Question

The rare earth elements, or lanthanides, commonly exist as \(3+\) ions. Using an orbital box diagram and noble gas notation, show the electron configurations of the following elements and ions. (a) Ce and \(\mathrm{Ce}^{3+}\) (cerium) (b) Ho and \(\mathrm{Ho}^{3+}\) (holmium)

Short answer

Ce: [Xe] 4f^1 5d^1 6s^2; Ce^{3+}: [Xe] 4f^1; Ho: [Xe] 4f^{11} 6s^2; Ho^{3+}: [Xe] 4f^{10}.

Step-by-step solution

Identify the Atomic Number

Cerium (Ce) has an atomic number of 58, and Holium (Ho) has an atomic number of 67. This information helps us determine the electron configuration.

Electron Configuration for Ce

The full electron configuration for Ce is: \[ [ ext{Xe}] 4f^1 5d^1 6s^2 \]Start with the noble gas that precedes Ce, which is xenon \([ ext{Xe}]\), then add the electrons in the respective orbitals.

Electron Configuration for Ce^{3+} Ion

For the \( ext{Ce}^{3+}\) ion, three electrons are removed from the neutral atom's configuration. Remove electrons first from the highest occupied energy level, which are the 6s and one from the 5d orbital:\[ [ ext{Xe}] 4f^1 \]

Electron Configuration for Ho

The full electron configuration for Ho is:\[ [ ext{Xe}] 4f^{11} 6s^2 \]Again start with the noble gas configuration \([ ext{Xe}]\) and fill the electrons in the 4f and 6s orbitals.

Electron Configuration for Ho^{3+} Ion

For the \( ext{Ho}^{3+}\) ion, three electrons need to be removed from the neutral Ho atom. Remove two from the 6s orbital and one from the 4f orbital:\[ [ ext{Xe}] 4f^{10} \]

Verify Orbital Diagrams

For each electron configuration, create orbital box diagrams that reflect the electron occupancy of the orbitals, showing spins and paired electrons appropriately. Confirm that the number of electrons corresponds to the configurations calculated.

Key concepts

Electron Configuration

Electron configuration allows us to understand how electrons are distributed in an atom. For lanthanides like Cerium (Ce) and Holmium (Ho), the electron configuration reflects the atomic structure by listing occupied orbitals. For example, Ce with an atomic number 58 has electrons filling up to the 4f, 5d, and 6s orbitals. This results in the configuration:

• \( [\text{Xe}] 4f^1 5d^1 6s^2 \)

This notation reveals where electrons reside, emphasizing the importance of quantum numbers in their specific order.
When ions like \( \text{Ce}^{3+} \) form, electrons are removed starting with the outermost orbitals. For \( \text{Ce}^{3+} \), three electrons are taken from 6s and 5d orbitals to yield:

• \( [\text{Xe}] 4f^1 \)

This process aligns with the concept of lower energy state preference.
Similarly, for Ho, with its configuration:

• \( [\text{Xe}] 4f^{11} 6s^2 \)

The \( \text{Ho}^{3+} \) ion configuration, after removing three electrons including one from 4f, becomes:

• \( [\text{Xe}] 4f^{10} \)

This systematic approach ensures clarity in understanding electron distribution.

Orbital Box Diagram

The orbital box diagram is a graphical way to depict the electron configuration by showing each occupied orbital as a box, with arrows representing electrons. These diagrams help visualize how electrons fill orbitals while adhering to principles like Hund's Rule and the Pauli Exclusion Principle.

• Hund's Rule: Electrons fill an unoccupied orbital before pairing up.
• Pauli Exclusion Principle: Every electron in an atom has a unique set of quantum numbers.

For example, in Ce, you would represent the 4f, 5d, and 6s electrons in separate boxes. For the \( [\text{Xe}] 4f^1 5d^1 6s^2 \) configuration, two arrows would indicate the 6s electrons pairing, one in 5d, and one in 4f.
For Ce\(^{3+}\), the simpler:

• \( [\text{Xe}] 4f^1 \)

would mean just a single box for the 4f orbital with one arrow, reflecting the lone unpaired electron.
By comparing box diagrams of Ho and its ion, you visualize the electron removal from the 6s and 4f orbitals, reinforcing the idea of electron distribution's impact on ion formation and stability.

Noble Gas Notation

Noble gas notation is a shorthand method for writing electron configurations, emphasizing efficiency and understanding. Using noble gases like Xenon ([Xe]) as benchmarks helps simplify electron configurations by reducing redundant information.
Instead of listing all electron shells from the nucleus outward, you reference the nearest preceding noble gas. For Ce, starting with [Xe] streamlines the configuration to:

• \( [\text{Xe}] 4f^1 5d^1 6s^2 \)

This reveals only the electrons that extend beyond the noble gas core.
For ion configurations like \( \text{Ho}^{3+} \), noble gas notation efficiently showcases:

• \( [\text{Xe}] 4f^{10} \)

By focusing on the electron changes post noble gas, it delineates transitions involving outermost electron removal.
This notation assists when analyzing how atoms and ions behave, such as their reactivity and magnetic properties, providing a clearer understanding of underlying electronic structures in chemistry.