The `O-O` bond length in `O_2, O_2 [AsF_4]` and `K [O_2]` is :

Options

A. ` O_2 [AsF_4] lt O_2 lt K [O_2]`
B. ` O_2 [AsF_4 ] gt K [O_2 `
C. `O_2 gt O_2 [AsF_4 ]gt K [O_2 ]`
D. `K [O_(2) ] lt O_(2) lt O_(2) [AsF_(4)]`

Explanation

To determine the bond length of the O-O bond in the compounds \( O_2 \), \( O_2[AsF_4] \), and \( KO_2 \), we need to analyze the bond order of each species. The bond length is inversely related to the bond order; as the bond order increases, the bond length decreases.

### Step-by-Step Solution:

1. **Identify the Compounds**: We have three compounds to analyze:
- \( O_2 \)
- \( O_2[AsF_4] \)
- \( KO_2 \)

2. **Determine the Bond Order for Each Compound**:
- **For \( O_2 \)**:
- The electronic configuration of \( O_2 \) is \( 1s^2 2s^2 2p^4 \).
- The bond order is calculated as:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]
- In \( O_2 \), there are 6 bonding electrons and 2 antibonding electrons:
\[ \text{Bond Order} = \frac{6 - 2}{2} = 2 \]

- **For \( O_2[AsF_4] \)**:
- \( O_2[AsF_4] \) can be considered as \( O_2^+ \) (since it is in a coordination complex).
- The bond order for \( O_2^+ \) is:
- The electronic configuration is \( 1s^2 2s^2 2p^3 \).
- Bond order calculation:
\[ \text{Bond Order} = \frac{6 - 1}{2} = 2.5 \]

- **For \( KO_2 \)**:
- \( KO_2 \) contains the superoxide ion \( O_2^- \).
- The bond order for \( O_2^- \) is:
- The electronic configuration is \( 1s^2 2s^2 2p^5 \).
- Bond order calculation:
\[ \text{Bond Order} = \frac{6 - 3}{2} = 1.5 \]

3. **Compare the Bond Orders**:
- \( O_2 \) has a bond order of 2.
- \( O_2[AsF_4] \) has a bond order of 2.5.
- \( KO_2 \) has a bond order of 1.5.

4. **Determine the Order of Bond Lengths**:
- Since bond length decreases with increasing bond order, we can conclude:
- \( O_2[AsF_4] \) (bond order 2.5) has the shortest bond length.
- \( O_2 \) (bond order 2) has a longer bond length than \( O_2[AsF_4] \).
- \( KO_2 \) (bond order 1.5) has the longest bond length.

5. **Final Order of Bond Lengths**:
- Shortest bond length: \( O_2[AsF_4] \)
- Medium bond length: \( O_2 \)
- Longest bond length: \( KO_2 \)

### Conclusion:
The order of bond lengths in the compounds is:
\[ O_2[AsF_4] < O_2 < KO_2 \]