The number of bonding electron pairs in `N_(2)` on the basis of molecular orbital theory is

Options

A. 3
B. 2
C. 5
D. 4

Answer

To determine the number of bonding electron pairs in \( N_2 \) based on molecular orbital theory, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Total Number of Electrons:**
- Each nitrogen atom has an atomic number of 7, which means it has 7 electrons.
- Since there are two nitrogen atoms in \( N_2 \), the total number of electrons is:
\[ 7 + 7 = 14 \text{ electrons} \]

2. **Construct the Molecular Orbital Diagram:**
- According to molecular orbital theory, the molecular orbitals for \( N_2 \) are filled in the following order of increasing energy:
- \( \sigma_{1s} \) (2 electrons)
- \( \sigma^*_{1s} \) (2 electrons)
- \( \sigma_{2s} \) (2 electrons)
- \( \sigma^*_{2s} \) (2 electrons)
- \( \sigma_{2p_z} \) (2 electrons)
- \( \pi_{2p_x} \) (2 electrons)
- \( \pi_{2p_y} \) (2 electrons)
- \( \sigma^*_{2p_z} \) (0 electrons)

3. **Fill the Molecular Orbitals:**
- Fill the molecular orbitals with the 14 electrons:
- \( \sigma_{1s} \): 2 electrons
- \( \sigma^*_{1s} \): 2 electrons
- \( \sigma_{2s} \): 2 electrons
- \( \sigma^*_{2s} \): 2 electrons
- \( \sigma_{2p_z} \): 2 electrons
- \( \pi_{2p_x} \): 2 electrons
- \( \pi_{2p_y} \): 2 electrons
- The filling results in:
- \( \sigma_{1s}^2 \)
- \( \sigma^*_{1s}^2 \)
- \( \sigma_{2s}^2 \)
- \( \sigma^*_{2s}^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_x}^2 \)
- \( \pi_{2p_y}^2 \)

4. **Count the Bonding and Antibonding Electrons:**
- Bonding orbitals (filled):
- \( \sigma_{1s} \): 2
- \( \sigma_{2s} \): 2
- \( \sigma_{2p_z} \): 2
- \( \pi_{2p_x} \): 2
- \( \pi_{2p_y} \): 2
- Total bonding electrons = \( 2 + 2 + 2 + 2 + 2 = 10 \)

5. **Calculate the Number of Bonding Electron Pairs:**
- Since each pair of electrons constitutes a bonding pair, we divide the total number of bonding electrons by 2:
\[ \text{Number of bonding electron pairs} = \frac{10}{2} = 5 \]

### Final Answer:
The number of bonding electron pairs in \( N_2 \) is **5**.