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The increasing order of the bond order of O2,O2+,O2,O22 is:
A- O2+,O2,O2,O22
B- O22,O2,O2+,O2
C- O2,O2+,O2,O22
D- O22,O2,O2,O2+

Answer
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Hint: Try to find the configuration of oxygen molecules following molecular orbital theory. Bond order is the number of bonding electrons – the number of antibonding molecular orbitals divided by 2. Electrons configuration will be different for species with electrons less than 14 and greater than 14.

Complete answer:
We know that molecules form bonding and antibonding molecular orbitals by intermixing of atomic orbitals. In the intermixing of atomic orbitals, there are two types of interference. Constructive interference and destructive interference. Constructive interference has lower energy and it leads to the formation of bonding molecular orbital. Destructive interference has higher energy and it leads to the formation of antibonding molecular orbitals. Atomic orbitals in the atom mix with the same atomic orbitals of another atom.
The electronic configuration will be different for species with less than or equal to 14 electrons and for species with more than 14 electrons.
For species with electrons, less than or equal to 14 electronic configuration is
σ1s,σ1s,σ2s,σ2s,π2px,π2py,σ2pz,σ2pz,π2px,π2py
For species with electrons greater than 14 electronic configuration is
σ1s,σ1s,σ2s,σ2s,σ2pz,π2px,π2py,π2px,π2py,σ2pz
All the given species of oxygen contain more than 14 electrons so they follow the second type of electronic configuration.
Each orbital can accommodate 2 electrons each. O2 has 16 electrons, O2+ has 15 electrons, O2 has 17 electrons and O22 has 18 electrons.
Configuration of O2 is σ1s2,σ1s2,σ2s2,σ2s2,σ2pz2,π2px2,π2py2,π2px1,π2py1.
Configuration of O2+ is σ1s2,σ1s2,σ2s2,σ2s2,σ2pz2,π2px2,π2py2,π2px1.
Configuration of O2 is σ1s2,σ1s2,σ2s2,σ2s2,σ2pz2,π2px2,π2py2,π2px2,π2py1.
Configuration of O22 is σ1s2,σ1s2,σ2s2,σ2s2,σ2pz2,π2px2,π2py2,π2px2,π2py2.
Bond order = numberofbondingelectronsnumberofantibondingelectrons2
Bond order of O2 is 2, bond order of O2+ is 2.5, bond order of O2 is 1.5, bond order of O22 is 1.
Therefore, increasing the order of the bond order is O22,O2,O2,O2+. Option D is correct.

Note: Bond is not always an integer for molecules. Not all molecules obey this molecular orbital theory. Molecules containing unpaired electrons exhibit paramagnetism. Antibonding molecular orbitals have higher energy so they are filled after Bonding molecular orbitals.