According to molecular orbital theory, which of the following will not be a viable molecule?

Options

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

Explanation

To determine which of the given molecules will not be viable according to molecular orbital theory, we will follow these steps:

### Step 1: Identify the number of electrons in each molecule.
- **H2+**: Each hydrogen atom has 1 electron. For H2, there are 2 electrons, but since there is a positive charge, H2+ has 1 electron.
- **Be2**: Each beryllium atom has 4 electrons. Therefore, Be2 has a total of 8 electrons.
- **B2**: Each boron atom has 5 electrons. Thus, B2 has a total of 10 electrons.
- **C2**: Each carbon atom has 6 electrons. Therefore, C2 has a total of 12 electrons.

### Step 2: Construct the molecular orbital diagram for each molecule.
The molecular orbital energy levels are arranged as follows:
- σ 1s
- σ* 1s
- σ 2s
- σ* 2s
- σ 2px
- σ 2py
- σ 2pz

### Step 3: Fill the molecular orbitals with the electrons for each molecule and calculate the bond order.
1. **H2+** (1 electron):
- Fill the molecular orbitals: σ 1s (1 electron).
- Bonding electrons = 1, Anti-bonding electrons = 0.
- Bond order (BO) = (Bonding - Anti-bonding) / 2 = (1 - 0) / 2 = 0.5.
- Since BO > 0, H2+ exists.

2. **Be2** (8 electrons):
- Fill the molecular orbitals: σ 1s (2), σ* 1s (2), σ 2s (2), σ* 2s (2).
- Bonding electrons = 4, Anti-bonding electrons = 4.
- Bond order (BO) = (4 - 4) / 2 = 0.
- Since BO = 0, Be2 does not exist.

3. **B2** (10 electrons):
- Fill the molecular orbitals: σ 1s (2), σ* 1s (2), σ 2s (2), σ* 2s (2), σ 2px (2).
- Bonding electrons = 6, Anti-bonding electrons = 4.
- Bond order (BO) = (6 - 4) / 2 = 1.
- Since BO > 0, B2 exists.

4. **C2** (12 electrons):
- Fill the molecular orbitals: σ 1s (2), σ* 1s (2), σ 2s (2), σ* 2s (2), σ 2px (2), σ 2py (2).
- Bonding electrons = 8, Anti-bonding electrons = 4.
- Bond order (BO) = (8 - 4) / 2 = 2.
- Since BO > 0, C2 exists.

### Conclusion:
Based on the calculations, the molecule that does not exist according to molecular orbital theory is **Be2**.

### Final Answer:
**Be2 will not be a viable molecule.**

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