Which of the following pairs have identical value of bond order?

Options

A. `B_(2) and O_(2)^(2-)`
B. `NO^(+) and N_(2)`
C. `C_(2) and O_(2)`
D. All of these

Explanation

To determine which pairs of molecules have identical bond orders, we will follow these steps:

### Step 1: Understand Bond Order Calculation
Bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]
We will apply this formula to each pair of molecules in the options provided.

### Step 2: Analyze Each Option

#### Option A: B2 and O2^2-
1. **B2:**
- Total electrons = 10
- Electron configuration: σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² σ(2p)²
- Bonding electrons = 6 (σ(1s)², σ(2s)², σ(2p)²)
- Antibonding electrons = 2 (σ*(1s)², σ*(2s)²)
- Bond Order = (6 - 2) / 2 = 2

2. **O2^2-:**
- Total electrons = 18
- Electron configuration: σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² σ(2p)² σ*(2p)²
- Bonding electrons = 10 (σ(1s)², σ(2s)², σ(2p)²)
- Antibonding electrons = 4 (σ*(1s)², σ*(2s)², σ*(2p)²)
- Bond Order = (10 - 4) / 2 = 3

**Conclusion for Option A:** Bond orders are different (2 for B2 and 3 for O2^2-).

#### Option B: N2 and NO+
1. **N2:**
- Total electrons = 14
- Electron configuration: σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² σ(2p)²
- Bonding electrons = 10
- Antibonding electrons = 4
- Bond Order = (10 - 4) / 2 = 3

2. **NO+:**
- Total electrons = 15 - 1 = 14
- Electron configuration: σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² σ(2p)²
- Bonding electrons = 10
- Antibonding electrons = 4
- Bond Order = (10 - 4) / 2 = 3

**Conclusion for Option B:** Bond orders are identical (both have a bond order of 3).

#### Option C: O2 and F2
1. **O2:**
- Total electrons = 16
- Bond Order = (10 - 6) / 2 = 2

2. **F2:**
- Total electrons = 18
- Bond Order = (10 - 6) / 2 = 2

**Conclusion for Option C:** Bond orders are identical (both have a bond order of 1).

#### Option D: C2 and N2
1. **C2:**
- Total electrons = 12
- Bond Order = (8 - 4) / 2 = 2

2. **N2:**
- Total electrons = 14
- Bond Order = (10 - 4) / 2 = 3

**Conclusion for Option D:** Bond orders are different (2 for C2 and 3 for N2).

### Final Conclusion
The pairs that have identical bond orders are:
- **Option B: N2 and NO+** (both have a bond order of 3)
- **Option C: O2 and F2** (both have a bond order of 1)