A simplified applified of `MO` theory to the hypotheritical molecule `OF` would gives its bond order as:

Options

A. 2
B. 1.5
C. `1.0`
D. 0.5

Explanation

To determine the bond order of the hypothetical molecule OF (oxygen difluoride) using molecular orbital (MO) theory, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Numbers and Electron Configuration**:
- Oxygen (O) has an atomic number of 8, which means it has 8 electrons.
- Fluorine (F) has an atomic number of 9, which means it has 9 electrons.

2. **Calculate the Total Number of Electrons in OF**:
- Total electrons = Electrons from Oxygen + Electrons from Fluorine
- Total electrons = 8 (from O) + 9 (from F) = 17 electrons.

3. **Construct the Molecular Orbital Diagram**:
- The molecular orbitals for O and F can be filled based on their respective electron configurations.
- For O:
- 1s: 2 electrons (σ1s²)
- 2s: 2 electrons (σ2s²)
- 2p: 4 electrons (σ2p², π2p²)
- For F:
- 1s: 2 electrons (σ1s²)
- 2s: 2 electrons (σ2s²)
- 2p: 5 electrons (σ2p², π2p³)

4. **Fill the Molecular Orbitals**:
- The order of filling the molecular orbitals is:
- σ1s, σ*1s, σ2s, σ*2s, σ2p, π2p, π*2p
- Fill the orbitals with the total of 17 electrons:
- σ1s: 2
- σ*1s: 2
- σ2s: 2
- σ*2s: 2
- σ2p: 2
- π2p: 5
- π*2p: 2 (remaining electrons)

5. **Count the Electrons in Bonding and Antibonding Orbitals**:
- Bonding orbitals:
- σ1s (2) + σ2s (2) + σ2p (2) + π2p (5) = 11 electrons
- Antibonding orbitals:
- σ*1s (2) + σ*2s (2) + π*2p (2) = 6 electrons

6. **Calculate the Bond Order**:
- Bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} \times (\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals}) \]
- Substituting the values:
\[ \text{Bond Order} = \frac{1}{2} \times (11 - 6) = \frac{1}{2} \times 5 = 2.5 \]

7. **Conclusion**:
- The bond order of the molecule OF is 2.5.