According to molecular orbital theory, the number of unpaired electron(s) in `O_(2)^(2-)` is _______.

Answer

To determine the number of unpaired electrons in \( O_2^{2-} \) using molecular orbital theory, we can follow these steps:

### Step 1: Write the Molecular Orbital Configuration for \( O_2 \)

The molecular orbital configuration for \( O_2 \) (dioxygen) is:
- \( \sigma_{2s}^2 \)
- \( \sigma_{2s}^*^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_y}^2 \)
- \( \pi_{2p_x}^2 \)
- \( \pi_{2p_z}^*^1 \)
- \( \pi_{2p_y}^*^1 \)

In total, \( O_2 \) has 16 electrons, and the configuration shows that there are two unpaired electrons in the \( \pi^* \) orbitals.

### Step 2: Determine the Configuration for \( O_2^{2-} \)

For \( O_2^{2-} \), we need to add 2 additional electrons to the \( O_2 \) configuration:
- The two additional electrons will fill the \( \pi_{2p_z}^* \) and \( \pi_{2p_y}^* \) orbitals.

The new configuration for \( O_2^{2-} \) becomes:
- \( \sigma_{2s}^2 \)
- \( \sigma_{2s}^*^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_y}^2 \)
- \( \pi_{2p_x}^2 \)
- \( \pi_{2p_z}^*^2 \)
- \( \pi_{2p_y}^*^2 \)

### Step 3: Count the Unpaired Electrons

In the configuration of \( O_2^{2-} \), all electrons are paired:
- \( \sigma_{2s}^2 \) (paired)
- \( \sigma_{2s}^*^2 \) (paired)
- \( \sigma_{2p_z}^2 \) (paired)
- \( \pi_{2p_y}^2 \) (paired)
- \( \pi_{2p_x}^2 \) (paired)
- \( \pi_{2p_z}^*^2 \) (paired)
- \( \pi_{2p_y}^*^2 \) (paired)

Thus, there are **no unpaired electrons** in \( O_2^{2-} \).

### Final Answer:
The number of unpaired electrons in \( O_2^{2-} \) is **0**.

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