To solve the question regarding the assertion (A) and reason (R) about the bond order of \(N_2\), \(CO\), and \(CN^-\), we will follow these steps:
### Step 1: Determine the number of electrons in each species
- **For \(N_2\)**: Nitrogen has an atomic number of 7. Thus, \(N_2\) has \(7 + 7 = 14\) electrons.
- **For \(CO\)**: Carbon has 6 electrons and Oxygen has 8 electrons. Therefore, \(CO\) has \(6 + 8 = 14\) electrons.
- **For \(CN^-\)**: Carbon has 6 electrons, Nitrogen has 7 electrons, and there is an extra electron due to the negative charge. Thus, \(CN^-\) has \(6 + 7 + 1 = 14\) electrons.
### Step 2: Confirm that all three species are isoelectronic
Since all three species \(N_2\), \(CO\), and \(CN^-\) have the same number of electrons (14), they are isoelectronic.
### Step 3: Calculate the bond order for each species using Molecular Orbital Theory
The bond order can be calculated using the formula:
\[
\text{Bond Order} = \frac{1}{2} \times (\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals})
\]
1. **Molecular Orbital Configuration**:
- For \(N_2\): The configuration is \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2\)
- For \(CO\): The configuration is similar to \(N_2\) due to the same number of electrons.
- For \(CN^-\): The configuration will also be similar, with the same filling.
2. **Counting Electrons**:
- **Bonding Orbitals**: 10 electrons (2 in \(\sigma_{1s}\), 2 in \(\sigma_{2s}\), 2 in \(\sigma_{2p_z}\), 4 in \(\pi_{2p_x}\) and \(\pi_{2p_y}\))
- **Antibonding Orbitals**: 4 electrons (2 in \(\sigma^*_{1s}\) and 2 in \(\sigma^*_{2s}\))
3. **Calculating Bond Order**:
\[
\text{Bond Order} = \frac{1}{2} \times (10 - 4) = \frac{1}{2} \times 6 = 3
\]
### Step 4: Conclusion
Since the bond order for \(N_2\), \(CO\), and \(CN^-\) is 3, the assertion (A) is true. The reason (R) states that isoelectronic species always have the same bond order, which is also true. Therefore, both the assertion and reason are correct, and the reason is a correct explanation for the assertion.
### Final Answer
Both assertion and reason are true, and the reason is the correct explanation for the assertion.
---
