The bond order of  will be respectively:

The correct answer is - 4)

Concept:

Bond order- It is a measurement of the number of electrons involved in bonds between two atoms in a molecule.

• It is also an indicator of bond strength and is used extensively in valence bond theory.
• Usually, the higher the bond order, the stronger the chemical bond.
• Most of the time, bond order is equal to the number of bonds between two atoms.

In Molecular Orbital Theory, bond order is defined as half the difference between the number of bonding electrons and the number of anti-bonding electrons.

Explanation:

According to MOT, for the number of electrons  > 14, the electronic configuration is -

 σ_g^1s  < σ*_u^1s < σg2s  < σ*u2s < σ_g^2pz < πu2px =  πu2py <  π*g2px = π*g2py < σ*_u^2pz  

For O2  -  σ2g(1s)  < σ*2u(1s) < σ2g(2s)  < σ*2u(2s) < σ2g(2pz) < π2u(2px) =  π2u(2py) <  π*1g(2px) = π*1g(2py) < σ*u(2pz)  

• Number of bonding electrons - 10
• Number of antibonding electrons - 6
• Bond order of O2 = = 2

For O₂^- -  σ2g(1s)  < σ*2u(1s) < σ2g(2s)  < σ*2u(2s) < σ2g(2pz) < π2u(2px) =  π2u(2py) <  π*2g(2px) = π*1g(2py) < σ*u(2pz)  

• Number of bonding electrons - 10
• Number of antibonding electrons - 7
• Bond order of O2- =  1.5

For O₂⁺  -  σ2g(1s)  < σ*2u(1s) < σ2g(2s)  < σ*2u(2s) < σ2g(2pz) < π2u(2px) =  π2u(2py) <  π*¹g(2px) = π*g(2py) < σ*u(2pz)  

• Number of bonding electrons - 10
• Number of antibonding electrons - 5
• Bond order of O2+  =  = 2.5

For O2^2-  -  σ2g(1s)  < σ*2u(1s) < σ2g(2s)  < σ*2u(2s) < σ2g(2pz) < π2u(2px) =  π2u(2py) <  π*2g(2px) = π*2g(2py) < σ*u(2pz)  

• Number of bonding electrons - 10
• Number of antibonding electrons - 5
• Bond order of O22- =  = 1

Therefore, the bond order of O2+ = 2.5 , O2 = 2, O2- = 1.5, O22- = 1