Which of the following shows correct order of bond length?

Options

A. `O _(2) ^(+) gt O _(2) gt O _(2) ^(-) gt O _(2) ^(2-)`
B. `O _(2) ^(+) gt O _(2) ^(-) gt O _(2) lt O _(2) ^(2-)`
C. `O _(2) ^(+) gt O _(2) lt O _(2) ^(-) gt O _(2)^(2-)`
D. `O _(2) ^(+) gt O _(2) lt O _(2) ^(-) gt O _(2) ^(2-)`

Answer

To determine the correct order of bond lengths for the given species, we need to analyze the bond order of each species and how it relates to bond length. The bond order is inversely proportional to bond length, meaning that as bond order increases, bond length decreases.

### Step-by-Step Solution:

1. **Identify the Species**: We are given the following species to analyze: O2^+, O2, O2^-, and O2^2-.

2. **Determine the Atomic Mass**:
- For O2^+: The atomic mass is 16 (for O) - 1 (due to the positive charge) = 15.
- For O2: The atomic mass is 16 + 16 = 32.
- For O2^-: The atomic mass is 16 + 1 (due to the negative charge) = 17.
- For O2^2-: The atomic mass is 16 + 2 (due to the double negative charge) = 18.

3. **Calculate the Bond Order**:
- The bond order can be determined based on the number of electrons and the atomic number.
- For O2^+: The bond order is calculated as follows:
- The total number of electrons is 15 (for O2^+), which gives a bond order of 2.
- For O2: The bond order is 2 (as it has 16 electrons).
- For O2^-: The bond order is 1.5 (as it has 17 electrons).
- For O2^2-: The bond order is 1 (as it has 18 electrons).

4. **Establish the Order of Bond Order**:
- The bond order from highest to lowest is:
- O2^+ (2) > O2 (2) > O2^- (1.5) > O2^2- (1).

5. **Determine the Order of Bond Length**:
- Since bond length is inversely proportional to bond order, the order of bond length from longest to shortest is:
- O2^2- > O2^- > O2 = O2^+.

### Final Order of Bond Length:
- The correct order of bond length is: O2^2- > O2^- > O2 = O2^+.