There are some species given below :-
`{:((a)O_(2)^(+),,,,(b)CO),((c)B_(2),,,,(d)O_(2)^(+)),((e)NO^(+),,,,(f)He_(2)^(+)),((g)C_(2)^(+2),,,,(h)CN^(-)),((i)N_(2)^(-),,,,):}`
Total no. of species which have their fractional bond order.

Options

A. 3
B. 4
C. 5
D. 6

Answer

To determine the total number of species with fractional bond orders from the given list, we will follow these steps:

### Step 1: Understand the concept of bond order
The bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} \times (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]
A fractional bond order occurs when there is an odd number of total electrons in the molecular orbitals.

### Step 2: Identify the total number of electrons for each species
We will calculate the total number of electrons for each species given:

1. **O₂⁺**: Oxygen has 8 electrons, so O₂ has 16 electrons. O₂⁺ loses 1 electron, giving us 15 electrons.
2. **CO**: Carbon has 6 electrons and Oxygen has 8 electrons, so CO has 14 electrons.
3. **B₂**: Boron has 5 electrons, so B₂ has 10 electrons.
4. **O₂⁺**: (Repeated) This is already calculated as 15 electrons.
5. **NO⁺**: Nitrogen has 7 electrons and Oxygen has 8 electrons, so NO has 15 electrons. NO⁺ loses 1 electron, giving us 14 electrons.
6. **He₂⁺**: Helium has 2 electrons, so He₂ has 4 electrons. He₂⁺ loses 1 electron, giving us 3 electrons.
7. **C₂²⁺**: Carbon has 6 electrons, so C₂ has 12 electrons. C₂²⁺ loses 2 electrons, giving us 10 electrons.
8. **CN⁻**: Carbon has 6 electrons and Nitrogen has 7 electrons, so CN has 13 electrons. CN⁻ gains 1 electron, giving us 14 electrons.
9. **N₂⁻**: Nitrogen has 7 electrons, so N₂ has 14 electrons. N₂⁻ gains 1 electron, giving us 15 electrons.

### Step 3: List the total number of electrons for each species
- O₂⁺: 15 electrons
- CO: 14 electrons
- B₂: 10 electrons
- O₂⁺: 15 electrons (repeated)
- NO⁺: 14 electrons
- He₂⁺: 3 electrons
- C₂²⁺: 10 electrons
- CN⁻: 14 electrons
- N₂⁻: 15 electrons

### Step 4: Identify species with an odd number of electrons
Now, we will identify which of these species have an odd number of electrons:
- O₂⁺: 15 (odd)
- CO: 14 (even)
- B₂: 10 (even)
- O₂⁺: 15 (odd) (repeated)
- NO⁺: 14 (even)
- He₂⁺: 3 (odd)
- C₂²⁺: 10 (even)
- CN⁻: 14 (even)
- N₂⁻: 15 (odd)

### Step 5: Count the species with odd number of electrons
The species with an odd number of electrons are:
1. O₂⁺ (15)
2. O₂⁺ (15) - counted once
3. He₂⁺ (3)
4. N₂⁻ (15)

Thus, there are **4 species** that have a fractional bond order.

### Final Answer:
The total number of species which have their fractional bond order is **4**.

---