Two pi and half sigma bonds are present in -

CONCEPT:

Molecular Orbital Theory

• Molecular Orbital Theory (MOT) describes bonding in terms of molecular orbitals, which are formed by the combination of atomic orbitals.
• Bonds in diatomic molecules like \( {O}_2 , {O}_2^+ , {N}_2 , and \ \ {N}_2^+\) can be analyzed using this theory.
• Molecular orbitals are filled according to energy levels: first bonding molecular orbitals, then antibonding ones.

EXPLANATION:

• O₂:
  • Electronic configuration is \((1s\sigma_{g})^2 (1s\sigma_{u}^*)^2 (2s\sigma_{g})^2 (2s\sigma_{u}^*)^2 (2p\sigma_{g})^2 (2pπ_u)^4 (2pπ_g^*)^2\)
  • Total bond order: 2 (from MOT theory:1/2(10 - 6) = 2 )
  • Contains one sigma -bond and one π  -bonds.
• O₂⁺:
  • Electronic configuration is \((1s\sigma_{g})^2 (1s\sigma_{u}^*)^2 (2s\sigma_{g})^2 (2s\sigma_{u}^*)^2 (2p\sigma_{g})^2 (2pπ_u)^4 (2pπ_g^*)^1\)
  • Total bond order: 1.5 (from MOT theory:1/2(9 - 6) = 1.5 )
  • Contains one sigma -bond, one π -bonds, and a half sigma* -bond due to the unpaired electron.
• N₂⁺:
  • Electronic configuration is \((1s\sigma_{g})^2 (1s\sigma_{u}^*)^2 (2s\sigma_{g})^2 (2s\sigma_{u}^*)^2 (2p\sigma_{g})^2 (2pπ_u)^4 (2pπ_g^*)^1\)
  • Total bond order: 2.5 (from MOT theory: 1/2(10 - 5) = 2.5 )
  • Contains one sigma -bond, two π  -bonds, and a half sigma* -bond due to the unpaired electron.
• N₂:
  • Electronic configuration is \((1s\sigma_{g})^2 (1s\sigma_{u}^*)^2 (2s\sigma_{g})^2 (2s\sigma_{u}^*)^2 (2p\sigma_{g})^2 (2pπ_u)^4\)
  • Total bond order: 3 (from MOT theory: 1/2(10 - 4) = 3 )
  • Contains one sigma -bond and two pi -bonds.

Among these molecules,  N₂⁺ contains 2 pi bonds and half a sigma bond.

The correct option is N2+