Choose the correct regarding bond length

Options

A. `CO^(+) lt CO`
B. `NO^(+) lt NO`
C. `N lt N_(2)^(+)`
D. `All of these

Answer

To solve the question regarding bond lengths and determine which statements are correct, we will analyze each option based on bond order and bond length relationships.

### Step-by-Step Solution:

1. **Understanding Bond Order and Bond Length Relationship**:
- Bond order is defined as the number of bonding electrons minus the number of antibonding electrons, divided by two.
- Bond length is inversely proportional to bond order: higher bond order means shorter bond length, and lower bond order means longer bond length.

2. **Analyzing Option 1: CO⁺ is less than CO**:
- For CO:
- Number of bonding electrons = 10
- Number of antibonding electrons = 4
- Bond order (BO) = (10 - 4) / 2 = 3
- For CO⁺:
- Number of bonding electrons = 10
- Number of antibonding electrons = 3
- Bond order (BO) = (10 - 3) / 2 = 3.5
- Since CO⁺ has a higher bond order than CO, it has a shorter bond length.
- Therefore, CO⁺ < CO in terms of bond length, making this option **correct**.

3. **Analyzing Option 2: NO⁺ is less than NO**:
- For NO:
- Number of bonding electrons = 10
- Number of antibonding electrons = 5
- Bond order (BO) = (10 - 5) / 2 = 2.5
- For NO⁺:
- Number of bonding electrons = 10
- Number of antibonding electrons = 4
- Bond order (BO) = (10 - 4) / 2 = 3
- NO⁺ has a higher bond order than NO, therefore NO⁺ has a shorter bond length.
- Thus, NO⁺ < NO in terms of bond length, making this option **correct**.

4. **Analyzing Option 3: N is less than N₂⁺**:
- For N (N₂):
- Bond order = 3 (as it has 10 bonding and 0 antibonding electrons).
- For N₂⁺:
- Number of bonding electrons = 10
- Number of antibonding electrons = 5
- Bond order (BO) = (10 - 5) / 2 = 2.5
- N has a higher bond order than N₂⁺, thus N has a shorter bond length.
- Therefore, N₂⁺ > N in terms of bond length, making this option **correct**.

5. **Analyzing Option 4: All of these**:
- Since options 1, 2, and 3 are all correct, option 4 stating "all of these" is also **correct**.

### Conclusion:
The correct answer is that all of the options regarding bond lengths are correct.