Which one of the following is a diamagnetic ion? (a) \(\mathrm{Cu}^{2+}\) (b) \(\mathrm{Mn}^{2+}\) (c) \(\mathrm{Sc}^{3+}\) (d) \(\mathrm{Co}^{2+}\)

Understanding electron configuration is key to comprehending a variety of chemical properties, including magnetic characteristics. Electron configuration refers to the arrangement of electrons around the nucleus of an atom in atomic orbitals. According to the aufbau principle, electrons fill lower-energy orbitals first before moving to higher-energy orbitals. The order of filling is based on n+l rules, where 'n' stands for the principal quantum number and 'l' for the azimuthal quantum number.

For ions, the electron configuration can change depending on the charge. A positive charge indicates the loss of electrons. As seen in the step-by-step solution, to determine the electron configuration of an ion like \(\mathrm{Cu}^{2+}\), we start with the neutral copper atom and remove two electrons from the highest energy orbitals, which in this case would be the 4s and 3d orbitals. It's essential to correctly determine the electron configuration, as this reveals whether the electrons are paired or unpaired, which is directly related to the concept of diamagnetism.

The magnetic moment of an atom or ion is a vector quantity that represents the strength and direction of its magnetism. It arises from the spin and orbital motion of electrons. Each electron has a magnetic moment due to its spin, and when electrons are paired, their opposite spins produce magnetic fields that cancel out, resulting in no overall magnetic moment. This is the case with diamagnetic materials.

In the context of the given problem, diamagnetic ions such as \(\mathrm{Sc}^{3+}\) have no unpaired electrons, and subsequently no net magnetic moment. This contrasts with ions like \(\mathrm{Cu}^{2+}\) or \(\mathrm{Mn}^{2+}\) that have unpaired electrons, giving rise to a net magnetic moment and thus showing paramagnetic or even ferromagnetic properties. Knowing the relationship between electron configuration and magnetic moment helps in identifying whether a species is diamagnetic.

The periodic table is an organized chart of elements arranged in increasing order of atomic number. It is a powerful tool for predicting the properties of elements, including their electron configurations. Each row, or period, in the periodic table corresponds to the principal quantum number \(n\), while columns, or groups, share common chemical characteristics. Learning how to read the periodic table is crucial for determining the electron configuration, especially when dealing with ions.

When identifying the diamagnetic ion, as with \(\mathrm{Sc}^{3+}\), we utilized the periodic table to determine the ground-state electron configuration before considering the effect of ionization. By locating an element within the periodic table and understanding its electron configuration, we can deduce the magnetic properties of atoms and ions, aiding in solving problems involving magnetism and chemical reactivity.