Most common oxidation states of Ce are (a) \(+3,+4\) (b) \(+2,+3\) (c) \(+2,+4\) (d) \(+3,+5\)

In exploring the fundamentals of chemistry, understanding the position of an element on the periodic table is vital. The location of an element provides insights into its properties and its most common oxidation states. Cerium (Ce), a member of the lanthanide series, is situated in the 'f-block' of the periodic table. This block contains elements known for having electrons that can be easily removed from their f-orbitals.
Positioned after the actinides, lanthanides like Ce are often referred to as 'rare earth metals'. Though not truly rare, they possess distinct chemical behaviors distinct from the s-block and d-block metals traditionally taught in introductory chemistry. The f-block elements are tucked away at the bottom of the periodic table, primarily because their electron configurations are a continuation of the sixth period. Cerium's position, in this unique setting, hints at its capability of adopting multiple oxidation states; a phenomenon critical for understanding its chemistry.

Diving deeper into the classification of Cerium (Ce), we find that it belongs to a fascinating group of elements known as the lanthanide series. These are the 15 metallic elements numbered from 57 (Lanthanum) through 71 (Lutetium) and characterized by their filling of f-orbitals. What makes the lanthanide series particularly interesting is their strikingly similar chemical properties. This similarity arises from the shielding effect, where the 4f electrons are deeply buried under the outer 5d and 6s shells, making the lanthanides behave in a chemically uniform manner.
Cerium and its neighbors often exhibit variable oxidation states. The reason for this variability lies in the delicate energy balance within their electron configurations, where electrons from the f-orbits can be stripped away in chemical reactions. This phenomenon is essential for technologies such as catalysis, where Ce's oxidation states play a defining role. As a part of the lanthanide series, Ce exhibits some of the highest oxidation number potentials, which is why the +3 and +4 states are the most prevalent.

Understanding an element's electron configuration is like having a map of its atomic structure, which guides us through the properties that dictate its behavior in chemical reactions. The electron configuration of Cerium (Ce) is [Xe]4f^1 5d^1 6s^2. In simple terms, beyond the electron configuration of Xenon (Xe), Ce has one electron in the 4f orbital, one in the 5d orbital, and two in the 6s orbital.
When cerium loses three electrons, specifically the two from the 6s orbital and one from the 4f or 5d orbital, it adopts a +3 oxidation state, matching the behavior expected from lanthanide series elements. This is a stable and common configuration for Ce in reactions and compounds. When an additional electron is lost from the 4f orbital, Ce takes on a +4 oxidation state. This higher oxidation state is particularly significant in Ce-based catalysts and is stable enough to be encountered frequently. Although it's feasible for Ce to lose just two electrons, resulting in a +2 state, or five electrons for a +5 state, these are not commonly observed and thus are less relevant for most practical applications. Overall, the primary electron configuration of Ce greatly influences its chemical reactivity and the commonality of its oxidation states.