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

Options

A. `Be_(2)^(+)`
B. `Be_(2)`
C. `B_2 `
D. `Li_(2)`

Explanation

To determine which of the given species does not exist under normal conditions, we need to calculate the bond order for each species. A bond order of zero indicates that the species cannot exist.

### Step-by-Step Solution:

1. **Understanding Bond Order**:
The bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of electrons in bonding orbitals}) - (\text{Number of electrons in anti-bonding orbitals})}{2} \]
A bond order of zero means the species does not exist.

2. **Analyzing Be2+**:
- Beryllium (Be) has an atomic number of 4.
- For Be2+, we have 4 electrons from two Be atoms and one less due to the positive charge:
\[ 4 + 4 - 1 = 7 \text{ electrons} \]
- The electron configuration is:
\[ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^1 \]
- Bonding electrons = 4 (2 from σ 1s and 2 from σ 2s)
- Anti-bonding electrons = 3 (2 from σ* 1s and 1 from σ* 2s)
- Bond order calculation:
\[ \text{Bond Order} = \frac{4 - 3}{2} = 0.5 \]
- Conclusion: Be2+ exists.

3. **Analyzing Be2**:
- For Be2, we have:
\[ 4 + 4 = 8 \text{ electrons} \]
- The electron configuration is:
\[ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2 \]
- Bonding electrons = 4
- Anti-bonding electrons = 4
- Bond order calculation:
\[ \text{Bond Order} = \frac{4 - 4}{2} = 0 \]
- Conclusion: Be2 does not exist.

4. **Analyzing B2**:
- For B2, we have:
\[ 5 + 5 = 10 \text{ electrons} \]
- The electron configuration is:
\[ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \pi 2p_x^1, \pi 2p_y^1 \]
- Bonding electrons = 6
- Anti-bonding electrons = 4
- Bond order calculation:
\[ \text{Bond Order} = \frac{6 - 4}{2} = 1 \]
- Conclusion: B2 exists.

5. **Analyzing Li2**:
- For Li2, we have:
\[ 3 + 3 = 6 \text{ electrons} \]
- The electron configuration is:
\[ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2 \]
- Bonding electrons = 4
- Anti-bonding electrons = 2
- Bond order calculation:
\[ \text{Bond Order} = \frac{4 - 2}{2} = 1 \]
- Conclusion: Li2 exists.

### Final Conclusion:
The species that does not exist under normal conditions is **Be2**.