With the help of molecular orbital theory predict which of the following species are diamagnetic ?
`H_(2)^(+),O_(2)O_(2)^(2+)`

Answer

To determine which of the species \( H_2^+, O_2, \) and \( O_2^{2+} \) are diamagnetic using molecular orbital theory, we will analyze the electron configurations of each species.

### Step 1: Analyze \( H_2^+ \)

1. **Count the Electrons**:
- \( H_2^+ \) has 1 electron (since it is a hydrogen molecule with one electron removed).

2. **Molecular Orbital Configuration**:
- The molecular orbital configuration for \( H_2^+ \) is \( \sigma_{1s}^1 \).

3. **Check for Unpaired Electrons**:
- There is 1 unpaired electron in \( H_2^+ \), which makes it paramagnetic.

### Conclusion for \( H_2^+ \):
- **Not Diamagnetic** (it is paramagnetic).

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### Step 2: Analyze \( O_2 \)

1. **Count the Electrons**:
- \( O_2 \) has 16 electrons (8 from each oxygen atom).

2. **Molecular Orbital Configuration**:
- The molecular orbital configuration for \( O_2 \) is:
- \( \sigma_{1s}^2 \)
- \( \sigma^*_{1s}^2 \)
- \( \sigma_{2s}^2 \)
- \( \sigma^*_{2s}^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_x}^1 \)
- \( \pi_{2p_y}^1 \)
- This gives us a total of 16 electrons.

3. **Check for Unpaired Electrons**:
- The \( \pi_{2p_x} \) and \( \pi_{2p_y} \) orbitals each contain 1 unpaired electron. Thus, \( O_2 \) has 2 unpaired electrons.

### Conclusion for \( O_2 \):
- **Not Diamagnetic** (it is paramagnetic).

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### Step 3: Analyze \( O_2^{2+} \)

1. **Count the Electrons**:
- \( O_2^{2+} \) has 14 electrons (2 electrons removed from \( O_2 \)).

2. **Molecular Orbital Configuration**:
- The molecular orbital configuration for \( O_2^{2+} \) is:
- \( \sigma_{1s}^2 \)
- \( \sigma^*_{1s}^2 \)
- \( \sigma_{2s}^2 \)
- \( \sigma^*_{2s}^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_x}^2 \)
- \( \pi_{2p_y}^2 \)
- This gives us a total of 14 electrons.

3. **Check for Unpaired Electrons**:
- All electrons are paired in the \( O_2^{2+} \) configuration.

### Conclusion for \( O_2^{2+} \):
- **Diamagnetic** (all electrons are paired).

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### Final Answer:
- The species that are diamagnetic is \( O_2^{2+} \).

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