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

Options

A. 3, diamagnetic
B. 3, paramagnetic
C. 2.5, paramagnetic
D. 2.5, diamagnetic

Answer

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

### Step 1: Determine the total number of electrons
Cyanide ion (CN⁻) consists of carbon (C) and nitrogen (N). The atomic numbers of carbon and nitrogen are 6 and 7, respectively. Since CN⁻ has an extra electron due to the negative charge, we calculate the total number of electrons as follows:

- Carbon (C): 6 electrons
- Nitrogen (N): 7 electrons
- Additional electron from the negative charge: 1 electron

Total electrons = 6 + 7 + 1 = 14 electrons

### Step 2: Write the molecular orbital configuration
According to molecular orbital theory, we fill the molecular orbitals in order of increasing energy. The order of filling for diatomic molecules like CN is:

1. σ(1s)
2. σ*(1s)
3. σ(2s)
4. σ*(2s)
5. π(2p_x) = π(2p_y)
6. σ(2p_z)

Now, we fill these molecular orbitals with the 14 electrons:

- σ(1s)²
- σ*(1s)²
- σ(2s)²
- σ*(2s)²
- π(2p_x)²
- π(2p_y)²
- σ(2p_z)²

This gives us the following configuration:
- σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² π(2p_x)² π(2p_y)² σ(2p_z)²

### Step 3: Count the electrons in bonding and antibonding orbitals
Now we count the number of electrons in bonding (Nb) and antibonding (Na) molecular orbitals:

- Bonding orbitals (σ and π):
- σ(1s): 2
- σ(2s): 2
- π(2p_x): 2
- π(2p_y): 2
- σ(2p_z): 2

Total bonding electrons (Nb) = 2 + 2 + 2 + 2 + 2 = 10

- Antibonding orbitals (σ*):
- σ*(1s): 2
- σ*(2s): 2

Total antibonding electrons (Na) = 2 + 2 = 4

### Step 4: Calculate the bond order
The bond order is calculated using the formula:

\[ \text{Bond Order} = \frac{N_b - N_a}{2} \]

Substituting the values we found:

\[ \text{Bond Order} = \frac{10 - 4}{2} = \frac{6}{2} = 3 \]

### Step 5: Determine the magnetic nature
To determine the magnetic nature, we check for unpaired electrons in the molecular orbital configuration. In our configuration, all electrons are paired, indicating that CN⁻ is diamagnetic.

### Final Answer
The bond order and magnetic nature of CN⁻ are respectively:
**3, diamagnetic.**

---