Which pair of species doesn.t exist ?

Options

A. `B_(2)`
B. `Be_(2)`
C. `Li_(2)`
D. `H_(2)^(+)`

Answer

To determine which pair of species does not exist, we need to analyze the bond order of each species. The bond order is calculated using the formula:

\[ \text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2} \]

A species will not exist if its bond order is zero or negative. Let's evaluate each species given in the question.

### Step-by-Step Solution:

1. **Evaluate V2:**
- **Electronic Configuration:** For V2, the electronic configuration is 1s² 2s² 2p².
- **Bonding and Antibonding Electrons:**
- Bonding: 1s² (2 electrons), 2s² (2 electrons), 2p (2 electrons, 1 in each of the two degenerate pi orbitals).
- Antibonding: None.
- **Bond Order Calculation:**
- Bonding Electrons = 6 (2 from 1s + 2 from 2s + 2 from 2p)
- Antibonding Electrons = 0
- Bond Order = (6 - 0) / 2 = 3
- **Conclusion:** V2 exists.

2. **Evaluate BE2:**
- **Electronic Configuration:** For BE2, the electronic configuration is 1s² 2s².
- **Bonding and Antibonding Electrons:**
- Bonding: 1s² (2 electrons), 2s² (2 electrons).
- Antibonding: 1s² (2 electrons), 2s² (2 electrons).
- **Bond Order Calculation:**
- Bonding Electrons = 4 (2 from 1s + 2 from 2s)
- Antibonding Electrons = 4 (2 from 1s* + 2 from 2s*)
- Bond Order = (4 - 4) / 2 = 0
- **Conclusion:** BE2 does not exist.

3. **Evaluate Li2:**
- **Electronic Configuration:** For Li2, the electronic configuration is 1s² 2s².
- **Bonding and Antibonding Electrons:**
- Bonding: 1s² (2 electrons), 2s (1 electron).
- Antibonding: None.
- **Bond Order Calculation:**
- Bonding Electrons = 3 (2 from 1s + 1 from 2s)
- Antibonding Electrons = 0
- Bond Order = (3 - 0) / 2 = 1.5
- **Conclusion:** Li2 exists.

4. **Evaluate H2+:**
- **Electronic Configuration:** For H2+, the electronic configuration is 1s¹.
- **Bonding and Antibonding Electrons:**
- Bonding: 1s (1 electron).
- Antibonding: None.
- **Bond Order Calculation:**
- Bonding Electrons = 1
- Antibonding Electrons = 0
- Bond Order = (1 - 0) / 2 = 0.5
- **Conclusion:** H2+ exists.

### Final Conclusion:
The species that does not exist is **BE2**.