Which of the following pair is expected to have the same bond order ?

Options

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

Explanation

To determine which pair of molecules has the same bond order, we need to calculate the bond order for each molecule in the given options. 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 go through the steps to find the bond order for the pairs mentioned in the question.

### Step 1: Identify the molecules and their electron configurations
1. **O2**: Oxygen has 8 electrons, so O2 has a total of 16 electrons.
2. **N2**: Nitrogen has 7 electrons, so N2 has a total of 14 electrons.
3. **O2+**: This is O2 with one electron removed, so it has 15 electrons.
4. **N2-**: This is N2 with one electron added, so it has 15 electrons.

### Step 2: Calculate the bond order for O2 and N2
- **O2**:
- Bonding electrons = 10 (from the molecular orbital theory)
- Antibonding electrons = 6
- Bond Order = (10 - 6) / 2 = 2.0

- **N2**:
- Bonding electrons = 10
- Antibonding electrons = 0
- Bond Order = (10 - 0) / 2 = 5.0

### Step 3: Calculate the bond order for O2+ and N2-
- **O2+**:
- Bonding electrons = 10
- Antibonding electrons = 5
- Bond Order = (10 - 5) / 2 = 2.5

- **N2-**:
- Bonding electrons = 10
- Antibonding electrons = 1
- Bond Order = (10 - 1) / 2 = 4.5

### Step 4: Compare the bond orders
- O2 has a bond order of 2.0
- N2 has a bond order of 5.0
- O2+ has a bond order of 2.5
- N2- has a bond order of 4.5

### Conclusion
From the calculations, we find that **O2+** and **N2-** have the same bond order of **2.5**. Therefore, the expected answer is:

**Option 2: O2+ and N2- have the same bond order.**