Which of the following species is not expected to exist ?

Options

A. `He_2^(+)`
B. `H_2^(+)`
C. `Be_2`
D. `Be_2^+`

Answer

To determine which of the following species is not expected to exist, we need to calculate the bond order for each species. The bond order can be calculated using the formula:

\[ \text{Bond Order} = \frac{1}{2} \times (\text{Number of electrons in bonding orbitals} - \text{Number of electrons in anti-bonding orbitals}) \]

Let's analyze each option step by step:

### Step 1: Analyze He2⁺

1. **Determine the number of electrons**: Helium has an atomic number of 2, so He2 has 4 electrons. For He2⁺, we remove one electron, resulting in 3 electrons.
2. **Molecular orbital configuration**: The configuration is \(\sigma 1s^2 \sigma^* 1s^2 \sigma 1s^1\).
3. **Count bonding and anti-bonding electrons**:
- Bonding electrons: 2 (from \(\sigma 1s^2\))
- Anti-bonding electrons: 1 (from \(\sigma^* 1s^2\))
4. **Calculate bond order**:
\[ \text{Bond Order} = \frac{1}{2} \times (2 - 1) = \frac{1}{2} = 0.5 \]
- **Conclusion**: He2⁺ exists.

### Step 2: Analyze H2⁺

1. **Determine the number of electrons**: H2 has 2 electrons, and H2⁺ has 1 electron.
2. **Molecular orbital configuration**: The configuration is \(\sigma 1s^1\).
3. **Count bonding and anti-bonding electrons**:
- Bonding electrons: 1 (from \(\sigma 1s^1\))
- Anti-bonding electrons: 0
4. **Calculate bond order**:
\[ \text{Bond Order} = \frac{1}{2} \times (1 - 0) = \frac{1}{2} = 0.5 \]
- **Conclusion**: H2⁺ exists.

### Step 3: Analyze Be2

1. **Determine the number of electrons**: Beryllium has an atomic number of 4, so Be2 has 8 electrons.
2. **Molecular orbital configuration**: The configuration is \(\sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2\).
3. **Count bonding and anti-bonding electrons**:
- Bonding electrons: 4 (2 from \(\sigma 1s^2\) and 2 from \(\sigma 2s^2\))
- Anti-bonding electrons: 4 (2 from \(\sigma^* 1s^2\) and 2 from \(\sigma^* 2s^2\))
4. **Calculate bond order**:
\[ \text{Bond Order} = \frac{1}{2} \times (4 - 4) = \frac{1}{2} \times 0 = 0 \]
- **Conclusion**: Be2 does not exist.

### Step 4: Analyze Be2⁺

1. **Determine the number of electrons**: Be2 has 8 electrons, and Be2⁺ has 7 electrons.
2. **Molecular orbital configuration**: The configuration is \(\sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^1\).
3. **Count bonding and anti-bonding electrons**:
- Bonding electrons: 4 (2 from \(\sigma 1s^2\) and 2 from \(\sigma 2s^2\))
- Anti-bonding electrons: 3 (2 from \(\sigma^* 1s^2\) and 1 from \(\sigma^* 2s^1\))
4. **Calculate bond order**:
\[ \text{Bond Order} = \frac{1}{2} \times (4 - 3) = \frac{1}{2} = 0.5 \]
- **Conclusion**: Be2⁺ exists.

### Final Conclusion

From the analysis, the species that is not expected to exist is **Be2** since its bond order is 0.