Paramagnetism is exhibited by: (a) \(\mathrm{ClO}_{2}\) (b) \(\mathrm{Cl}_{2} \mathrm{O}\) (c) \(\mathrm{ClO}_{3}\) (solid state) (d) Both A, B

In chemistry, understanding the magnetic properties of molecules helps us predict how they interact with magnetic fields. A fundamental aspect of this is the number of unpaired electrons present in a molecule, as they are the ones responsible for magnetic behavior. When a molecule has one or more unpaired electrons, it can exhibit paramagnetism, meaning it will be attracted to an external magnetic field.

Molecules can also be diamagnetic if they lack unpaired electrons and thus are repelled by a magnetic field. Paramagnetic materials have permanent magnetic moments, even in the absence of an external field, due to those unpaired electrons. Analyzing a molecule's electronic configuration, we can deduce its magnetic properties. We also use experiments, such as measuring its interaction with a magnetic field or employing spectroscopic methods to determine the exact nature of this paramagnetism.

Role of Unpaired Electrons in Magnetism

It's the unpaired electrons in an atom or molecule that are central to its magnetic properties. Electrons have a property called 'spin', and electrons in a pair have opposite spins that cancel each other out magnetically. Unpaired electrons, however, do not have a partner to cancel out their magnetic moment, so they contribute to an overall magnetic effect.

Determining Unpaired Electrons

To determine if a molecule has unpaired electrons, we look at its electron configuration. Techniques such as Electron Spin Resonance (ESR) spectroscopy can also help identify the presence of unpaired electrons. In the exercise example, identifying the molecule with an odd number of valence electrons quickly points to the likelihood of unpaired electrons, hence paramagnetic behavior.

Molecular Orbital (MO) Theory provides a nuanced understanding of chemical bonding and the magnetic properties of molecules. This theory posits that atomic orbitals combine to form molecular orbitals, which are then filled with the molecule's electrons. There are bonding molecular orbitals, which are lower in energy and promote stability, and antibonding molecular orbitals, which are higher in energy and can destabilize a molecule.

The filling of these molecular orbitals is subject to the Pauli Exclusion Principle and Hund's Rule, leading to a particular distribution of electrons. If there are electrons in antibonding or non-bonding molecular orbitals, they may remain unpaired, contributing to paramagnetism. MO Theory thus explains why certain molecules with an even number of electrons could still be paramagnetic due to their molecular orbital structure. For complex molecules, detailed MO diagrams are often required to determine the distribution of electrons and the resulting magnetic properties.