Diamagnetic species are those which contain no unpaired electrons. Which among the following are diamagnetic ?

Options

A. `N_(2)`
B. `N_(2)^(2-)`
C. `O_(2)`
D. `O_(2)^(2-)`

Explanation

To determine which of the given species are diamagnetic, we need to analyze each species based on their electron configurations and identify the presence of unpaired electrons. Diamagnetic species are characterized by having no unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Species**: The species we need to analyze are N2, N2^2-, O2, and O2^2-.

2. **Determine the Total Number of Electrons**:
- **N2**: Each nitrogen atom has 7 electrons, so N2 has a total of 14 electrons.
- **N2^2-**: This species has 2 additional electrons, giving it a total of 16 electrons.
- **O2**: Each oxygen atom has 8 electrons, so O2 also has a total of 16 electrons.
- **O2^2-**: This species has 2 additional electrons compared to O2, resulting in a total of 18 electrons.

3. **Write the Molecular Orbital Configurations**:
- **N2**: The molecular orbital configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \]
- **N2^2-**: The configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1 \]
- **O2**: The configuration is the same as N2^2-:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \]
- **O2^2-**: The configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^2 \pi^*_{2p_y}^2 \]

4. **Check for Unpaired Electrons**:
- **N2**: All electrons are paired. Therefore, N2 is **diamagnetic**.
- **N2^2-**: Contains unpaired electrons in the π* orbitals. Therefore, N2^2- is **paramagnetic**.
- **O2**: Contains unpaired electrons in the π* orbitals. Therefore, O2 is **paramagnetic**.
- **O2^2-**: All electrons are paired. Therefore, O2^2- is **diamagnetic**.

5. **Conclusion**: The diamagnetic species among the given options are **N2** and **O2^2-**.

### Final Answer:
- The diamagnetic species are: **N2 and O2^2-**.