Among the following species, which has the minimum bond length?

Options

A. `B_(2)`
B. `C_(2)`
C. `F_(2)`
D. `O_(2)^(-)`

Explanation

To determine which species has the minimum bond length among the given options, we will follow these steps:

### Step 1: Understand the Relationship Between Bond Order and Bond Length
Bond length is inversely proportional to bond order. This means that as bond order increases, bond length decreases. Therefore, to find the species with the minimum bond length, we need to calculate the bond order for each species.

### Step 2: Calculate the Bond Order for Each Species

#### Species A: B2
- **Total Electrons**: 10
- **Molecular Orbital Filling**:
- σ1s (2)
- σ1s* (2)
- σ2s (2)
- σ2s* (2)
- π2px (2)
- π2py (2)
- **Bonding Electrons**: 6 (σ1s, σ2s, π2px, π2py)
- **Antibonding Electrons**: 4 (σ1s*, σ2s*)
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{\text{Bonding Electrons} - \text{Antibonding Electrons}}{2} = \frac{6 - 4}{2} = 1 \]

#### Species B: C2
- **Total Electrons**: 12
- **Molecular Orbital Filling**:
- σ1s (2)
- σ1s* (2)
- σ2s (2)
- σ2s* (2)
- π2px (2)
- π2py (2)
- **Bonding Electrons**: 8
- **Antibonding Electrons**: 4
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{8 - 4}{2} = 2 \]

#### Species C: F2
- **Total Electrons**: 18
- **Molecular Orbital Filling**:
- σ1s (2)
- σ1s* (2)
- σ2s (2)
- σ2s* (2)
- σ2p z (2)
- π2p x (2)
- π2p y (2)
- π*2p x (2)
- π*2p y (2)
- **Bonding Electrons**: 10
- **Antibonding Electrons**: 8
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 8}{2} = 1 \]

#### Species D: O2^-
- **Total Electrons**: 17
- **Molecular Orbital Filling**:
- σ1s (2)
- σ1s* (2)
- σ2s (2)
- σ2s* (2)
- σ2p z (2)
- π2p x (2)
- π2p y (2)
- π*2p x (1)
- **Bonding Electrons**: 10
- **Antibonding Electrons**: 7
- **Bond Order Calculation**:
\[ \text{Bond Order} = \frac{10 - 7}{2} = 1.5 \]

### Step 3: Compare the Bond Orders
- **B2**: Bond Order = 1
- **C2**: Bond Order = 2
- **F2**: Bond Order = 1
- **O2^-**: Bond Order = 1.5

### Conclusion
The species with the highest bond order is C2, which has a bond order of 2. Therefore, C2 has the minimum bond length among the given species.

**Final Answer**: C2

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