The bond order for `Ne_2` and `C_2`, respectively are

Options

A. 3.0,2.5
B. 2.5,2
C. 0,2
D. 2.5,2

Answer

To determine the bond order for \( \text{Ne}_2 \) and \( \text{C}_2 \), we will use the Molecular Orbital Theory (MOT). The bond order can be calculated using the formula:

\[ \text{Bond Order} = \frac{1}{2} (N_b - N_a) \]

where \( N_b \) is the number of bonding electrons and \( N_a \) is the number of anti-bonding electrons.

### Step 1: Calculate Bond Order for \( \text{Ne}_2 \)

1. **Determine the number of electrons in \( \text{Ne}_2 \)**:
- Each Neon (Ne) atom has 10 electrons. Therefore, \( \text{Ne}_2 \) has a total of \( 20 \) electrons.

2. **Write the molecular orbital configuration for \( \text{Ne}_2 \)**:
- The configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^0 \pi_{2p_y}^*^0 \sigma_{2p_z}^*^0 \]
- Bonding electrons \( N_b = 10 \) (from \( \sigma_{1s}, \sigma_{2s}, \sigma_{2p_z}, \pi_{2p_x}, \pi_{2p_y} \)).
- Anti-bonding electrons \( N_a = 10 \) (from \( \sigma_{1s}^*, \sigma_{2s}^*, \pi_{2p_x}^*, \pi_{2p_y}^*, \sigma_{2p_z}^* \)).

3. **Calculate the bond order**:
\[ \text{Bond Order} = \frac{1}{2} (N_b - N_a) = \frac{1}{2} (10 - 10) = \frac{1}{2} (0) = 0 \]

### Step 2: Calculate Bond Order for \( \text{C}_2 \)

1. **Determine the number of electrons in \( \text{C}_2 \)**:
- Each Carbon (C) atom has 6 electrons. Therefore, \( \text{C}_2 \) has a total of \( 12 \) electrons.

2. **Write the molecular orbital configuration for \( \text{C}_2 \)**:
- The configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^0 \pi_{2p_y}^*^0 \sigma_{2p_z}^*^0 \]
- Bonding electrons \( N_b = 8 \) (from \( \sigma_{1s}, \sigma_{2s}, \sigma_{2p_z}, \pi_{2p_x}, \pi_{2p_y} \)).
- Anti-bonding electrons \( N_a = 4 \) (from \( \sigma_{1s}^*, \sigma_{2s}^* \)).

3. **Calculate the bond order**:
\[ \text{Bond Order} = \frac{1}{2} (N_b - N_a) = \frac{1}{2} (8 - 4) = \frac{1}{2} (4) = 2 \]

### Final Answer
The bond order for \( \text{Ne}_2 \) and \( \text{C}_2 \) are:
- \( \text{Ne}_2 \): 0
- \( \text{C}_2 \): 2