Assertion Bond order for `N_(2)^(o+)` and `N_(2)^(Theta)` are same (i.e2.5)
Reasoning `N_(2)^(o+)` is more stable than `N_(2)^(Theta)` .

Options

A. If both `(A)` and `(R )` are correct and `(R )` is the correct
explanation of `(A)`
B. If both `(A)` and `(R )` are correct and `(R )` is not the correct
explanation of `(A)`
C. If `(A)` is correct but `(R )` is incorrect
D. If `(A)` is incorrect but `(R )` is correct

Explanation

To solve the question regarding the assertion and reasoning about the bond order of \( N_2^+ \) and \( N_2^- \), we will follow these steps:

### Step 1: Determine the Electron Configuration
- For \( N_2^+ \) (which has 13 electrons):
- The electron configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^1 \]

- For \( N_2^- \) (which has 15 electrons):
- The electron configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \pi_{2p_x}^*^1 \]

### Step 2: Calculate the Bond Order
- Bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \]

- For \( N_2^+ \):
- Bonding electrons = 9 (from \( \sigma_{1s}, \sigma_{2s}, \pi_{2p_x}, \pi_{2p_y}, \sigma_{2p_z} \))
- Antibonding electrons = 2 (from \( \sigma_{1s}^* \) and \( \sigma_{2s}^* \))
- Bond Order = \( \frac{9 - 2}{2} = \frac{7}{2} = 3.5 \)

- For \( N_2^- \):
- Bonding electrons = 10 (from \( \sigma_{1s}, \sigma_{2s}, \pi_{2p_x}, \pi_{2p_y}, \sigma_{2p_z} \))
- Antibonding electrons = 2 (from \( \sigma_{1s}^* \) and \( \sigma_{2s}^* \), and \( \pi_{2p_x}^* \))
- Bond Order = \( \frac{10 - 2}{2} = \frac{8}{2} = 4 \)

### Step 3: Analyze the Assertion and Reasoning
- The assertion states that the bond order for \( N_2^+ \) and \( N_2^- \) is the same (2.5). This is incorrect based on our calculations.
- The reasoning states that \( N_2^+ \) is more stable than \( N_2^- \). This is true since \( N_2^+ \) has a higher bond order, indicating greater stability.

### Conclusion
- Therefore, the assertion is false, while the reasoning is true. The correct answer is that the assertion is incorrect, but the reasoning is correct.