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 \( C_2 \) while assuming that Hund’s rule is violated, we can follow these steps:

### Step 1: Determine the Total Number of Electrons
Each carbon atom has 6 electrons. Therefore, for the diatomic molecule \( C_2 \):
\[ \text{Total electrons} = 6 + 6 = 12 \]

### Step 2: Understand the Molecular Orbital (MO) Energy Order
For diatomic molecules with up to 14 electrons, the molecular orbital energy order is as follows:
\[ \sigma_{2s} < \sigma_{2s}^* < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi_{2p_x}^* = \pi_{2p_y}^* < \sigma_{2p_z}^* \]

### Step 3: Fill the Molecular Orbitals
We will fill the molecular orbitals with the 12 electrons, violating Hund's rule. The filling will be as follows:
1. Fill \( \sigma_{2s} \) with 2 electrons.
2. Fill \( \sigma_{2s}^* \) with 2 electrons.
3. Fill \( \sigma_{2p_z} \) with 2 electrons.
4. Fill \( \pi_{2p_x} \) and \( \pi_{2p_y} \) with 4 electrons (both orbitals filled with paired electrons).

Thus, the filling will look like this:
- \( \sigma_{2s} \): 2 electrons
- \( \sigma_{2s}^* \): 2 electrons
- \( \sigma_{2p_z} \): 2 electrons
- \( \pi_{2p_x} \): 2 electrons (paired)
- \( \pi_{2p_y} \): 2 electrons (paired)

This gives us:
- Total bonding electrons = 2 (from \( \sigma_{2s} \)) + 2 (from \( \sigma_{2p_z} \)) + 4 (from \( \pi_{2p_x} \) and \( \pi_{2p_y} \)) = 8
- Total antibonding electrons = 2 (from \( \sigma_{2s}^* \)) = 2

### Step 4: Calculate the Bond Order
The bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]
Substituting the values:
\[ \text{Bond Order} = \frac{8 - 2}{2} = \frac{6}{2} = 3 \]

### Step 5: Determine the Magnetic Nature
To determine the magnetic nature, we look at the number of unpaired electrons. In this configuration, all electrons are paired. Therefore, the magnetic nature of \( C_2 \) is:
- **Diamagnetic** (since all electrons are paired).

### Final Answer
- **Bond Order**: 2
- **Magnetic Nature**: Diamagnetic