Which one paramagnetic and has a bond order of `0.5` ? .

Options

A. `H_(2)^(o+)`
B. `F_(2)`
C. `N_(2)^(o+)`
D. `O_(2)`

Explanation

To determine which molecule is paramagnetic and has a bond order of 0.5, we will analyze each option step by step.

### Step 1: Understand Paramagnetism and Bond Order
- **Paramagnetic**: A molecule is paramagnetic if it has unpaired electrons.
- **Bond Order**: It is calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]

### Step 2: Analyze Each Option

#### Option A: H2+
1. **Determine the number of electrons**:
- Each hydrogen atom has 1 electron. For H2, there would be 2 electrons, but since it has a positive charge (+1), we subtract 1 electron.
- Total electrons = 1.

2. **Fill the Molecular Orbitals**:
- Fill the available molecular orbital:
- σ1s (1 electron).
- This leaves us with 1 unpaired electron.

3. **Check for Paramagnetism**:
- Since there is 1 unpaired electron, H2+ is paramagnetic.

4. **Calculate Bond Order**:
- Bonding electrons = 1, Antibonding electrons = 0.
\[ \text{Bond Order} = \frac{(1 - 0)}{2} = 0.5 \]

#### Option B: F2
1. **Determine the number of electrons**:
- Each fluorine atom has 9 electrons, so for F2, there are 18 electrons.

2. **Fill the Molecular Orbitals**:
- Fill the orbitals:
- σ1s (2), σ*1s (2), σ2s (2), σ*2s (2), σ2p (2), π2p (4), π*2p (2).
- All 18 electrons are paired.

3. **Check for Paramagnetism**:
- Since there are no unpaired electrons, F2 is diamagnetic.

4. **Calculate Bond Order**:
- Bonding electrons = 12, Antibonding electrons = 6.
\[ \text{Bond Order} = \frac{(12 - 6)}{2} = 3 \]

#### Option C: N2+
1. **Determine the number of electrons**:
- Each nitrogen atom has 7 electrons, so for N2, there are 14 electrons. With a positive charge (+1), we have 13 electrons.

2. **Fill the Molecular Orbitals**:
- Fill the orbitals:
- σ1s (2), σ*1s (2), σ2s (2), σ*2s (2), π2p (4), σ2p (2).
- This leaves us with 1 unpaired electron.

3. **Check for Paramagnetism**:
- Since there is 1 unpaired electron, N2+ is paramagnetic.

4. **Calculate Bond Order**:
- Bonding electrons = 8, Antibonding electrons = 4.
\[ \text{Bond Order} = \frac{(8 - 4)}{2} = 2 \]

#### Option D: O2
1. **Determine the number of electrons**:
- Each oxygen atom has 8 electrons, so for O2, there are 16 electrons.

2. **Fill the Molecular Orbitals**:
- Fill the orbitals:
- σ1s (2), σ*1s (2), σ2s (2), σ*2s (2), σ2p (2), π2p (4), π*2p (2).
- This leaves us with 2 unpaired electrons.

3. **Check for Paramagnetism**:
- Since there are 2 unpaired electrons, O2 is paramagnetic.

4. **Calculate Bond Order**:
- Bonding electrons = 10, Antibonding electrons = 6.
\[ \text{Bond Order} = \frac{(10 - 6)}{2} = 2 \]

### Conclusion
- **H2+** is the only molecule that is paramagnetic and has a bond order of 0.5.

### Final Answer
**H2+**