Assuming that Hund’s rule is violated, the bond order and magnetic nature of the diatomic molecule `C_(2)` is :

Options

A. 2 and diamagnetic
B. 0 and diamagnetic
C. 1 and paramagnetic
D. 0 and paramagnetic

Explanation

To determine the bond order and magnetic nature of the diatomic molecule \( C_2 \) assuming that Hund’s rule is violated, we will follow these steps:

### Step 1: Understand the Electronic Configuration of Carbon
Carbon has an atomic number of 6, and its electronic configuration is \( 1s^2 2s^2 2p^2 \). For the \( C_2 \) molecule, we need to consider the contribution from two carbon atoms.

### Step 2: Write the Total Electron Configuration for \( C_2 \)
Since each carbon contributes 6 electrons, the total number of electrons in \( C_2 \) is \( 6 + 6 = 12 \). Therefore, the electron configuration for \( C_2 \) will be \( 1s^2 2s^2 2p^2 \) for each carbon.

### Step 3: Construct the Molecular Orbital Diagram
In the molecular orbital theory, the molecular orbitals for \( C_2 \) are arranged as follows (considering \( sp \) mixing):
- \( \sigma_{1s} \)
- \( \sigma^*_{1s} \)
- \( \sigma_{2s} \)
- \( \sigma^*_{2s} \)
- \( \sigma_{2p_z} \)
- \( \pi_{2p_x} \) and \( \pi_{2p_y} \) (degenerate)
- \( \pi^*_{2p_x} \) and \( \pi^*_{2p_y} \)

### Step 4: Fill the Molecular Orbitals
According to the molecular orbital filling:
1. Fill \( \sigma_{1s} \) with 2 electrons.
2. Fill \( \sigma^*_{1s} \) with 2 electrons.
3. Fill \( \sigma_{2s} \) with 2 electrons.
4. Fill \( \sigma^*_{2s} \) with 2 electrons.
5. Now, for the \( 2p \) orbitals, we have 4 electrons to place in \( \sigma_{2p_z} \) and \( \pi_{2p_x}, \pi_{2p_y} \).

Assuming Hund’s rule is violated, we pair the electrons in the \( \pi \) orbitals:
- Fill \( \pi_{2p_x} \) with 2 electrons.
- Fill \( \pi_{2p_y} \) with 2 electrons.

### Step 5: Count the Bonding and Antibonding Electrons
- Bonding electrons: \( 2 (1s) + 2 (1s^*) + 2 (2s) + 2 (2s^*) + 2 (2p_x) + 2 (2p_y) = 12 \)
- Antibonding electrons: \( 0 \) (since all \( \pi^* \) orbitals are empty)

### Step 6: Calculate the Bond Order
Using the bond order formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]
Substituting the values:
\[ \text{Bond Order} = \frac{12 - 0}{2} = 6 \]

### Step 7: Determine the Magnetic Nature
Since all electrons are paired in the molecular orbitals, \( C_2 \) is **diamagnetic**.

### Final Answer
- **Bond Order**: 6
- **Magnetic Nature**: Diamagnetic