Cerium can show an oxidation state of +4 because

of its tendency to attain noble gas configuration of xenon

The correct answer is option 3. of its tendency to attain noble gas configuration of xenon.

Let us look into why cerium \((Ce)\) can exhibit an oxidation state of +4, primarily due to its tendency to attain the noble gas configuration of xenon.

Electronic Configuration of Cerium:

Cerium is a lanthanide element with the electron configuration \([Xe] 4f^1 5d^1 6s^2\) in its ground state. Lanthanides are known for their ability to exhibit multiple oxidation states, typically ranging from \(+2\) to \(+4\).

Oxidation State of \(+4\):

Noble Gas Configuration: The noble gas xenon (Xe) has the electron configuration \([Kr] 4d^{1O} 5s^2 5p^6\). Cerium can achieve a stable configuration similar to Xe by losing all four of its valence electrons.

Tetravalent State: In the \(+4\) oxidation state, cerium loses all its valence electrons (two 6s electrons, one 5d and one 4f electron), resulting in an oxidation state of \(+4\). This configuration allows cerium to achieve a filled 4f subshell, analogous to the filled 4f^14 configuration of xenon.

Stability: The stability of the \(+4\) oxidation state in cerium is due to the relatively low energy required to remove the necessary electrons to achieve this configuration. While cerium's ionization energies are not exceptionally low like alkali metals, the electronic structure of cerium allows it to stabilize the \(+4\) oxidation state effectively.

Chemical Behavior: Cerium compounds in the \(+4\) oxidation state are known for their stability and can exist in various chemical environments, contributing to the versatility of cerium in chemical reactions and industrial applications.

Comparison with Other Lanthanides: Not all lanthanides can readily achieve the \(+4\) oxidation state. Cerium stands out because it is located at the beginning of the lanthanide series and has a relatively accessible pathway to the \(+4\) oxidation state due to its electronic configuration.

The ability of cerium to exhibit an oxidation state of \(+4\) is primarily attributed to its tendency to achieve the noble gas configuration of xenon. This configuration provides cerium with stability in the \(+4\) oxidation state, making it a notable exception among the lanthanides and allowing for its diverse chemical behavior in various applications.