what is the nature of bond in O2 and C2 molecule. explain with the help of MOT

accoding to molecular orbital theory O2 has paramagntetic nature .VBT and VESPER theory are failed to explain paramagnetic nature of O2.

You Already Got The Answer Of O2 .

So, I am just providing you the answer of C2

Carbon Normally Made or it is well known to form Single, Double,Triple C-C bond .

As per VBT   ---  According to the recent theory the carbon forms _{Quadraple bond (4-bond in between two carbon ) just to satisfy the octet rule for carbon.}

Like :

Where Along with 1-Sigma and 2-Pi bond , One weak "inverted" bond is also there as shown in picture which is basically made by the interaction of electrons in two outwardly pointing sp-Hybrd Orbitals.

As Per Molecular Orbital Theory (MOT) --- shows that there are two sets of paired electrons in a degenerate pi bonding set of orbitals. This gives a bond order of 2, meaning that there should exist a double bond between the two carbons in a C₂ molecule.

In C₂ there are  2∏ bonnds and in O₂ there is only one ∏ bond and one sigma bond. U can understand this by

c₂= σ1S² σ^*1S² σ2S² σ^*2S² ∏2p_x² ∏p_y² it is diamagnetic.

o_2=σ1s²  σ^*1s²  _σ2s²  σ^*2s² ∏2P_x²=2∏p_y²

it is paramagnetic in nature.