In `MO` energy diagram for heteronuclear diatomic molecule is
similar However, the energies of the `AO` s of the atom having higher atomic number being lower, the diagram will be unsymmetrical, but that will not make a difference in the electron count The bond order is half the difference in the number of electrns of the bonding `(sigma and pi)` and anti-bonding `(sigma and pi)` `MO s` For a bond to have been formed the bond order the shorter is the bond distance and the greater is the bond dissociation energey But if the bond order is smae in the above two cases, then the bond distance will be greater and the bond dissocation energy smaller in the case which has more populated anti-bonding orbitals The presence of unpaired electron(s) in a molecualr orbital will make the system paramagnetic
Which of the following species is not expected to exist ? .

Options

A. `He_(2)^(o+)`
B. `H_(2)^(o+)`
C. `Be_(2)`
D. `Be_(2)^(o+)`

Explanation

To determine which species is not expected to exist based on molecular orbital theory, we will analyze the bond order of each given species. The bond order is 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 zero indicates that the species does not exist.

### Step-by-Step Solution:

1. **Analyze He2+**:
- Total electrons = 3.
- Electronic configuration: \( \sigma_{1s}^2 \sigma^*_{1s}^1 \).
- Bonding electrons \( n_B = 2 \), Anti-bonding electrons \( n_A = 1 \).
- Bond Order = \( \frac{2 - 1}{2} = \frac{1}{2} = 0.5 \).
- **Conclusion**: He2+ exists.

2. **Analyze H2+**:
- Total electrons = 1.
- Electronic configuration: \( \sigma_{1s}^1 \).
- Bonding electrons \( n_B = 1 \), Anti-bonding electrons \( n_A = 0 \).
- Bond Order = \( \frac{1 - 0}{2} = \frac{1}{2} = 0.5 \).
- **Conclusion**: H2+ exists.

3. **Analyze Be2**:
- Total electrons = 8.
- Electronic configuration: \( \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \).
- Bonding electrons \( n_B = 4 \), Anti-bonding electrons \( n_A = 4 \).
- Bond Order = \( \frac{4 - 4}{2} = \frac{0}{2} = 0 \).
- **Conclusion**: Be2 does not exist.

4. **Analyze Be2+**:
- Total electrons = 7.
- Electronic configuration: \( \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^1 \).
- Bonding electrons \( n_B = 4 \), Anti-bonding electrons \( n_A = 3 \).
- Bond Order = \( \frac{4 - 3}{2} = \frac{1}{2} = 0.5 \).
- **Conclusion**: Be2+ exists.

### Final Conclusion:
The species that is not expected to exist is **Be2** because its bond order is zero.