Which of the following have identical bond order ?

Options

A. `CN^(-)`
B. `O_(2)^(-)`
C. `NO^(+)`
D. `CN^(+).`

Explanation

To determine which of the given species have identical bond orders, we need to calculate the bond order for each species based on their electron configurations. The bond order can be calculated using the formula:

\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]

Let's analyze each species step by step:

### Step 1: Identify the species and their electron counts
1. **C⁻ (Carbon anion)**: Carbon has 6 electrons, and with an additional electron (due to the negative charge), it has a total of 7 electrons.
2. **O₂²⁻ (Oxygen dianion)**: Each oxygen has 8 electrons. With 2 additional electrons (due to the -2 charge), it has a total of 18 electrons.
3. **NO⁺ (Nitric oxide cation)**: Nitrogen has 7 electrons, oxygen has 8 electrons. With one less electron (due to the +1 charge), it has a total of 14 electrons.
4. **CN⁻ (Cyanide anion)**: Carbon has 6 electrons, nitrogen has 7 electrons, and with one additional electron (due to the negative charge), it has a total of 14 electrons.

### Step 2: Calculate the bond order for each species
1. **C⁻**:
- Total electrons = 7
- Bonding electrons = 6 (in a hypothetical molecular orbital configuration)
- Antibonding electrons = 1
- Bond Order = (6 - 1) / 2 = 2.5

2. **O₂²⁻**:
- Total electrons = 18
- Bonding electrons = 10
- Antibonding electrons = 8
- Bond Order = (10 - 8) / 2 = 1

3. **NO⁺**:
- Total electrons = 14
- Bonding electrons = 10
- Antibonding electrons = 4
- Bond Order = (10 - 4) / 2 = 3

4. **CN⁻**:
- Total electrons = 14
- Bonding electrons = 10
- Antibonding electrons = 4
- Bond Order = (10 - 4) / 2 = 3

### Step 3: Compare the bond orders
- C⁻ has a bond order of 2.5
- O₂²⁻ has a bond order of 1
- NO⁺ has a bond order of 3
- CN⁻ has a bond order of 3

### Conclusion
The species that have identical bond orders are **NO⁺ and CN⁻**, both with a bond order of 3.