Question

In which of the following pair, both the molecular orbitals are gerade or ungerade?
A) ${\sigma _{2s}},{\pi _{2px}}$
B) ${\sigma _{*2s}},{\pi _{*2px}}$
C) ${\sigma _{*2s}},{\pi _{2px}}$
D) ${\pi _{2px}},{\pi _{*2px}}$

Answer 1

Hint : Orbitals that are left unaffected by the inversion action (are symmetric) are labelled with a subscript g, whereas those that shift sign (are antisymmetric) are labelled with a subscript u. The letters g and u are derived from the German words "gerade" and "ungerade," respectively, which signify "even" and "odd."

Complete Step By Step Answer:
If inversion of a molecule's centre of symmetry results in the same phases for the molecular orbital, the MO is said to have gerade (g) symmetry, which comes from the German term "even." If a molecule's centre of symmetry inversion causes a phase shift in the molecular orbital, the MO is said to have ungerade (u) symmetry, which comes from the German term for odd.
Now, lets look at each options:
A) $
  {\sigma _{2s}} \to gerade \\
  {\pi _{2px}} \to ungerade \\
 $
B) $
  {\sigma _{*2s}} \to ungerade \\
  {\pi _{*2px}} \to gerade \\
 $
C) $
  {\sigma _{*2s}} \to ungerade \\
  {\pi _{2px}} \to ungerade \\
 $
D) $
  {\pi _{2px}} \to ungerade \\
  {\pi _{*2px}} \to gerade \\
 $
We observe that there is only one pair of molecular orbitals which are either gerade or ungerade and that is option (C) both of the orbitals are ungerade. Rest all other options are combination of gerade and ungerade.
Hence, the correct answer is option ( C) ${\sigma _{*2s}},{\pi _{2px}}$

Note :
There are two resulting orbitals as two atomic orbitals merge. stands for gerade, or symmetric in relation to an inversion centre. stands for ungerade, or asymmetric in relation to an inversion middle.