Which of the following species has shortest Bond length?

Options

A. `N_2^+`
B. `N_2`
C. `N_2^-`
D. `N_2^(2-)`

Answer

To determine which species has the shortest bond length, we need to analyze the bond order of the given species. The bond order is inversely proportional to the bond length; that is, a higher bond order corresponds to a shorter bond length.

### Step-by-Step Solution:

1. **Identify the Species**: Let's assume the species we are comparing are N2+, N2, N2-, and N2- (as inferred from the video transcript).

2. **Determine the Total Number of Electrons**:
- For **N2+**: N2 has 14 electrons (7 from each nitrogen), so N2+ has 13 electrons.
- For **N2**: It has 14 electrons.
- For **N2-**: It has 15 electrons.
- For **N2-**: It has 16 electrons.

3. **Calculate the Bond Order**:
- **N2+**:
- Bond order = (Number of bonding electrons - Number of antibonding electrons) / 2
- For 13 electrons, the bond order is calculated to be 2.5.
- **N2**:
- For 14 electrons, the bond order is 3.
- **N2-**:
- For 15 electrons, the bond order is 2.5.
- **N2-**:
- For 16 electrons, the bond order is 2.

4. **Compare Bond Orders**:
- N2+ has a bond order of 2.5.
- N2 has a bond order of 3.
- N2- has a bond order of 2.5.
- N2- has a bond order of 2.

5. **Determine the Shortest Bond Length**:
- Since bond length is inversely related to bond order, the species with the highest bond order will have the shortest bond length.
- Here, N2 has the highest bond order of 3.

### Conclusion:
The species with the shortest bond length is **N2**.