Which of the following diatomic molecular species has only `pi` at bonds according to molecular orbital theory?

Options

A. `C_2 `
B. `Be_2`
C. `O_2`
D. `N_2`

Explanation

To determine which diatomic molecular species has only π bonds according to molecular orbital theory, we will analyze the molecular orbital configurations and bond orders of the given species: C₂, Be₂, O₂, and N₂.

### Step-by-Step Solution:

1. **Identify the Total Number of Electrons:**
- For each diatomic molecule, we first need to find the total number of valence electrons.
- C (Carbon) has 4 valence electrons, so C₂ has 8 electrons.
- Be (Beryllium) has 2 valence electrons, so Be₂ has 4 electrons.
- O (Oxygen) has 6 valence electrons, so O₂ has 12 electrons.
- N (Nitrogen) has 5 valence electrons, so N₂ has 10 electrons.

2. **Write the Molecular Orbital Configuration:**
- **C₂:**
- Configuration: σ1s² σ*1s² σ2s² σ*2s² π2p_y² π2p_z²
- **Be₂:**
- Configuration: σ1s² σ*1s² σ2s² σ*2s²
- **O₂:**
- Configuration: σ1s² σ*1s² σ2s² σ*2s² π2p_y² π2p_z²
- **N₂:**
- Configuration: σ1s² σ*1s² σ2s² σ*2s² π2p_y² π2p_z²

3. **Calculate the Bond Order:**
- Bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]
- **C₂:**
- Bonding electrons = 8 (σ2s² + π2p_y² + π2p_z²)
- Antibonding electrons = 4 (σ*1s² + σ*2s²)
- Bond Order = (8 - 4) / 2 = 2 (2 π bonds)
- **Be₂:**
- Bonding electrons = 4 (σ2s²)
- Antibonding electrons = 4 (σ*1s² + σ*2s²)
- Bond Order = (4 - 4) / 2 = 0 (unstable)
- **O₂:**
- Bonding electrons = 10 (σ2s² + π2p_y² + π2p_z²)
- Antibonding electrons = 6 (σ*1s² + σ*2s²)
- Bond Order = (10 - 6) / 2 = 2 (1 σ bond + 2 π bonds)
- **N₂:**
- Bonding electrons = 10 (σ2s² + π2p_y² + π2p_z²)
- Antibonding electrons = 4 (σ*1s² + σ*2s²)
- Bond Order = (10 - 4) / 2 = 3 (1 σ bond + 2 π bonds)

4. **Conclusion:**
- From the analysis, only **C₂** has a bond order of 2 with both bonds being π bonds.
- Therefore, the diatomic molecular species that has only π bonds is **C₂**.

### Final Answer:
The diatomic molecular species that has only π bonds according to molecular orbital theory is **C₂**.