Which of the following have been arranged in increasing bond order as well as bond dissociation energy ? .

Options

A. `O_(2)^(-2) lt O_(2)^(Theta) lt O_(2)^(o+) lt O_(2)`
B. `O_(2)^(-2) lt O_(2)^(Theta) lt O_(2) lt O_(2)^(o+)`
C. `O_(2)ltO_(2)^(o+) lt O_(2)^(2-)lt O_(2)^(Theta)`
D. `O_(2)^(o+) lt O_(2)^(2-)lt O_(2)^(Theta)ltO_(2)`

Answer

To solve the question regarding the increasing bond order and bond dissociation energy of the species O2, O2-, O2+, and O2 2-, we will follow these steps:

### Step 1: Determine the number of electrons in each species
- O2 has 16 electrons.
- O2- has 17 electrons.
- O2+ has 15 electrons.
- O2 2- has 18 electrons.

### Step 2: Write the electronic configuration for each species
Using Molecular Orbital Theory (MOT), we can write the electronic configurations:
1. **O2**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2pz² π2px² π2py² π*2px¹ π*2py¹
2. **O2+**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2pz² π2px² π2py² π*2px¹
3. **O2-**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2pz² π2px² π2py² π*2px² π*2py¹
4. **O2 2-**:
- Configuration: σ1s² σ*1s² σ2s² σ*2s² σ2pz² π2px² π2py² π*2px² π*2py²

### Step 3: Calculate the bond order for each species
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{n_B - n_A}{2} \]
where \( n_B \) is the number of electrons in bonding orbitals and \( n_A \) is the number of electrons in anti-bonding orbitals.

1. **For O2**:
- Bonding electrons (n_B): 10 (σ and π orbitals)
- Anti-bonding electrons (n_A): 6 (π* orbitals)
- Bond Order = (10 - 6) / 2 = 2

2. **For O2+**:
- Bonding electrons (n_B): 10
- Anti-bonding electrons (n_A): 5 (removal of one electron from π*)
- Bond Order = (10 - 5) / 2 = 2.5

3. **For O2-**:
- Bonding electrons (n_B): 10
- Anti-bonding electrons (n_A): 6 (addition of one electron to π*)
- Bond Order = (10 - 7) / 2 = 1.5

4. **For O2 2-**:
- Bonding electrons (n_B): 10
- Anti-bonding electrons (n_A): 8 (addition of two electrons to π*)
- Bond Order = (10 - 8) / 2 = 1

### Step 4: Arrange the species in increasing order of bond order and bond dissociation energy
From the calculations:
- O2 2-: Bond Order = 1
- O2-: Bond Order = 1.5
- O2: Bond Order = 2
- O2+: Bond Order = 2.5

Thus, the increasing order of bond order and bond dissociation energy is:
**O2 2- < O2- < O2 < O2+**

### Final Answer
The correct arrangement in increasing bond order and bond dissociation energy is:
**O2 2- < O2- < O2 < O2+**