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 that have a fractional bond order from the given list, we will calculate the bond order for each species using the formula:

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

Now, let's analyze each species step by step:

### Step 1: Calculate Bond Order for Each Species

**(a) O₂⁺**
- Total electrons = 16 - 1 (due to +1 charge) = 15 electrons
- Bonding electrons = 6, Antibonding electrons = 5
- Bond Order = (6 - 5) / 2 = 1 / 2 = 2.5 (Fractional)

**(b) CO**
- Total electrons = 6 (C) + 8 (O) = 14 electrons
- Bonding electrons = 10, Antibonding electrons = 4
- Bond Order = (10 - 4) / 2 = 6 / 2 = 3 (Not Fractional)

**(c) B₂**
- Total electrons = 10 (5 from each B)
- Bonding electrons = 8, Antibonding electrons = 2
- Bond Order = (8 - 2) / 2 = 6 / 2 = 3 (Not Fractional)

**(d) O₂⁺ (again)**
- Total electrons = 15 (same as (a))
- Bond Order = 2.5 (Fractional)

**(e) NO⁺**
- Total electrons = 7 (N) + 8 (O) - 1 = 14 electrons
- Bonding electrons = 10, Antibonding electrons = 4
- Bond Order = (10 - 4) / 2 = 3 (Not Fractional)

**(f) He₂⁺**
- Total electrons = 2 (He) - 1 = 1 electron
- Bonding electrons = 1, Antibonding electrons = 0
- Bond Order = (1 - 0) / 2 = 1 / 2 = 0.5 (Fractional)

**(g) C₂²⁺**
- Total electrons = 12 - 2 = 10 electrons
- Bonding electrons = 8, Antibonding electrons = 2
- Bond Order = (8 - 2) / 2 = 6 / 2 = 3 (Not Fractional)

**(h) CN⁻**
- Total electrons = 6 (C) + 7 (N) + 1 = 14 electrons
- Bonding electrons = 10, Antibonding electrons = 4
- Bond Order = (10 - 4) / 2 = 3 (Not Fractional)

**(i) N₂⁻**
- Total electrons = 14 + 1 = 15 electrons
- Bonding electrons = 10, Antibonding electrons = 5
- Bond Order = (10 - 5) / 2 = 5 / 2 = 2.5 (Fractional)

### Step 2: Count the Species with Fractional Bond Orders
From the calculations:
- Species with fractional bond order: O₂⁺ (a), O₂⁺ (d), He₂⁺ (f), N₂⁻ (i)
- Total = 4 species

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

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