To solve the problem, we need to analyze the assertion (A) and the reason (R) provided in the question.
### Step 1: Analyze Assertion (A)
The assertion states that \( N_2 \), CO, and \( CN^- \) have the same bond order.
1. **Determine the number of electrons in each species:**
- \( N_2 \): Each nitrogen atom has 7 electrons, so for \( N_2 \) (2 nitrogen atoms), the total is \( 7 \times 2 = 14 \) electrons.
- CO: Carbon has 6 electrons and oxygen has 8 electrons, so for CO, the total is \( 6 + 8 = 14 \) electrons.
- \( CN^- \): Carbon has 6 electrons, nitrogen has 7 electrons, and the negative charge adds 1 more electron, so the total is \( 6 + 7 + 1 = 14 \) electrons.
Since all three species have 14 electrons, we can proceed to calculate their bond orders.
### Step 2: Calculate Bond Order
The bond order can be calculated using the Molecular Orbital Theory (MOT) formula:
\[
\text{Bond Order} = \frac{1}{2} (\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals})
\]
1. **Filling the molecular orbitals for 14 electrons:**
- The order of filling for 14 electrons is:
- \( \sigma_{1s}^2 \)
- \( \sigma^*_{1s}^2 \)
- \( \sigma_{2s}^2 \)
- \( \sigma^*_{2s}^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_x}^2 \)
- \( \pi_{2p_y}^2 \)
The filling results in:
- Bonding orbitals: \( 2 + 2 + 2 + 2 + 2 + 2 = 10 \)
- Antibonding orbitals: \( 2 + 2 = 4 \)
2. **Calculate the bond order:**
\[
\text{Bond Order} = \frac{1}{2} (10 - 4) = \frac{6}{2} = 3
\]
Thus, the bond order for \( N_2 \), CO, and \( CN^- \) is 3.
### Step 3: Analyze Reason (R)
The reason states that isoelectronic species always have the same bond order.
1. **Definition of Isoelectronic Species:**
- Isoelectronic species are species that have the same number of electrons. Since \( N_2 \), CO, and \( CN^- \) all have 14 electrons, they are indeed isoelectronic.
2. **Conclusion on Reason:**
- The statement is true; isoelectronic species can have the same bond order, as seen in this case.
### Final Conclusion
Both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion. Therefore, the correct answer is:
**Option 1: If both assertion and reason are true and reason is giving correct explanation.**
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