Bond length order is

Options

A. a. `O_(2)lt O_(3)lt O_(2)^(2-)`
B. b. `O_(2)lt O_(2)^(2-)lt O_(3)`
C. c. `O_(2)^(2-)lt O_(3)lt O_(2)`
D. d. `O_(2)=O_(2)^(2-)gt O_(3)`

Explanation

To determine the bond length order of the given molecules, we will follow these steps:

### Step 1: Understand the Concept of Bond Order
Bond order is defined as the difference between the number of bonding electrons and the number of antibonding electrons, divided by two. It is a measure of the strength and stability of a bond. The higher the bond order, the shorter the bond length, and vice versa.

### Step 2: Analyze Each Molecule
We will analyze the bond order for each molecule in the question: O2, O2^(-2), and O3.

#### For O2:
- Total electrons = 16
- Bonding electrons (nB) = 10
- Antibonding electrons (nA) = 6
- Bond order = (nB - nA) / 2 = (10 - 6) / 2 = 2

#### For O2^(-2):
- Total electrons = 18
- Bonding electrons (nB) = 10
- Antibonding electrons (nA) = 8
- Bond order = (nB - nA) / 2 = (10 - 8) / 2 = 1

#### For O3:
- O3 has a bond order of 1.5 due to resonance structures, which implies that the bond character is delocalized among the oxygen atoms.

### Step 3: Determine the Bond Length Order
Now, we can summarize the bond orders:
- O2: Bond order = 2 (shortest bond length)
- O2^(-2): Bond order = 1 (longer bond length than O2)
- O3: Bond order = 1.5 (intermediate bond length)

Based on the bond order, we can conclude:
- O2 has the shortest bond length.
- O3 has a bond length longer than O2 but shorter than O2^(-2).
- O2^(-2) has the longest bond length.

### Final Bond Length Order
The order of bond lengths from longest to shortest is:
O2^(-2) > O3 > O2

### Conclusion
Thus, the correct bond length order is:
**O2^(-2) > O3 > O2**

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