Concept: Molecular Orbital Theory and Paramagnetism

Paramagnetism arises in substances that have unpaired electrons in their molecular orbitals. Diamagnetism, on the other hand, occurs when all electrons are paired. To determine if a molecule is paramagnetic or diamagnetic, we can use Molecular Orbital (MO) theory to fill electrons into the molecular orbitals and check for unpaired electrons.

Why (D) is correct:

Let's analyze the molecular orbital configurations for each option:

• A) ${\mathrm{N}}_2$ (Total electrons = 14):
  The MO configuration for ${\mathrm{N}}_2$ is $({\sigma }_{1s}{)}^2({\sigma }_{1s}^{\ast }{)}^2({\sigma }_{2s}{)}^2({\sigma }_{2s}^{\ast }{)}^2({\pi }_{2p_x}{)}^2({\pi }_{2p_y}{)}^2({\sigma }_{2p_z}{)}^2$. All electrons are paired. Therefore, ${\mathrm{N}}_2$ is diamagnetic.
• B) ${\mathrm{H}}_2$ (Total electrons = 2):
  The MO configuration for ${\mathrm{H}}_2$ is $({\sigma }_{1s}{)}^2$. All electrons are paired. Therefore, ${\mathrm{H}}_2$ is diamagnetic.
• C) ${\mathrm{Li}}_2$ (Total electrons = 6):
  The MO configuration for ${\mathrm{Li}}_2$ is $({\sigma }_{1s}{)}^2({\sigma }_{1s}^{\ast }{)}^2({\sigma }_{2s}{)}^2$. All electrons are paired. Therefore, ${\mathrm{Li}}_2$ is diamagnetic.
• D) ${\mathrm{O}}_2$ (Total electrons = 16):
  The MO configuration for ${\mathrm{O}}_2$ is $({\sigma }_{1s}{)}^2({\sigma }_{1s}^{\ast }{)}^2({\sigma }_{2s}{)}^2({\sigma }_{2s}^{\ast }{)}^2({\sigma }_{2p_z}{)}^2({\pi }_{2p_x}{)}^2({\pi }_{2p_y}{)}^2({\pi }_{2p_x}^{\ast }{)}^1({\pi }_{2p_y}^{\ast }{)}^1$. According to Hund's rule, the two electrons in the degenerate ${\pi }_{2p}^{\ast }$ orbitals occupy them singly with parallel spins. Thus, ${\mathrm{O}}_2$ has two unpaired electrons. Therefore, ${\mathrm{O}}_2$ is paramagnetic.

Correct Answer: (D)