To determine the increasing bond order of the given species (NO, C2, O2-, and B2), we will calculate the bond order for each molecule using the molecular orbital theory. The bond order can be calculated using the formula:
\[
\text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2}
\]
### Step 1: Calculate the Bond Order for NO
1. **Count the total number of electrons**:
- Nitrogen (N) has 7 electrons, and Oxygen (O) has 8 electrons.
- Total = 7 + 8 = 15 electrons.
2. **Molecular Orbital Configuration**:
- The configuration is:
\[
\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \sigma 2p_z^2, \pi 2p_x^2, \pi 2p_y^2, \pi^* 2p_x^1
\]
- Total bonding electrons = 10 (from σ and π orbitals).
- Total anti-bonding electrons = 5 (from σ* and π* orbitals).
3. **Calculate Bond Order**:
\[
\text{Bond Order} = \frac{10 - 5}{2} = 2.5
\]
### Step 2: Calculate the Bond Order for C2
1. **Count the total number of electrons**:
- Each Carbon (C) has 6 electrons.
- Total = 6 + 6 = 12 electrons.
2. **Molecular Orbital Configuration**:
- The configuration is:
\[
\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \pi 2p_x^2, \pi 2p_y^2
\]
- Total bonding electrons = 8.
- Total anti-bonding electrons = 4.
3. **Calculate Bond Order**:
\[
\text{Bond Order} = \frac{8 - 4}{2} = 2
\]
### Step 3: Calculate the Bond Order for B2
1. **Count the total number of electrons**:
- Each Boron (B) has 5 electrons.
- Total = 5 + 5 = 10 electrons.
2. **Molecular Orbital Configuration**:
- The configuration is:
\[
\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \pi 2p_x^1, \pi 2p_y^1
\]
- Total bonding electrons = 6.
- Total anti-bonding electrons = 4.
3. **Calculate Bond Order**:
\[
\text{Bond Order} = \frac{6 - 4}{2} = 1
\]
### Step 4: Calculate the Bond Order for O2-
1. **Count the total number of electrons**:
- Each Oxygen (O) has 8 electrons.
- Total = 8 + 8 - 1 (for the negative charge) = 17 electrons.
2. **Molecular Orbital Configuration**:
- The configuration is:
\[
\sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \sigma 2p_z^2, \pi 2p_x^2, \pi 2p_y^2, \pi^* 2p_x^1
\]
- Total bonding electrons = 10.
- Total anti-bonding electrons = 6.
3. **Calculate Bond Order**:
\[
\text{Bond Order} = \frac{10 - 6}{2} = 2
\]
### Summary of Bond Orders
- NO: 2.5
- C2: 2
- B2: 1
- O2-: 1.5
### Step 5: Arrange in Increasing Order
Now, we can arrange the bond orders in increasing order:
1. B2 (1)
2. O2- (1.5)
3. C2 (2)
4. NO (2.5)
### Final Answer
The correct order of increasing bond order is: **B2 < O2- < C2 < NO**.
