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 can follow these steps:

### Step 1: Understand the relationship between bond order and bond length
- The bond length is inversely proportional to the bond order. This means that a higher bond order corresponds to a shorter bond length.

### Step 2: Identify the species to compare
- The species we need to compare are:
1. N₂ (Nitrogen molecule)
2. N₂⁺ (Nitrogen cation)
3. N₂⁻ (Nitrogen anion)
4. N₂²⁻ (Dianion of nitrogen)

### Step 3: Determine the total number of valence electrons for each species
- **N₂**: Each nitrogen atom has 5 valence electrons, so N₂ has a total of 10 valence electrons.
- **N₂⁺**: This species has one less electron, so it has 9 valence electrons.
- **N₂⁻**: This species has one extra electron, so it has 11 valence electrons.
- **N₂²⁻**: This species has two extra electrons, so it has 12 valence electrons.

### Step 4: Calculate the bond order for each species
- **Bond Order Formula**:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]

- **For N₂ (10 electrons)**:
- Bonding electrons: 8 (from 2σ and 2π)
- Antibonding electrons: 2 (from 2σ*)
- Bond Order = (8 - 2) / 2 = 3

- **For N₂⁺ (9 electrons)**:
- Bonding electrons: 8
- Antibonding electrons: 1 (removing one electron from antibonding)
- Bond Order = (8 - 1) / 2 = 3.5

- **For N₂⁻ (11 electrons)**:
- Bonding electrons: 8
- Antibonding electrons: 3 (adding one electron to antibonding)
- Bond Order = (8 - 3) / 2 = 2.5

- **For N₂²⁻ (12 electrons)**:
- Bonding electrons: 8
- Antibonding electrons: 4 (adding two electrons to antibonding)
- Bond Order = (8 - 4) / 2 = 2

### Step 5: Compare the bond orders
- N₂: Bond Order = 3
- N₂⁺: Bond Order = 3.5
- N₂⁻: Bond Order = 2.5
- N₂²⁻: Bond Order = 2

### Step 6: Determine the shortest bond length
- Since bond order is highest for N₂ (3), it will have the shortest bond length.

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

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