To determine the correct order of bond order for the given diatomic species (C₂²⁻, He₂⁺, O₂⁻, and NO), we will calculate the bond order for each species step by step.
### Step 1: Calculate Bond Order for C₂²⁻
1. **Determine the number of electrons**: C₂ has 12 electrons (6 from each carbon), and C₂²⁻ has 14 electrons (12 + 2).
2. **Write the molecular electronic configuration**:
- σ1s², σ*1s², σ2s², σ*2s², π2px², π2py², σ2pz²
3. **Count electrons in bonding and antibonding orbitals**:
- Bonding: 10 electrons (σ1s: 2, σ2s: 2, π2px: 2, π2py: 2, σ2pz: 2)
- Antibonding: 4 electrons (σ*1s: 2, σ*2s: 2)
4. **Calculate bond order**:
\[
\text{Bond Order} = \frac{(10 - 4)}{2} = 3
\]
### Step 2: Calculate Bond Order for He₂⁺
1. **Determine the number of electrons**: He₂ has 4 electrons (2 from each helium), and He₂⁺ has 3 electrons (4 - 1).
2. **Write the molecular electronic configuration**:
- σ1s², σ*1s¹
3. **Count electrons in bonding and antibonding orbitals**:
- Bonding: 2 electrons (σ1s: 2)
- Antibonding: 1 electron (σ*1s: 1)
4. **Calculate bond order**:
\[
\text{Bond Order} = \frac{(2 - 1)}{2} = 0.5
\]
### Step 3: Calculate Bond Order for O₂⁻
1. **Determine the number of electrons**: O₂ has 16 electrons, and O₂⁻ has 17 electrons (16 + 1).
2. **Write the molecular electronic configuration**:
- σ1s², σ*1s², σ2s², σ*2s², σ2pz², π2px², π2py², π*2px², π*2py¹
3. **Count electrons in bonding and antibonding orbitals**:
- Bonding: 10 electrons (σ1s: 2, σ2s: 2, σ2pz: 2, π2px: 2, π2py: 2)
- Antibonding: 7 electrons (σ*1s: 2, σ*2s: 2, π*2px: 2, π*2py: 1)
4. **Calculate bond order**:
\[
\text{Bond Order} = \frac{(10 - 7)}{2} = 1.5
\]
### Step 4: Calculate Bond Order for NO
1. **Determine the number of electrons**: N has 7 electrons, O has 8 electrons, so NO has 15 electrons (7 + 8).
2. **Write the molecular electronic configuration**:
- σ1s², σ*1s², σ2s², σ*2s², σ2pz², π2px², π2py², π*2px¹
3. **Count electrons in bonding and antibonding orbitals**:
- Bonding: 10 electrons (σ1s: 2, σ2s: 2, σ2pz: 2, π2px: 2, π2py: 2)
- Antibonding: 5 electrons (σ*1s: 2, σ*2s: 2, π*2px: 1)
4. **Calculate bond order**:
\[
\text{Bond Order} = \frac{(10 - 5)}{2} = 2.5
\]
### Step 5: Summarize Bond Orders
- C₂²⁻: 3
- He₂⁺: 0.5
- O₂⁻: 1.5
- NO: 2.5
### Step 6: Order of Bond Orders
Now, we can arrange the bond orders in increasing order:
1. He₂⁺ (0.5)
2. O₂⁻ (1.5)
3. NO (2.5)
4. C₂²⁻ (3)
### Final Answer
The correct order of increasing bond order is:
**He₂⁺ < O₂⁻ < NO < C₂²⁻**
