Bond order and magnetic nature of `CN^-` are respectively

Options

A. 3, paramagnetic
B. 3, diamagnetic
C. `2(1)/(2),` paramagnetic
D. `2(1)/(2),` diamagnetic

Answer

To determine the bond order and magnetic nature of the cyanide ion (CN⁻), we will follow these steps:

### Step 1: Determine the Total Number of Electrons
- Carbon (C) has an atomic number of 6, which means it has 6 electrons.
- Nitrogen (N) has an atomic number of 7, which means it has 7 electrons.
- The cyanide ion (CN⁻) has an additional electron due to the negative charge.

**Total electrons = Electrons from C + Electrons from N + 1 (for the negative charge)**
\[ \text{Total electrons} = 6 + 7 + 1 = 14 \]

### Step 2: Write the Molecular Orbital Configuration
Using Molecular Orbital Theory (MOT), we fill the molecular orbitals in order of increasing energy. The order of filling for the molecular orbitals for CN is:
1. σ1s
2. σ*1s
3. σ2s
4. σ*2s
5. π2p_x
6. π2p_y
7. σ2p_z
8. π*2p_x
9. π*2p_y
10. σ*2p

Now, we fill the 14 electrons into these orbitals:
- σ1s: 2 electrons
- σ*1s: 2 electrons
- σ2s: 2 electrons
- σ*2s: 2 electrons
- π2p_x: 2 electrons
- π2p_y: 2 electrons
- σ2p_z: 2 electrons

The filling would look like this:
- σ1s: 2
- σ*1s: 2
- σ2s: 2
- σ*2s: 2
- π2p_x: 2
- π2p_y: 2
- σ2p_z: 2

### Step 3: Count the Bonding and Antibonding Electrons
- **Bonding Electrons**: Electrons in σ1s, σ2s, π2p_x, π2p_y, and σ2p_z
- Total bonding electrons = 2 (σ1s) + 2 (σ2s) + 2 (π2p_x) + 2 (π2p_y) + 2 (σ2p_z) = 10
- **Antibonding Electrons**: Electrons in σ*1s, σ*2s, π*2p_x, and π*2p_y
- Total antibonding electrons = 2 (σ*1s) + 2 (σ*2s) = 4

### Step 4: Calculate the Bond Order
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} \times (\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}) \]
Substituting the values:
\[ \text{Bond Order} = \frac{1}{2} \times (10 - 4) = \frac{1}{2} \times 6 = 3 \]

### Step 5: Determine the Magnetic Nature
To determine the magnetic nature, we check for unpaired electrons:
- In the configuration, all electrons are paired (there are no unpaired electrons).

Thus, CN⁻ is **diamagnetic**.

### Final Answer
The bond order of CN⁻ is **3**, and it is **diamagnetic**.

---