Correct order of stability of species
`N_(2),N_(2)^(+),N_(2)^(-)`

Options

A. `N_(2)gtN_(2)^(+)=N_(2)^(-)`
B. `N_(2)gtN_(2)^(+)gtN_(2)^(-)`
C. `N_(2)gtN_(2)^(-)gtN_(2)^(+)`
D. `N_(2)^(+)gtN_(2)gtN_(2)^(-)`

Answer

To determine the correct order of stability of the species \( N_2, N_2^+, N_2^- \), we will use molecular orbital theory (MOT) to find the bond order of each species. The bond order is directly proportional to the stability of the species, meaning a higher bond order indicates greater stability.

### Step 1: Determine the electronic configuration of \( N_2 \)

1. **Molecular Orbital Configuration**:
- For \( N_2 \), the molecular orbital configuration is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \]
- Total electrons = 10 (5 from each nitrogen atom)

2. **Bond Order Calculation**:
- Bond order formula:
\[ \text{Bond Order} = \frac{1}{2} (n_B - n_A) \]
where \( n_B \) is the number of bonding electrons and \( n_A \) is the number of anti-bonding electrons.
- For \( N_2 \):
- Bonding electrons = \( 2 (1s) + 2 (2s) + 4 (2p) = 8 \)
- Anti-bonding electrons = \( 2 (1s) + 2 (2s) = 4 \)
- Bond Order = \( \frac{1}{2} (10 - 0) = 3 \)

### Step 2: Determine the electronic configuration of \( N_2^+ \)

1. **Molecular Orbital Configuration**:
- For \( N_2^+ \), we remove one electron from the highest energy orbital, which is \( \sigma_{2p_z} \):
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^1 \]
- Total electrons = 9

2. **Bond Order Calculation**:
- Bonding electrons = \( 8 \)
- Anti-bonding electrons = \( 4 \)
- Bond Order = \( \frac{1}{2} (9 - 0) = 2.5 \)

### Step 3: Determine the electronic configuration of \( N_2^- \)

1. **Molecular Orbital Configuration**:
- For \( N_2^- \), we add one electron to the highest energy orbital, which is \( \sigma_{2p_z} \):
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \]
- Total electrons = 11

2. **Bond Order Calculation**:
- Bonding electrons = \( 9 \)
- Anti-bonding electrons = \( 4 \)
- Bond Order = \( \frac{1}{2} (11 - 0) = 3.5 \)

### Step 4: Compare the bond orders

- \( N_2 \): Bond Order = 3
- \( N_2^+ \): Bond Order = 2.5
- \( N_2^- \): Bond Order = 3.5

### Conclusion: Order of Stability

The stability order based on bond order is:
\[ N_2^- > N_2 > N_2^+ \]

Thus, the correct order of stability of the species is:
\[ N_2^- > N_2 > N_2^+ \]