Question

Which of the following lanthanoid ions is diamagnetic? (At nos. \(\mathrm{Ce}=58, \mathrm{Sm}=62, \mathrm{Eu}=63, \mathrm{Yb}=70)\) (1) \(\mathrm{Sm}^{2+}\) (2) \(\mathrm{Eu}^{2+}\) (3) \(\mathrm{Yb}^{2+}\) (4) \(\mathrm{Ce}^{2+}\)

Short answer

\(\text{Yb}^{2+}\) is diamagnetic.

Step-by-step solution

- Understand what diamagnetic means

Diamagnetic substances are those that do not have unpaired electrons. This means all the electrons are paired, resulting in zero net magnetic moment.

- Identify the electronic configurations

Calculate the electronic configurations of each of the ions given.For \(\text{Sm}^{2+}\): Atomic number of Sm is 62. In its 2+ ion form, Sm loses 2 electrons, so its electronic configuration is \[ \text{Sm}^{2+}: [Xe] 4f^6 \]\For \(\text{Eu}^{2+}\): Atomic number of Eu is 63. In its 2+ ion form, Eu loses 2 electrons, so its electronic configuration is \[ \text{Eu}^{2+}: [Xe] 4f^7 \]\For \(\text{Ce}^{2+}\): Atomic number of Ce is 58. In its 2+ ion form, Ce loses 2 electrons, so its electronic configuration is \[ \text{Ce}^{2+}: [Xe] 4f^2 \]\For \(\text{Yb}^{2+}\): Atomic number of Yb is 70. In its 2+ ion form, Yb loses 2 electrons, so its electronic configuration is \[ \text{Yb}^{2+}: [Xe] 4f^{14} \]

- Determine if the ions have unpaired electrons

Examine whether the ions have paired or unpaired electrons:\(\text{Sm}^{2+}\): \[ 4f^6 \] - 6 electrons, some will be unpaired, so it is not diamagnetic. \(\text{Eu}^{2+}\): \[ 4f^7 \] - 7 electrons, some will be unpaired, so it is not diamagnetic. \(\text{Ce}^{2+}\): \[ 4f^2 \] - 2 electrons, some will be unpaired, so it is not diamagnetic.\(\text{Yb}^{2+}\): \[ 4f^{14} \] - 14 electrons, all are paired, so it is diamagnetic.

- Conclusion

Based on the configurations, the only ion with all paired electrons is \(\text{Yb}^{2+}\). Therefore, \(\text{Yb}^{2+}\) is the diamagnetic ion.

Key concepts

diamagnetism

Diamagnetism is a phenomenon observed in materials that do not exhibit any net magnetic moments. This happens because all the electrons in diamagnetic substances are paired.
When electrons are paired, their magnetic fields cancel each other out, resulting in no net magnetic moment. Consequently, diamagnetic materials are slightly repelled by external magnetic fields.
Examples of diamagnetic materials include bismuth, copper, and some lanthanoid ions. These materials generate a weak magnetic field in the opposite direction of the applied external magnetic field.
In the context of lanthanoid ions, being diamagnetic means that the ion has no unpaired electrons in its electronic configuration.

lanthanoid chemistry

Lanthanoids, also known as the lanthanide series, consist of 15 elements. They are found in the f-block of the periodic table and are known for their f-orbital electrons.
These elements are typically characterized by their large atomic and ionic sizes, high magnetic susceptibility, and unique electronic configurations. Lanthanoids usually form +3 oxidation states, but some can also form +2 and +4 states, impacting their magnetic properties.
In chemical reactions, lanthanoids often exhibit similar behavior due to the gradual filling of the 4f subshell. This leads to trends in chemical reactivity and ionic radii across the series.
Understanding lanthanoid chemistry is essential for various applications, including catalysis, magnetic materials, and phosphors in display technology.

electronic configuration

Electronic configuration refers to the arrangement of electrons in an atom or ion. Electrons occupy orbitals based on a set of principles and rules, such as the Aufbau principle, Pauli exclusion principle, and Hund's rule.
The Aufbau principle states that electrons fill the lowest energy orbitals first. The Pauli exclusion principle asserts that no two electrons in an atom can have the same set of quantum numbers. Hund's rule indicates that electrons will occupy degenerate orbitals singly before pairing up.
For lanthanoids, the electronic configuration generally involves the 4f, 5d, and 6s orbitals. For example, Ytterbium (Yb) with an atomic number of 70 in its neutral form has the configuration \( [Xe] 4f^{14} 6s^{2} \), and as \( \text{Yb}^{2+} \) ion, it becomes \( [Xe] 4f^{14} \).
Knowing the electronic configuration is critical for determining the magnetic properties of ions. For instance, \( \text{Yb}^{2+} \) is diamagnetic because all its electrons are paired in the \( 4f \) orbital.