Cerium (Ce) and ytterbium (Yb) exhibit some oxidation states in addition to +3 . (a) Write the electron configurations of \(\mathrm{Ce}^{2+}, \mathrm{Ce}^{3+},\) and \(\mathrm{Ce}^{4+}\). (b) Write the electron configurations of \(\mathrm{Yb}^{2+}, \mathrm{Yb}^{3+},\) and \(\mathrm{Yb}^{4+} .(\mathrm{c})\) In addition to the \(3+\mathrm{ions},\) the ions \(\mathrm{Ce}^{4+}\) and \(\mathrm{Yb}^{2+}\) are stable. Suggest a reason for this stability.

Cerium (Ce) is an element in the lanthanide series with an atomic number of 58. It exhibits a range of oxidation states, although the most common one is +3. Understanding these oxidation states can give insight into chemical properties and reactivity. Here's a breakdown of the electron configurations for its common oxidation states:

\[\text{Ce:} [Xe] 4f^1 5d^1 6s^2\] - This is the neutral cerium atom, reflecting the electron count that includes its position in the periodic table.

\[\text{Ce}^{2+}: [Xe] 4f^2\] - By removing two electrons from the 6s and 5d orbitals, cerium goes into the +2 oxidation state.

\[\text{Ce}^{3+}: [Xe] 4f^1\] - Here, an additional electron is removed, leading to the more stable +3 state which is common among lanthanides.

\[\text{Ce}^{4+}: [Xe]\] - When another electron is detached, we achieve the +4 state, where cerium has a noble gas configuration, making it exceptionally stable.

Cerium’s ability to exist in these various oxidation states, especially +3 and +4, makes it useful in different industrial applications, including catalysts and glass production.

Ytterbium (Yb) is another element in the lanthanide series with an atomic number of 70. Like cerium, ytterbium commonly exhibits the +3 oxidation state, but it can also be found in other states. Here's a look at its electron configurations:

\[\text{Yb:} [Xe] 4f^{14} 6s^2\] - This is the electron configuration of a neutral ytterbium atom.

\[\text{Yb}^{2+}: [Xe] 4f^{14}\] - By removing two electrons from the 6s orbital, ytterbium reaches the +2 oxidation state, which is unusually stable for this element due to the fully filled 4f orbital.

\[\text{Yb}^{3+}: [Xe] 4f^{13}\] - Removing one more electron results in the +3 state, which is the most common and stable state for ytterbium, similar to other lanthanides.

\[\text{Yb}^{4+}: [Xe] 4f^{12}\] - The +4 oxidation state involves the removal of four electrons, though it is less common and less stable than the +2 and +3 states.

Understanding these configurations helps us to grasp ytterbium's chemical behavior and its applications in fields such as material science and medicine.

The stability of f-orbitals plays a pivotal role in the chemistry of lanthanides like cerium and ytterbium. In particular, the stability of certain oxidation states can be explained by their electron configurations, particularly within the f-orbital:

- **Noble Gas Configuration:** \[\text{Ce}^{4+}: [Xe]\] has a noble gas configuration which is highly stable due to its filled electron shells. This makes Ce^{4+} especially stable despite the energy needed to remove four electrons.

- **Fully Filled Orbitals:** \[\text{Yb}^{2+}: [Xe] 4f^{14}\] has a completely filled 4f orbital, lending extra stability due to the low energy and high symmetry associated with fully filled orbitals.

- **Half-Filled Stability:** In general, lanthanides exhibit notable stability when they have either half-filled or fully filled f-orbitals. This is because such configurations result in lower total energy and enhanced symmetry, making them less reactive.

Thus, the seemingly complex nature of these elements often boils down to their quest to attain stable configurations, be it through filled, half-filled, or noble gas states.