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 of the following species does not exist under normal conditions, we need to calculate the bond order for each species. The bond order is calculated using the formula:

\[ \text{Bond Order} = \frac{1}{2} (\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}) \]

Let's analyze each species one by one.

### Step 1: Analyze Li2
- **Electron Configuration**: For Li2, each lithium atom has 3 electrons. Therefore, Li2 has a total of 6 electrons.
- **Filling the Molecular Orbitals**:
- \(\sigma_{1s}^2\)
- \(\sigma_{1s}^*^2\)
- \(\sigma_{2s}^2\)
- **Bonding Electrons**: 4 (2 from \(\sigma_{1s}\) and 2 from \(\sigma_{2s}\))
- **Antibonding Electrons**: 2 (from \(\sigma_{1s}^*\))
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{1}{2} (4 - 2) = \frac{2}{2} = 1 \]
- **Conclusion**: Li2 exists.

### Step 2: Analyze Be2^+
- **Electron Configuration**: Beryllium has 4 electrons. For Be2^+, we remove one electron, giving us 7 electrons.
- **Filling the Molecular Orbitals**:
- \(\sigma_{1s}^2\)
- \(\sigma_{1s}^*^2\)
- \(\sigma_{2s}^2\)
- \(\sigma_{2s}^*^1\)
- **Bonding Electrons**: 4 (2 from \(\sigma_{1s}\) and 2 from \(\sigma_{2s}\))
- **Antibonding Electrons**: 3 (2 from \(\sigma_{1s}^*\) and 1 from \(\sigma_{2s}^*\))
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{1}{2} (4 - 3) = \frac{1}{2} = 0.5 \]
- **Conclusion**: Be2^+ exists.

### Step 3: Analyze Be2
- **Electron Configuration**: For Be2, we have 8 electrons.
- **Filling the Molecular Orbitals**:
- \(\sigma_{1s}^2\)
- \(\sigma_{1s}^*^2\)
- \(\sigma_{2s}^2\)
- \(\sigma_{2s}^*^2\)
- **Bonding Electrons**: 4 (2 from \(\sigma_{1s}\) and 2 from \(\sigma_{2s}\))
- **Antibonding Electrons**: 4 (2 from \(\sigma_{1s}^*\) and 2 from \(\sigma_{2s}^*\))
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{1}{2} (4 - 4) = \frac{0}{2} = 0 \]
- **Conclusion**: Be2 does not exist.

### Step 4: Analyze B2
- **Electron Configuration**: For B2, we have 10 electrons.
- **Filling the Molecular Orbitals**:
- \(\sigma_{1s}^2\)
- \(\sigma_{1s}^*^2\)
- \(\sigma_{2s}^2\)
- \(\sigma_{2s}^*^2\)
- \(\pi_{2p_x}^1\) and \(\pi_{2p_y}^1\) (due to degenerate orbitals)
- **Bonding Electrons**: 6 (2 from \(\sigma_{1s}\), 2 from \(\sigma_{2s}\), and 2 from \(\pi_{2p_x}\) and \(\pi_{2p_y}\))
- **Antibonding Electrons**: 4 (2 from \(\sigma_{1s}^*\) and 2 from \(\sigma_{2s}^*\))
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{1}{2} (6 - 4) = \frac{2}{2} = 1 \]
- **Conclusion**: B2 exists.

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