Question

Effective magnetic moment of \(\mathrm{Sc}^{3+}\) ion is: (a) 0 (b) \(1.73\) (c) \(2.83\) (d) \(3.87\)

Short answer

The effective magnetic moment of Sc^{3+} is 0.

Step-by-step solution

Determine Electron Configuration

Scandium (Sc) has an atomic number of 21. In the case of the Sc^{3+} ion, three electrons are removed from the neutral scandium atom. The electron configuration of neutral Sc is [Ar]3d^1 4s^2. Removing three electrons results in [Ar], which means all 3d and 4s electrons are removed.

Determine Unpaired Electrons

The electron configuration [Ar] means that all orbitals are filled, and there are no remaining unpaired electrons in the Sc^{3+} ion.

Calculate Magnetic Moment

The effective magnetic moment ( ext{ ext{}) can be calculated using the formula  ext{m} = b(b(b+2)) units, where  ext{m} is the number of unpaired electrons. As calculated, m=0. This results in an effective magnetic moment of 0.

Key concepts

Electron Configuration

Electron configuration is a way of representing the arrangement of electrons in an atom or ion. For an atom, the electrons are placed in specific energy levels and sublevels around the nucleus. This configuration helps in understanding the chemical properties and reactivity of the element.

To determine the electron configuration of an ion, we need to consider its charge. In the case of the scandium ion, \( \mathrm{Sc}^{3+} \), we start with the neutral scandium atom. Scandium has an atomic number of 21, which means it has 21 protons and, in the neutral state, 21 electrons. Its ground state electron configuration is \([\text{Ar}]3d^1 4s^2\).

When scandium becomes \( \mathrm{Sc}^{3+} \), it loses three electrons. Electrons are removed from the outermost shell first, so we remove the two 4s electrons and one 3d electron, leaving just the configuration of \([\text{Ar}]\). After removing these electrons, the scandium \( \mathrm{Sc}^{3+} \) ion has an electron configuration of \([\text{Ar}]\), indicating a stable, noble gas arrangement.

Unpaired Electrons

Unpaired electrons are electrons that are alone in an orbital and not part of an electron pair. These electrons are pivotal in determining the magnetic properties of an atom or ion.

In the context of electron configurations, each electron in an atom occupies an orbital, and these orbitals can hold a maximum of two electrons with opposite spins. When an orbital contains only one electron, it is termed unpaired.

• Unpaired electrons contribute to magnetism because they have a magnetic moment due to their spin.
• If there are no unpaired electrons, the substance is typically diamagnetic, meaning it does not interact with magnetic fields.

For the \( \mathrm{Sc}^{3+} \) ion, its electron configuration is \([\text{Ar}]\), with no unpaired electrons present. The absence of unpaired electrons indicates that the \( \mathrm{Sc}^{3+} \) ion is diamagnetic, and it does not exhibit any magnetic properties under normal circumstances.

Scandium Ion

The scandium ion, represented as \( \mathrm{Sc}^{3+} \), is a positively charged form of scandium. Scandium itself is a transition metal found in the same group as yttrium and lanthanides, typically exhibiting the oxidation state of +3 when it forms ions.

This \( +3 \) charge results from the atom losing three electrons, which changes its electron configuration. Losing these electrons results in a stable electronic arrangement analogous to that of a noble gas.

• Scandium, in its ion form \( \mathrm{Sc}^{3+} \), often partakes in various chemical reactions and is a component in materials with specific properties.
• The lack of unpaired electrons, as a result of reaching the \( \mathrm{Sc}^{3+} \) oxidation state, typically leads to the ion being non-magnetic.

Understanding scandium in its ionic form is crucial in fields such as materials science, where it is used in some metal alloys, and in the study of chemical reactions where it may serve as a catalyst.