Which of the following does not exist

Options

A. a. `Be_(2)`
B. b, `B_(2)`
C. c. `C_(2)`
D. d. `N_(2)`

Explanation

To determine which of the following molecules does not exist, we will analyze the bond orders of the given molecules using molecular orbital theory.

### Step-by-Step Solution:

1. **Identify the Molecules**: We need to analyze the bond order of the molecules provided in the options. Let's assume the options are: A) Be2, B) B2, C) C2, D) N2.

2. **Determine the Electron Configuration**:
- For **Beryllium (Be)**: The atomic number is 4, so the electron configuration is 1s² 2s².
- For **Boron (B)**: The atomic number is 5, so the electron configuration is 1s² 2s² 2p¹.
- For **Carbon (C)**: The atomic number is 6, so the electron configuration is 1s² 2s² 2p².
- For **Nitrogen (N)**: The atomic number is 7, so the electron configuration is 1s² 2s² 2p³.

3. **Construct Molecular Orbital Diagrams**:
- For **Be2**: Each Be contributes 4 electrons (2 from each atom), giving a total of 8 electrons. The molecular orbitals will be filled as follows:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)².
- Bonding electrons = 4 (from σ(1s) and σ(2s)), Anti-bonding electrons = 4 (from σ*(1s) and σ*(2s)).
- **Bond Order = (Bonding - Anti-bonding) / 2 = (4 - 4) / 2 = 0**. This means Be2 does not exist.

4. **Calculate Bond Orders for Other Molecules**:
- For **B2**: Total of 10 electrons.
- Fill the molecular orbitals: σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)².
- Bond Order = (6 - 4) / 2 = 1. B2 exists.
- For **C2**: Total of 12 electrons.
- Fill the molecular orbitals: σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁴.
- Bond Order = (8 - 4) / 2 = 2. C2 exists.
- For **N2**: Total of 14 electrons.
- Fill the molecular orbitals: σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁶.
- Bond Order = (10 - 4) / 2 = 3. N2 exists.

5. **Conclusion**: From the calculations above, the molecule that does not exist is **Be2** (option A).