Problem 196 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following species is diamagnetic in nature? (a) \(\mathrm{H}_{2}^{-}\) (b) \(\mathrm{H}_{2}\) (c) \(\mathrm{H}_{2}^{+}\) (d) \(\mathrm{He}_{2}^{+}\)

Step-by-Step Solution

Answer

The species \( \mathrm{H}_{2} \) is diamagnetic.

Step 1: Understand Diamagnetism

Diamagnetic substances are those which possess no unpaired electrons. They are not attracted to a magnetic field, and might be even slightly repelled by it. This means, when analyzing a species, we need to determine if all electrons are paired.

Step 2: Molecular Orbital (MO) Theory for Each Species

Use molecular orbital (MO) theory to write the electron configuration for each given species: - For \( \mathrm{H}_{2}^{-} \), MO configuration is \( \sigma_{1s}^{2}(\mathrm{H}_{2})\), but with an extra electron: \( \sigma_{1s}^{2}\sigma_{1s}^{*1} \), making it have an unpaired electron.- \( \mathrm{H}_{2} \) has the MO configuration \( \sigma_{1s}^{2} \), with no unpaired electrons.- \( \mathrm{H}_{2}^{+} \) has the MO configuration \( \sigma_{1s}^{1} \), one unpaired electron.- \( \mathrm{He}_{2}^{+} \) has the MO configuration \( \sigma_{1s}^{2}\sigma_{1s}^{*1} \), with one unpaired electron.

Step 3: Identify the Diamagnetic Species

From the above configurations:- \( \mathrm{H}_{2}^{-} \) is paramagnetic (unpaired electron present).- \( \mathrm{H}_{2} \) is diamagnetic (all electrons are paired).- \( \mathrm{H}_{2}^{+} \) is paramagnetic (unpaired electron present).- \( \mathrm{He}_{2}^{+} \) is paramagnetic (unpaired electron present).Therefore, \( \mathrm{H}_{2} \) is the only species that is diamagnetic.

Key Concepts

Understanding Molecular Orbital Theory

Molecular Orbital (MO) Theory provides us with a deeper understanding of how electrons are distributed in molecules. Unlike the atomic orbital theory, which describes the electron configuration within a single atom, MO theory explains how atomic orbitals combine when atoms bond to form molecules. This approach gives a comprehensive picture of molecular bonding.

In MO theory, atomic orbitals overlap to form molecular orbitals, which are delocalized over multiple atoms rather than centered on a single atom. These molecular orbitals are classified as bonding, anti-bonding, or non-bonding, based on their energy levels and how they affect molecular stability.

• Bonding Orbitals: These are lower in energy than the atomic orbitals they come from, and filling these orbitals contributes to the stability of the molecule.
• Anti-bonding Orbitals: These have higher energy levels and filling them can decrease molecular stability.
• Non-bonding Orbitals: Energy levels similar to their respective atomic orbitals and don't significantly affect molecular stability.

When constructing a molecular orbital diagram, electrons fill the lowest energy MO first, according to the Aufbau principle. Important rule to remember: In diamagnetic species, all electrons in these MOs are paired, contributing to the lack of magnetic attraction.

Electron Configuration and its Role in Magnetism

Electron configuration pertains to the distribution of electrons among the orbitals of atoms or molecules. When examining electron configurations, we can determine certain magnetic properties of elements or compounds.

For molecules like \(\mathrm{H}_{2}\), the electron configuration will indicate whether we have paired or unpaired electrons. For instance:

• In \(\mathrm{H}_{2}\), the configuration \(\sigma_{1s}^{2}\) signifies a filled bonding molecular orbital with all electrons paired showcasing its diamagnetic nature.
• In \(\mathrm{H}_{2}^{-} \) and \(\mathrm{H}_{2}^{+}\), configurations show unpaired electrons in their anti-bonding or bonding MO, giving them paramagnetic properties.

A filled orbital with paired electrons results in no net magnetic moment, thus making substances like \(\mathrm{H}_{2}\) resistant to external magnetic fields. Conversely, unpaired electrons in \(\mathrm{H}_{2}^{-}\) make it responsive to such fields.

The Nature of Paramagnetism

Paramagnetism is a property that arises in substances containing unpaired electrons. Unlike diamagnetic materials, paramagnetic substances are attracted to magnetic fields, albeit weakly. This occurs because these unpaired electrons have individual magnetic moments that align with an external magnetic field, thereby producing a net magnetic effect.

For example, both \(\mathrm{H}_{2}^{+}\) and \(\mathrm{He}_{2}^{+}\) are paramagnetic. Their molecular orbital configurations, \(\sigma_{1s}^{1}\) and \(\sigma_{1s}^{2}\sigma_{1s}^{*1}\) respectively, contain unpaired electrons that contribute to these characteristics.

• In magnetic fields, the unpaired electrons in these ions align, resulting in paramagnetism.
• Unlike diamagnetic species, they are attracted into the magnetic field, making them useful for various applications such as MRI machines.

Understanding these concepts illuminates why paramagnetic substances behave as they do under magnetic conditions, in contrast to diamagnetic ones which naturally repel.