Identify a molecule which does not exist.

Options

A. `He_2`
B. `Li_2`
C. `C_2`
D. `O_2`

Answer

To identify a molecule that does not exist, we will calculate the bond order for each of the given options. The bond order is determined by the formula:

\[ \text{Bond Order} = \frac{1}{2} (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]

A bond order of zero indicates that the molecule does not exist.

### Step-by-Step Solution:

1. **Analyze the first option: Helium (He₂)**
- Helium has an atomic number of 2, which means it has 2 electrons.
- For He₂, the total number of electrons = 2 (from one He) + 2 (from another He) = 4 electrons.
- The electronic configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \]
- Bonding electrons = 2 (from \(\sigma_{1s}\)), Antibonding electrons = 2 (from \(\sigma^*_{1s}\)).
- Calculate the bond order:
\[ \text{Bond Order} = \frac{1}{2} (2 - 2) = \frac{1}{2} (0) = 0 \]
- Since the bond order is 0, He₂ does not exist.

2. **Analyze the second option: Lithium (Li₂)**
- Lithium has an atomic number of 3, which means it has 3 electrons.
- For Li₂, the total number of electrons = 3 (from one Li) + 3 (from another Li) = 6 electrons.
- The electronic configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \]
- Bonding electrons = 4 (2 from \(\sigma_{1s}\) and 2 from \(\sigma_{2s}\)), Antibonding electrons = 2 (from \(\sigma^*_{1s}\)).
- Calculate the bond order:
\[ \text{Bond Order} = \frac{1}{2} (4 - 2) = \frac{1}{2} (2) = 1 \]
- Since the bond order is 1, Li₂ exists.

3. **Analyze the third option: Dicarbon (C₂)**
- Carbon has an atomic number of 6, which means it has 6 electrons.
- For C₂, the total number of electrons = 6 (from one C) + 6 (from another C) = 12 electrons.
- The electronic configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \]
- Bonding electrons = 8 (2 from \(\sigma_{1s}\), 2 from \(\sigma_{2s}\), 2 from \(\pi_{2p_x}\), 2 from \(\pi_{2p_y}\)), Antibonding electrons = 4 (2 from \(\sigma^*_{1s}\) and 2 from \(\sigma^*_{2s}\)).
- Calculate the bond order:
\[ \text{Bond Order} = \frac{1}{2} (8 - 4) = \frac{1}{2} (4) = 2 \]
- Since the bond order is 2, C₂ exists.

4. **Analyze the fourth option: Dioxygen (O₂)**
- Oxygen has an atomic number of 8, which means it has 8 electrons.
- For O₂, the total number of electrons = 8 (from one O) + 8 (from another O) = 16 electrons.
- The electronic configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1 \]
- Bonding electrons = 10, Antibonding electrons = 6.
- Calculate the bond order:
\[ \text{Bond Order} = \frac{1}{2} (10 - 6) = \frac{1}{2} (4) = 2 \]
- Since the bond order is 2, O₂ exists.

### Conclusion:
The molecule that does not exist is **He₂** (option A).