Question

According to Molecular orbital theory which of the following is correct?
A) LUMO level for ${C_2}$ molecule is $\sigma 2{p_x}$ ​​ orbital
B) In ${C_2}$​ molecules, both the bonds are $\pi$ bonds
C) In $C_2^{2 - }$ ​ion, there is one $\sigma$ and two $\pi$ bonds
D) All the above are correct

Answer 1

MOT which stands for Molecular Orbital Theory is defined as a chemical bonding theory developed in the early twentieth century which describes properties and the structure of different molecules. It explains about the prevalence of single bond and double bond in the resonating structure of the molecules.

Complete step by step answer:
According to molecular orbital theory the electronic configuration of ${C_2}$ molecule is
$\sigma 1{s^2},{\sigma ^*}1{s^2},\sigma 2{s^2},{\sigma ^*}2{s^2},\pi 2p_x^2,\pi 2p_y^2,\sigma 2p_x^0$ ( ${C_2}$​ molecule has 12 electrons)
In the given question, LUMO stands for lowest unoccupied molecular orbital, and as we can see from the electronic configuration of ${C_2}$ the LUMO level of ${C_2}$ molecule is $\sigma 2{p_x}$ ​​ orbital hence first option is correct.
As we can see when the ${C_2}$ molecule is formed it has both $\pi$bond present in it in its electronic configuration, therefore the second option is also correct.
In $C_2^{2 - }$ion there will be 3 bonds joining the carbon atoms with 2 electron in excess, according to molecular orbital theory out of those 3 bonds, one will be $\sigma$ bond and other two will be $\pi$ bonds. Hence the third option is also correct.
Therefore, all the given options are correct.
Thus the correct option is D.

Additional information: There are two types of covalent bonds in an atom Sigma and pi bonds. They are formed by the overlapping between their atomic orbitals. There is end-to-end overlapping in sigma bonds and in Pi bonds the lobe of one atomic orbital overlaps over another atom. The strong bonding is shown by sigma bonds in an atom.

Note:
Molecular orbital theory is advantage over the valence bond theory which fails to explain the presence of bonds in resonance-stabilized molecules i.e. the presence of two or more equivalent bonds whose bond orders occurs between that of a single bond and that of a double bond.