In which of the following pair, the two molecules have identical bond orders :

Options

A. `N_(2),O_(2)^(2+)`
B. `N_(2),O_(2)^(-)`
C. `N_(2)^(-),O_(2)`
D. `N_(2)^(2-),N_(2).`

Explanation

To determine which pair of molecules has identical bond orders, we need to calculate the bond order for each molecule in the given pairs. The bond order can be calculated using the formula:

\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]

Let's analyze each pair step by step.

### Step 1: Identify the molecules and their electron counts
1. **N₂**: Contains 14 electrons (7 from each nitrogen atom).
2. **O₂⁺**: Contains 14 electrons (16 in O₂ minus 2 for the positive charge).

### Step 2: Calculate the bond order for N₂
- **Bonding electrons in N₂**: 10
- **Antibonding electrons in N₂**: 4
- **Bond Order**:
\[ \text{Bond Order} = \frac{(10 - 4)}{2} = \frac{6}{2} = 3 \]

### Step 3: Calculate the bond order for O₂⁺
- **Bonding electrons in O₂⁺**: 10 (same as O₂)
- **Antibonding electrons in O₂⁺**: 4 (same as O₂)
- **Bond Order**:
\[ \text{Bond Order} = \frac{(10 - 4)}{2} = \frac{6}{2} = 3 \]

### Step 4: Compare bond orders
Both N₂ and O₂⁺ have a bond order of 3.

### Conclusion
The pair of molecules N₂ and O₂⁺ has identical bond orders.