According to MO theory which of thhe following lists makes the nitrogen species in terms of increasing bond order?

Options

A. `N_(2)^(-) lt N_(2)^(2-) lt N_(2)`
B. `N_(2)^(-) lt N_(2) lt N_(2)^(2-)`
C. `N_(2)^(2-) lt N_(2)^(-) lt N_(2)`
D. `N_(2) lt N_(2)^(2-) lt N_(2)^(-)`

Explanation

To solve the problem of determining the bond order of nitrogen species according to molecular orbital (MO) theory, we will analyze the molecular orbitals of nitrogen (N2), N2−, and N2²− step by step.

### Step 1: Understand the Molecular Orbital Configuration
- The electronic configuration of nitrogen (N) is 1s² 2s² 2p³.
- For N2, we combine two nitrogen atoms, leading to a total of 14 electrons (7 from each nitrogen atom).

### Step 2: Draw the Molecular Orbital Diagram
- The molecular orbitals for N2 are filled as follows:
- σ(1s)²
- σ*(1s)²
- σ(2s)²
- σ*(2s)²
- σ(2p z)²
- π(2p x)²
- π(2p y)²
- π*(2p x)¹
- π*(2p y)¹

### Step 3: Count the Electrons in Bonding and Antibonding Orbitals
- For N2:
- Bonding electrons = 2 (σ(1s)) + 2 (σ(2s)) + 2 (σ(2p z)) + 2 (π(2p x)) + 2 (π(2p y)) = 10
- Antibonding electrons = 2 (σ*(1s)) + 2 (σ*(2s)) = 4
- Bond order for N2 = (Number of bonding electrons - Number of antibonding electrons) / 2 = (10 - 4) / 2 = 3.

### Step 4: Calculate Bond Order for N2−
- N2− has one extra electron, which will go into the antibonding π*(2p x) or π*(2p y) orbital.
- For N2−:
- Bonding electrons = 10 (same as N2)
- Antibonding electrons = 4 + 1 = 5
- Bond order for N2− = (10 - 5) / 2 = 2.5.

### Step 5: Calculate Bond Order for N2²−
- N2²− has two extra electrons, both of which will go into the antibonding orbitals.
- For N2²−:
- Bonding electrons = 10 (same as N2)
- Antibonding electrons = 4 + 2 = 6
- Bond order for N2²− = (10 - 6) / 2 = 2.

### Step 6: Arrange the Bond Orders
- Now we have the bond orders:
- N2: 3
- N2−: 2.5
- N2²−: 2
- In increasing order of bond order, we have:
- N2²− < N2− < N2

### Final Answer
The increasing order of bond order for the nitrogen species is:
**N2²− < N2− < N2**