Problem 70 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is diamagnetic? (a) \(\mathrm{H}_{2}^{+}\) (b) \(\mathrm{O}_{2}\) (c) \(\mathrm{Li}_{2}\) (d) \(\mathrm{He}_{2}^{+}\)

Step-by-Step Solution

Answer

(c) \(\mathrm{Li}_{2}\) is diamagnetic.

Step 1: Define Diamagnetism

Diamagnetic substances have all their electrons paired. As a result, they do not have any net magnetic moment and are repelled by a magnetic field.

Step 2: Understand the Molecular Orbital Theory for Diatomics

Using molecular orbital theory, we populate the available molecular orbitals for diatomic molecules by the given electron count, starting from the lowest energy orbitals and going up.

Step 3: Apply to \\(\mathrm{H}_{2}^{+}\\)

\(\mathrm{H}_{2}^{+}\) has one electron. In molecular orbital terms, it fills the \(\sigma_{1s}\) orbital with one electron. As it has an unpaired electron, it is not diamagnetic.

Step 4: Apply to \\(\mathrm{O}_{2}\\)

Oxygen, \(\mathrm{O}_{2}\), has a total of 16 electrons. Filling the molecular orbitals up to \(\pi^{*}_{2p}\), it has two unpaired electrons in these antibonding orbitals, making it paramagnetic.

Step 5: Apply to \\(\mathrm{Li}_{2}\\)

\(\mathrm{Li}_{2}\) has a total of 6 electrons, filling the \(\sigma_{1s}\), \(\sigma^{*}_{1s}\), and \(\sigma_{2s}\) molecular orbitals. All electrons are paired, so \(\mathrm{Li}_{2}\) is diamagnetic.

Step 6: Apply to \\(\mathrm{He}_{2}^{+}\\)

\(\mathrm{He}_{2}^{+}\) has a total of 3 electrons. The orbitals are filled as \(\sigma_{1s}^2\) and \(\sigma^{*}_{1s}^1\), resulting in one unpaired electron, making it paramagnetic.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory (MOT) is a fundamental concept in chemistry that explains how atomic orbitals combine to form molecular orbitals. These are spread over the entire molecule, rather than being confined to a single bond or pair of atoms. Unlike atomic orbitals, which are associated with individual atoms, molecular orbitals merge them together across the molecule.

Key features of Molecular Orbital Theory include:

• Molecular orbitals are filled with electrons in a way that minimizes energy, starting with the lowest energy orbitals first.
• Each molecular orbital can hold a maximum of two electrons with opposite spins, according to the Pauli exclusion principle.
• Different molecular orbitals include bonding orbitals (which lower the energy of a molecule and make it more stable) and antibonding orbitals (which increase energy and make the molecule less stable).

Understanding this theory helps explain phenomena such as the bonding and magnetic properties of molecules. For example, in diatomic molecules, we start filling the molecular orbitals from the lowest energy level upwards based on the number of electrons in the molecule.

Paramagnetism

Paramagnetism is a type of magnetism that occurs in materials with unpaired electrons. This property is due to the presence of these unpaired electrons which have magnetic moments that align with an external magnetic field.

Key aspects of paramagnetism include:

• Materials with one or more unpaired electrons display paramagnetism.
• These materials are attracted to external magnetic fields.
• The induced magnetic attraction is usually weak compared to ferromagnetism (like in iron magnets).

For example, in oxygen (\(\mathrm{O}_{2}\)), the presence of unpaired electrons in the highest occupied molecular orbitals results in paramagnetic behavior. This is because the magnetic moments of the unpaired electrons do not cancel each other out, allowing them to interact with an external magnetic field.

Electron Pairing

Electron pairing refers to the distribution of electrons in atomic or molecular orbitals, where two electrons occupy the same orbital. They must have opposite spins as dictated by the Pauli exclusion principle. When electrons are paired, the magnetic moments of the pair cancel out, resulting in no net magnetic moment.

Important points about electron pairing include:

• Electron pairing results in a stable arrangement of electrons within an atom or molecule.
• Paired electrons contribute to diamagnetism, where there are no unpaired electrons in the molecule.
• Diamagnetic substances do not interact with magnetic fields.

For instance, in diatomic lithium (\(\mathrm{Li}_{2}\)), all six electrons are involved in electron pairing within their molecular orbitals, ensuring that the molecule is diamagnetic. This complete pairing contrasts with molecules like oxygen, where unpaired electrons exist, leading to paramagnetism.