Q.Dimagnetic species are those which contain no unpaired electrons. Which among the following are dimagnetic? (Note: more than one of the given options may be correct.)

The key idea is molecular orbital theory: bond order and magnetic behaviour depend on the number of electrons in bonding and antibonding orbitals.

Step 1 — Electron configurations (diatomic molecules up to $O_2$):

For $N_2$ (14 e⁻): \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 — all paired, diamagnetic.

For $N_2^{2-}$ (16 e⁻): add 2 e⁻ to $\pi^*_{2p}$ orbitals → two unpaired, paramagnetic. …

The key to this question is understanding that diamagnetic substances have all electrons paired, while paramagnetic substances have one or more unpaired electrons. For diatomic molecules, we can determine the electron configuration using the molecular orbital (MO) theory. The number of unpaired electrons directly follows from the filling of bonding and antibonding orbitals.

Let’s work through each species step by step.

1. N₂ (Nitrogen molecule)

   Nitrogen has 7 electrons per atom, so N₂ has 14 electrons total. The MO order for homonuclear diatomic molecules up to N₂ is:

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

   All 14 electrons fill these orbitals in pairs. The last filled orbital is $\sigma_{2p_z}^2$, which is bonding. There are no unpaired electrons.

   Bond order = $\frac{10 - 4}{2} = 3$ (strong triple bond).

   N₂ is diamagnetic.

2. N₂²⁻ (Nitrogen dianion)

   This species has 14 + 2 = 16 electrons. The extra two electrons go into the next available orbitals: the $\pi_{2p_x}^{*}$ and $\pi_{2p_y}^{*}$ orbitals (which are degenerate). According to Hund’s rule, each of these gets one electron with parallel spins before pairing. So the configuration becomes:

   $\ldots \pi_{2p_x}^2 = \pi_{2p_y}^2, \sigma_{2p_z}^2, \pi_{2p_x}^{*1} = \pi_{2p_y}^{*1}$

   There are two unpaired electrons.

   Bond order = $\frac{10 - 6}{2} = 2$ (a double bond).

   N₂²⁻ is paramagnetic.

3. O₂ (Oxygen molecule)

   Oxygen has 8 electrons per atom, so O₂ has 16 electrons. For O₂ and beyond, the MO order changes slightly: the $\sigma_{2p_z}$ orbital is higher in energy than the $\pi_{2p}$ orbitals. The filling order is:

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

   The last two electrons go into the degenerate $\pi^{*}$ orbitals, one each (Hund’s rule). This gives two unpaired electrons. …