In the following questions, a statement of assertion (A) is followed by a statement of reason (R )
A : `N_(2)` is more stable than `N_(2)^(+)` .
R : Bond order of `N_(2)` is 3 while `N_(2)^(+)` is 2.5.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements , then mark (4).

Answer

To solve the question regarding the stability of \( N_2 \) compared to \( N_2^+ \) and the corresponding bond orders, we can follow these steps:

### Step 1: Understand the Assertion and Reason
- **Assertion (A)**: \( N_2 \) is more stable than \( N_2^+ \).
- **Reason (R)**: The bond order of \( N_2 \) is 3 while that of \( N_2^+ \) is 2.5.

### Step 2: Define Bond Order
Bond order is defined as the difference between the number of bonding electrons and anti-bonding electrons divided by two. It is a measure of the stability of a bond; higher bond order indicates greater stability.

### Step 3: Calculate the Bond Order for \( N_2 \)
1. **Electron Configuration of \( N_2 \)**:
- Total electrons = 14 (7 from each nitrogen atom).
- Molecular Orbital Configuration:
- \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \)
- Bonding Electrons = 10 (from \( \sigma_{1s}, \sigma_{2s}, \pi_{2p_x}, \pi_{2p_y}, \sigma_{2p_z} \))
- Anti-bonding Electrons = 4 (from \( \sigma_{1s}^* \) and \( \sigma_{2s}^* \))

2. **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{(10 - 4)}{2} = \frac{6}{2} = 3 \]

### Step 4: Calculate the Bond Order for \( N_2^+ \)
1. **Electron Configuration of \( N_2^+ \)**:
- Total electrons = 13 (one electron removed from \( N_2 \)).
- Molecular Orbital Configuration:
- \( \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^1 \)
- Bonding Electrons = 9 (same as before, but one less due to the removed electron)
- Anti-bonding Electrons = 4 (remains the same)

2. **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{(9 - 4)}{2} = \frac{5}{2} = 2.5 \]

### Step 5: Compare the Bond Orders
- \( N_2 \) has a bond order of 3.
- \( N_2^+ \) has a bond order of 2.5.
- Since a higher bond order indicates greater stability, \( N_2 \) is indeed more stable than \( N_2^+ \).

### Step 6: Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion. Therefore, the answer is that both statements are correct.

### Final Answer
1. Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.

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