atoms)
- Bonds: 3 (N≡N and N=O)
- Lone pairs on central N: 1
- Steric number = (5 + 0 - 0)/2 = 2.5 (not linear)

2. **SO₂ (Sulfur dioxide)**
- Valence electrons: S (6) + O (6) + O (6) = 18
- Central atom: S
- Bonds: 2 (S=O) and 1 lone pair
- Steric number = (6 + 0 - 0)/2 = 3 (not linear)

3. **I₃⁺ (Triiodide cation)**
- Valence electrons: I (7) + I (7) + I (7) - 1 (positive charge) = 20
- Central atom: I
- Bonds: 2 (I-I) and 2 lone pairs
- Steric number = (7 + 2 - 1)/2 = 4 (not linear)

4. **I₃⁻ (Triiodide anion)**
- Valence electrons: I (7) + I (7) + I (7) + 1 (negative charge) = 21
- Central atom: I
- Bonds: 2 (I-I) and 3 lone pairs
- Steric number = (7 + 2 + 1)/2 = 5 (linear)

5. **H₂O (Water)**
- Valence electrons: H (1) + H (1) + O (6) = 8
- Central atom: O
- Bonds: 2 (O-H) and 2 lone pairs
- Steric number = (6 + 0 - 0)/2 = 4 (not linear)

6. **NO₂⁻ (Nitrite ion)**
- Valence electrons: N (5) + O (6) + O (6) + 1 (negative charge) = 18
- Central atom: N
- Bonds: 2 (N=O) and 1 lone pair
- Steric number = (5 + 0 + 1)/2 = 3 (not linear)

7. **N₃⁻ (Azide ion)**
- Valence electrons: N (5) + N (5) + N (5) + 1 (negative charge) = 16
- Central atom: N (central nitrogen)
- Bonds: 2 (N≡N) and 1 lone pair
- Steric number = (5 + 0 + 1)/2 = 3 (not linear)

### Step 3: Conclusion
The only linear species from the list is **I₃⁻ (Triiodide anion)**.

### Summary of Linear Species:
- **Linear Species**: I₃⁻