Question

(a) What does the term diamagnetism mean? (b) How does a diamagnetic substance respond to a magnetic field? (c) Which of the following ions would you expect to be diamagnetic: \(\mathrm{N}_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{Be}_{2}^{2+}, \mathrm{C}_{2}^{-} ?\)

Short answer

Diamagnetism refers to substances having no net internal magnetic field due to all electrons being paired. Diamagnetic substances repel external magnetic fields and do not retain magnetization. Among the given ions \(\mathrm{N}_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{Be}_{2}^{2+}\), and \(\mathrm{C}_{2}^{-}\), the diamagnetic ions are \(\mathrm{N}_{2}^{2-}\) and \(\mathrm{Be}_{2}^{2+}\).

Step-by-step solution

Define diamagnetism

Diamagnetism refers to the property of a substance where it has no net internal magnetic field (or moment) because all its electrons are paired, which means they cancel each other's magnetic fields. Diamagnetic substances repel external magnetic fields and do not get attracted to them.

Response of a diamagnetic substance to a magnetic field

When an external magnetic field is applied to a diamagnetic substance, it induces a weak opposing magnetic field within the substance. This induced field opposes the applied field, causing the substance to be slightly repelled by the magnetic field. Diamagnetic substances do not retain any magnetization in the absence of an external magnetic field.

Determine diamagnetic species among the given ions

We will analyze the molecular orbital electron configurations of the ions \(\mathrm{N}_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{Be}_{2}^{2+},\) and \(\mathrm{C}_{2}^{-}\) to determine whether they are diamagnetic or not. (a) \(\mathrm{N}_{2}^{2-}\): Since N has 7 valence electrons, \(\mathrm{N}_{2}\) has 14 valence electrons. With the 2 extra electrons in \(\mathrm{N}_{2}^{2-}\), there are 16 valence electrons, which means that all orbitals up to and including the \(\pi_{2p}(4)\) orbitals are completely filled. Thus, all electrons are paired, and \(\mathrm{N}_{2}^{2-}\) is diamagnetic. (b) \(\mathrm{O}_{2}^{2-}\): An O atom has six valence electrons, resulting in \(\mathrm{O}_{2}\) having 12 valence electrons. \(\mathrm{O}_{2}^{2-}\) has 14 valence electrons, with 8 electrons filling the \(\sigma_{1s}(2), \sigma_{1s}^{*}(2), \sigma_{2s}(2),\) and \(\sigma_{2s}^{*}(2)\) orbitals, and the remaining 6 electrons partially filling the \(\pi_{2p}(4)\) and \(\pi_{2p}^{*}(2)\) orbitals. Since there are unpaired electrons in the \(\pi_{2p}^{*}\) orbitals, \(\mathrm{O}_{2}^{2-}\) is not diamagnetic. (c) \(\mathrm{Be}_{2}^{2+}\): A Be atom has two valence electrons, so \(\mathrm{Be}_{2}\) has 4 valence electrons. \(\mathrm{Be}_{2}^{2+}\) has only 2 valence electrons, thus only filling the \(\sigma_{1s}(2)\) orbital. All electrons are paired, so \(\mathrm{Be}_{2}^{2+}\) is diamagnetic. (d) \(\mathrm{C}_{2}^{-}\): A C atom has 4 valence electrons, which results in \(\mathrm{C}_{2}\) having 8 valence electrons. \(\mathrm{C}_{2}^{-}\) has 9 valence electrons, with 8 electrons filling the \(\sigma_{1s}(2), \sigma_{1s}^{*}(2), \sigma_{2s}(2),\) and \(\sigma_{2s}^{*}(2)\) orbitals, and one unpaired electron in the \(\pi_{2p}(1)\) orbital. Since there is one unpaired electron, \(\mathrm{C}_{2}^{-}\) is not diamagnetic.

Conclusion

Among the given ions \(\mathrm{N}_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{Be}_{2}^{2+},\) and \(\mathrm{C}_{2}^{-}\), the following ions are diamagnetic: - \(\mathrm{N}_{2}^{2-}\) - \(\mathrm{Be}_{2}^{2+}\)

Key concepts

Magnetic Field Response

Understanding the behavior of materials in the presence of a magnetic field is essential in various scientific and technological fields. For diamagnetic substances, their response to an external magnetic field is one of subtle repulsion rather than attraction. When a magnetic field is applied, these materials create an induced magnetic field in the opposite direction, effectively pushing back against the external influence. This occurs due to the presence of paired electrons which circulate in such a way as to oppose the applied magnetic field.

From a practical standpoint, diamagnetism may be considered weak compared to other types of magnetic behaviors, such as ferromagnetism or paramagnetism, because no permanent magnetization is observed once the external field is removed. This transient and counteractive property is why diamagnetic materials, like bismuth or water, may levitate above a strong magnet but will never cling to it as iron does.

Molecular Orbital Electron Configurations

Delving deeper into the atomic level, molecular orbital (MO) theory provides a framework for predicting the electronic structure of molecules and ions. In MO theory, atomic orbitals from individual atoms combine to form molecular orbitals that are spread across the molecule. Electrons within a molecule can occupy these MOs, which are classified as bonding, non-bonding, or anti-bonding, depending on their energy levels and the constructive or destructive interference of the atomic wave functions.

For a layperson's interpretation, you can think of these molecular orbitals as houses where electrons live, with bonding orbitals acting as cozy low-energy homes that stabilize the molecule. Anti-bonding orbitals, on the other hand, are like less stable, high-energy abodes that can destabilize it. The MO electron configuration is vital for determining whether an ion or molecule is diamagnetic; all electrons must be paired and fill the MOs like responsible roommates who leave no bed empty, to achieve this status.

Paired Electrons

At the core of diamagnetism are paired electrons. These electrons have opposite spins—a property termed as 'spin pairing'. This means that for every electron spinning in one direction, there is another spinning in the opposite direction. This pairing is crucial because it leads to the cancellation of their individual magnetic moments, giving the substance its diamagnetic property.

Think of each pair of electrons as a couple dancing a perfectly coordinated waltz: when they revolve in harmony, their movements cancel out, creating a balanced system without any leftover momentum to contribute to a magnetic field. This concept is akin to two kids on a seesaw who weigh the same; the seesaw remains level because their weights are balanced, analogous to how paired electrons balance each other out magnetically. When an atom or molecule has all its electrons paired up, as seen in the solved exercises for \(\mathrm{N}_2^{2-}\) and \(\mathrm{Be}_2^{2+}\), diamagnetism occurs.