Question

Which of the following is incorrect according to the Molecular orbital theory?

• A. LUMO level for $C_2$ molecule is ${\sigma }_{2p_x}$ 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. Bond length in $N_2^{+}$ is less than $N_2$

Answer 1

Answer: (D)

Bond length in $N_2^{+}$ is less than $N_2$

(A) M.O for $C_2={\sigma }_1{s}^2<{\sigma }_1^{\ast }{s}^2<{\sigma }_2{s}^2<{\sigma }_2^{\ast }{s}^2<\underset{HOMO}{\underset{}{{\pi }_2{p}_y^2={\pi }_2{p}_z^2}}<\underset{LUMO}{\underset{}{{\sigma }_2{p}_x}}$

Hence, LUMO is ${\sigma }_{2p_x}$.
(B) It is important to note that double bond in $C_2$ consists of both pi bonds because of the presence of four electrons in two pi molecular orbitals.
(C) $C_2^{2-}$ has two pi bonds and one sigma bond.
(D) The bond order of $N_2$ is $\frac{1}{2}\times (10-4)=3$

The bond order of $N_2^{+}$ is $\frac{1}{2}\times (9-4)=2.5$

Hence, the bond length of $N_2^{+}$ is more than $N_2$.

Therefore, option D is incorrect.