Molecular orbital theory as developed by Hund and Mulliken concerns with the formation of molecular orbitals formed by linear combination of atomic orbitals. The electrons are present in these molecular orbitals. The molecular orbitals are filled. The molecular orbital configuration helps us to calculate bond order which gives information about the number of bonds present between atoms. The bond order is related to bond length and bond strength.
Which one of the following does not have single electron in a bonding molecular orbital?

Options

A. `CN`
B. `B_(2)`
C. `NO`
D. `N_(2)^(+)`

Explanation

To solve the question of which molecule does not have a single electron in a bonding molecular orbital, we will analyze the molecular orbital configurations of the given species.

### Step-by-Step Solution:

1. **Understanding Molecular Orbital Theory**:
- Molecular orbital (MO) theory explains how atomic orbitals combine to form molecular orbitals. Electrons fill these MOs according to the Pauli exclusion principle and Hund's rule.

2. **Determine the Total Number of Electrons**:
- For each molecule, we need to calculate the total number of valence electrons by adding the electrons from each atom involved.

3. **Write the Molecular Orbital Configuration**:
- For each molecule, we will write down the molecular orbital configuration based on the total number of electrons calculated.

4. **Identify Bonding and Antibonding Orbitals**:
- In the molecular orbital configuration, we will identify which orbitals are bonding (lower energy) and which are antibonding (higher energy).

5. **Check for Single Electrons in Bonding Orbitals**:
- We will check the bonding molecular orbitals to see if there are any single electrons present. A bonding molecular orbital is considered to have a single electron if it is half-filled.

6. **Evaluate Each Option**:
- Analyze each molecule provided in the options to determine if it has single electrons in its bonding molecular orbitals.

### Analyzing Each Option:

- **C-N (Cyanide)**:
- Total Electrons: 6 (C) + 7 (N) = 13 electrons.
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_z¹ π2p_x¹ π2p_y⁰.
- Bonding MOs: σ2p_z has 1 single electron. **(Not the answer)**

- **B₂ (Diboron)**:
- Total Electrons: 5 (B) + 5 (B) = 10 electrons.
- Configuration: σ1s² σ*1s² σ2s² σ*2s² π2p_x¹ π2p_y¹.
- Bonding MOs: π2p_x and π2p_y each have 1 single electron. **(Not the answer)**

- **NO (Nitric Oxide)**:
- Total Electrons: 7 (N) + 8 (O) = 15 electrons.
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x¹ π2p_y¹.
- Bonding MOs: All bonding MOs are filled, no single electrons in bonding orbitals. **(This is the answer)**

- **N₂⁺ (Nitrogen Dication)**:
- Total Electrons: 7 (N) + 7 (N) - 1 (for the positive charge) = 13 electrons.
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y¹.
- Bonding MOs: π2p_y has 1 single electron. **(Not the answer)**

### Conclusion:
The molecule that does not have a single electron in a bonding molecular orbital is **NO (Nitric Oxide)**.