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NCERT Exemplar · Q9

Q.Which molecule/ion out of the following does not contain unpaired electrons?

(i) N2^+
(ii) O2
(iii) O2^2-
(iv) B2
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Unpaired electrons appear in species with odd total electrons or when molecular orbital filling leaves singly occupied orbitals. Only O22−\mathrm{O}_2^{2-} has all electrons paired in its molecular orbitals, making it diamagnetic.

Why molecular orbital theory reveals magnetic character

When atoms combine into molecules, their atomic orbitals merge into molecular orbitals that span the entire molecule. Electrons fill these MOs according to the aufbau principle, just as in atoms. The key insight: a species is paramagnetic (attracted to a magnetic field) if it has unpaired electrons, and diamagnetic if all electrons are paired.

For homonuclear diatomic molecules of the second period, the MO energy sequence depends on whether we're dealing with lighter atoms (B2\mathrm{B}_2, C2\mathrm{C}_2, N2\mathrm{N}_2) or heavier ones (O2\mathrm{O}_2, F2\mathrm{F}_2). The difference lies in the relative energies of σ2pz\sigma_{2p_z} and π2p\pi_{2p} orbitals due to ss-pp mixing.

For B2\mathrm{B}_2, C2\mathrm{C}_2, N2\mathrm{N}_2:

σ1s<σ1s∗<σ2s<σ2s∗<π2px=π2py<σ2pz<π2px∗=π2py∗<σ2pz∗\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \pi_{2p_x} = \pi_{2p_y} < \sigma_{2p_z} < \pi^*_{2p_x} = \pi^*_{2p_y} < \sigma^*_{2p_z}

For O2\mathrm{O}_2, F2\mathrm{F}_2:

σ1s<σ1s∗<σ2s<σ2s∗<σ2pz<π2px=π2py<π2px∗=π2py∗<σ2pz∗\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi^*_{2p_x} = \pi^*_{2p_y} < \sigma^*_{2p_z}

Let's examine each species systematically.

Step-by-step analysis

1. N2+\mathrm{N}_2^+ (14 electrons)

Neutral N2\mathrm{N}_2 has 14 electrons. The cation N2+\mathrm{N}_2^+ has 13 electrons. Using the lighter-atom sequence:

(σ1s)2(σ1s∗)2(σ2s)2(σ2s∗)2(π2p)4(σ2pz)1(\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\pi_{2p})^4 (\sigma_{2p_z})^1

The last electron sits alone in σ2pz\sigma_{2p_z}. One unpaired electron → paramagnetic.

2. O2\mathrm{O}_2 (16 electrons)

Oxygen molecule has 16 electrons total. Using the heavier-atom sequence:

(σ1s)2(σ1s∗)2(σ2s)2(σ2s∗)2(σ2pz)2(π2p)4(π2p∗)2(\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p})^4 (\pi^*_{2p})^2

The two antibonding π∗\pi^* orbitals are degenerate. By Hund's rule, the two electrons occupy them singly with parallel spins: (π2px∗)1(π2py∗)1(\pi^*_{2p_x})^1 (\pi^*_{2p_y})^1. Two unpaired electrons → paramagnetic (famously, liquid oxygen is attracted to magnets).

3. O22−\mathrm{O}_2^{2-} (18 electrons)

The peroxide ion adds two electrons to neutral O2\mathrm{O}_2:

(σ1s)2(σ1s∗)2(σ2s)2(σ2s∗)2(σ2pz)2(π2p)4(π2p∗)4(\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p})^4 (\pi^*_{2p})^4 …

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