Compare the relative stabilities of `O_(2) and O_(2)^(2-)` an indicate their magnetic behavior.

Answer

To compare the relative stabilities of \( O_2 \) and \( O_2^{2-} \) and indicate their magnetic behavior, we will follow these steps:

### Step 1: Determine the number of electrons in each species
- For \( O_2 \): Each oxygen atom has 8 electrons, so \( O_2 \) has \( 8 + 8 = 16 \) electrons.
- For \( O_2^{2-} \): The addition of 2 extra electrons gives \( 16 + 2 = 18 \) electrons.

### Step 2: Write the electronic configuration
- **For \( O_2 \)**:
- The electronic configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \pi_{2p_y}^*^1 \]

- **For \( O_2^{2-} \)**:
- The electronic configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^2 \pi_{2p_y}^*^2 \]

### Step 3: Calculate the bond order
- **Bond order formula**:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]

- **For \( O_2 \)**:
- Bonding electrons: 10 (from \( \sigma_{1s}^2, \sigma_{2s}^2, \sigma_{2p_z}^2, \pi_{2p_x}^2, \pi_{2p_y}^2 \))
- Antibonding electrons: 6 (from \( \sigma_{1s}^*, \sigma_{2s}^*, \pi_{2p_x}^*, \pi_{2p_y}^* \))
- Bond order:
\[ \text{Bond Order} = \frac{10 - 6}{2} = 2 \]

- **For \( O_2^{2-} \)**:
- Bonding electrons: 10 (same as \( O_2 \))
- Antibonding electrons: 8 (from \( \sigma_{1s}^*, \sigma_{2s}^*, \pi_{2p_x}^*, \pi_{2p_y}^* \))
- Bond order:
\[ \text{Bond Order} = \frac{10 - 8}{2} = 1 \]

### Step 4: Compare the relative stabilities
- The bond order of \( O_2 \) is 2, while the bond order of \( O_2^{2-} \) is 1.
- A higher bond order indicates greater stability. Therefore, \( O_2 \) is more stable than \( O_2^{2-} \).

### Step 5: Determine the magnetic behavior
- **For \( O_2 \)**:
- There are 2 unpaired electrons in the \( \pi^* \) orbitals.
- Thus, \( O_2 \) is **paramagnetic**.

- **For \( O_2^{2-} \)**:
- All electrons are paired, as there are no unpaired electrons.
- Thus, \( O_2^{2-} \) is **diamagnetic**.

### Final Summary
- **Stability**: \( O_2 \) is more stable than \( O_2^{2-} \).
- **Magnetic Behavior**: \( O_2 \) is paramagnetic, while \( O_2^{2-} \) is diamagnetic.