The correct bond order in the following species is:

Options

A. `O_(2)^(-) lt O_(2)^(+) lt O_(2)^(2+)`
B. `O_(2)^(2+) lt O_(2)^(+) lt O_(2)^(-)`
C. `O_(2)^(2+) lt O_(2)^(-) lt O_(2)^(+)`
D. `O_(2)^(+) lt O_(2)^(-) lt O_(2)^(2+)`

Answer

To determine the bond order of the given species (O2, O2+, O2-, and O2 2+), we will follow these steps:

### Step 1: Determine the Total Number of Electrons
- **O2**: Oxygen has an atomic number of 8. Therefore, O2 has 2 × 8 = 16 electrons.
- **O2+**: This species has one less electron than O2, so it has 15 electrons.
- **O2-**: This species has one more electron than O2, so it has 17 electrons.
- **O2 2+**: This species has two less electrons than O2, so it has 14 electrons.

### Step 2: Write the Molecular Orbital Configuration
Using the molecular orbital theory (MOT), we can determine the electron configuration for each species.

- **O2 (16 electrons)**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_z² (2 electrons in bonding σ2p) + π2p_x² + π2p_y² (4 electrons in bonding π2p) - π*2p_x¹ - π*2p_y¹ (2 electrons in antibonding π*2p)
- Total: 10 bonding and 6 antibonding electrons.

- **O2+ (15 electrons)**:
- Configuration: Same as O2 but with one less electron in the antibonding orbitals.
- Total: 10 bonding and 5 antibonding electrons.

- **O2- (17 electrons)**:
- Configuration: Same as O2 but with one additional electron in the antibonding orbitals.
- Total: 10 bonding and 7 antibonding electrons.

- **O2 2+ (14 electrons)**:
- Configuration: Same as O2 but with two less electrons in the antibonding orbitals.
- Total: 10 bonding and 4 antibonding electrons.

### Step 3: Calculate the Bond Order
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]

- **O2**:
\[ \text{Bond Order} = \frac{1}{2} (10 - 6) = \frac{4}{2} = 2 \]

- **O2+**:
\[ \text{Bond Order} = \frac{1}{2} (10 - 5) = \frac{5}{2} = 2.5 \]

- **O2-**:
\[ \text{Bond Order} = \frac{1}{2} (10 - 7) = \frac{3}{2} = 1.5 \]

- **O2 2+**:
\[ \text{Bond Order} = \frac{1}{2} (10 - 4) = \frac{6}{2} = 3 \]

### Step 4: Compare the Bond Orders
Now, we can summarize the bond orders:
- O2 2+: 3
- O2+: 2.5
- O2: 2
- O2-: 1.5

### Conclusion
The correct bond order for the species is:
- O2 2+ has the highest bond order of 3.
- O2+ has a bond order of 2.5.
- O2 has a bond order of 2.
- O2- has the lowest bond order of 1.5.