Question

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

Short answer

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

Step-by-step solution

Understand Diamagnetism

Diamagnetism occurs in molecules where all electrons are paired. In contrast, paramagnetism is observed when unpaired electrons are present. We need to determine the electron configuration of each molecule to find out which one has only paired electrons.

Analyze Each Option

Evaluate the electron configurations of the given molecules:- (a) \( \mathrm{H}_{2}^{+} \): This has 1 electron, unpaired, hence paramagnetic.- (b) \( \mathrm{O}_{2} \): According to the molecular orbital theory, \( \mathrm{O}_{2} \) has two unpaired electrons in the \( \pi^{*} \) antibonding orbitals, hence paramagnetic.- (c) \( \mathrm{Li}_{2} \): \( \mathrm{Li}_{2} \) has an electron configuration of \( (\sigma_{1s})^2 (\sigma^{*}_{1s})^2 (\sigma_{2s})^2 \), with all electrons paired, hence diamagnetic.- (d) \( \mathrm{He}_{2} \): This molecule, theoretical in nature, would have paired electrons in \( \sigma_{1s} \) and \( \sigma^{*}_{1s} \), making it diamagnetic but unstable.

Identify the Diamagnetic Molecule

After analysis, \( \mathrm{Li}_{2} \) has all its electrons paired, making it the stable diamagnetic molecule.

Key concepts

Molecular Orbital Theory

Molecular Orbital (MO) theory is a fundamental concept used to understand the bonding in molecules. Unlike the localized electron model, MO theory treats electrons in a molecule as being spread out over the entire molecule, occupying molecular orbitals that can extend over several atoms. These orbitals are formed from the combination of atomic orbitals, and they can be classified as bonding or antibonding.

• Bonding orbitals are lower in energy compared to the atomic orbitals from which they formed, leading to a more stable molecule.
• Antibonding orbitals, denoted with an asterisk (*), are higher in energy, which can lead to instability in the presence of unpaired electrons.

Molecular orbital theory is especially useful when analyzing diatomic molecules like \( ext{O}_2 \) and \( ext{Li}_2 \), as it helps predict their magnetic properties (paramagnetism or diamagnetism) by examining their electron configurations.

Electron Configuration

Understanding electron configuration is key when analyzing molecular properties. An electron configuration is an arrangement of electrons around an atom's nucleus or within a molecule's orbitals. In the context of molecular orbital theory, electron configurations are expressed through the occupation of molecular orbitals by electrons:

• Molecular orbitals are filled in order of increasing energy, following Hund's rule and the Pauli exclusion principle.
• Each molecular orbital can hold up to two electrons with opposite spins.

For example, the electron configuration of \( ext{Li}_2 \) as \( ( ext{σ}_{1s})^2 ( ext{σ}^{*}_{1s})^2 ( ext{σ}_{2s})^2 \) implies that all electrons are paired and therefore, the molecule is diamagnetic. Recognizing how electrons fill these orbitals allows us to predict properties like magnetism and stability of molecules.

Paired and Unpaired Electrons

Electrons can be paired or unpaired within molecular orbitals, and this significantly affects a molecule's magnetic properties. Paired electrons are those that occupy the same orbital but with opposite spins. Unpaired electrons are found alone in an orbital.

• Molecules with all paired electrons are diamagnetic, meaning they are not attracted to a magnetic field and may even slightly repel it.
• In contrast, molecules with one or more unpaired electrons are paramagnetic, showing a tendency to be attracted to magnetic fields.

In the given exercise, \( ext{Li}_2 \) is diamagnetic because all electrons are paired in its molecular orbitals. Analyzing the electron configuration helps to determine which electrons are paired and which are not, allowing for predictions about the magnetism of the molecule. This distinction is crucial in chemistry when examining and predicting molecule behavior based on electronic structure.