Which of the following species does not exist under normal conditions?

Options

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

Answer

To determine which species does not exist under normal conditions, we will calculate the bond order for each of the given species. The bond order can be calculated using the formula:

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

where \(N_b\) is the number of electrons in bonding molecular orbitals and \(N_a\) is the number of electrons in anti-bonding molecular orbitals. A bond order of 0 or less indicates that the species does not exist under normal conditions.

### Step 1: Calculate the bond order for Li2
- **Total Electrons in Li2**: 6 (2 from each lithium atom)
- **Molecular Orbital Configuration**:
- \( \sigma_{1s}^2 \)
- \( \sigma_{1s}^* \)
- \( \sigma_{2s}^2 \)
- \( \sigma_{2s}^* \)

- **Bonding Electrons**: 4 (2 in \( \sigma_{1s} \) and 2 in \( \sigma_{2s} \))
- **Anti-bonding Electrons**: 2 (in \( \sigma_{1s}^* \))

\[ \text{Bond Order} = \frac{(4 - 2)}{2} = 1 \]

### Step 2: Calculate the bond order for Be2
- **Total Electrons in Be2**: 8 (4 from each beryllium atom)
- **Molecular Orbital Configuration**:
- \( \sigma_{1s}^2 \)
- \( \sigma_{1s}^* \)
- \( \sigma_{2s}^2 \)
- \( \sigma_{2s}^* \)

- **Bonding Electrons**: 4 (2 in \( \sigma_{1s} \) and 2 in \( \sigma_{2s} \))
- **Anti-bonding Electrons**: 4 (2 in \( \sigma_{1s}^* \) and 2 in \( \sigma_{2s}^* \))

\[ \text{Bond Order} = \frac{(4 - 4)}{2} = 0 \]

### Step 3: Calculate the bond order for B2
- **Total Electrons in B2**: 10 (5 from each boron atom)
- **Molecular Orbital Configuration**:
- \( \sigma_{1s}^2 \)
- \( \sigma_{1s}^* \)
- \( \sigma_{2s}^2 \)
- \( \sigma_{2s}^* \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_x}^1 \)
- \( \pi_{2p_y}^1 \)

- **Bonding Electrons**: 6 (2 in \( \sigma_{1s} \), 2 in \( \sigma_{2s} \), 2 in \( \sigma_{2p_z} \))
- **Anti-bonding Electrons**: 4 (2 in \( \sigma_{1s}^* \) and 2 in \( \sigma_{2s}^* \))

\[ \text{Bond Order} = \frac{(6 - 4)}{2} = 1 \]

### Conclusion
Among the species analyzed:
- Li2 has a bond order of 1 (exists).
- Be2 has a bond order of 0 (does not exist under normal conditions).
- B2 has a bond order of 1 (exists).

Thus, the species that does not exist under normal conditions is **Be2**.

### Final Answer
**Be2**