Q.Write the formula to calculate the bond order of a molecule.

CO is the only one of the four species that is NOT paramagnetic — it is diamagnetic.

Using molecular orbital theory:

• N2+ (13 electrons, isoelectronic-type with an odd electron count) has 1 unpaired electron — paramagnetic.
• CO (14 electrons, isoelectronic with N2) has a fully-paired MO configuration — diamagnetic. …

O2 has 2 unpaired electrons (in the π2px and π2py antibonding orbitals), explaining its paramagnetism (visible in liquid O2 being attracted to a magnet).

By molecular orbital theory, the electronic configuration of O2 is:

$\sigma_{1s}^2 \sigma_{1s}^{*2} \sigma_{2s}^2 \sigma_{2s}^{*2} \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^{*1} \pi_{2p_y}^{*1}$

…

Oxygen is genuinely paramagnetic (assertion true), but its two unpaired electrons sit in the antibonding pi*2p molecular orbitals, not the bonding ones -- so the reason, as worded, is false.

By molecular orbital theory, the electronic configuration of O2 (16 electrons total) is:

sigma1s2 sigma1s2 sigma2s2 sigma2s2 sigma2pz2 pi2px2 pi2py2 pi2px1 pi2py1

The last two electrons singly occupy the two degenerate antibonding pi* molecular orbitals (pi2px and pi2py), each with one unpaired electron (following Hund's rule). This gives O2 a net of two unpaired electrons, which is exactly why it is paramagnetic (attracted into a magnetic field) -- a result MO theory correctly predicts, unlike simple Lewis/valence-bond structures which show all electrons paired …

Molecular orbital theory shows O2 and O2+ both have unpaired electrons in their pi* antibonding orbitals (paramagnetic), while O2^2- (peroxide, 18 valence-region electrons) has those pi* orbitals completely filled, leaving no unpaired electrons — so it is diamagnetic.

Building the molecular orbital electron configuration for the O2 family (order: sigma2s, sigma2s, sigma2pz, pi2px = pi2py, pi2px = pi2py, sigma2pz):

O2 (16 electrons): (sigma2s)2 (sigma2s)2 (sigma2pz)2 (pi2px)2(pi2py)2 (pi2px)1(pi2py)1 (sigma2pz)0

→ 2 unpaired electrons in the two pi* orbitals → PARAMAGNETIC.

O2+ (15 electrons, one less than O2): removes one electron from a pi* orbital → (pi2px)1(pi2py)0

→ 1 unpaired electron → PARAMAGNETIC.

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