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The most common oxidation state of Cerium?

Answer
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Hint :Cerium is the second element of Lanthanide series i.e. f-block. Depending upon the stability of the orbital , Lanthanides have different oxidation states. $ Ce $ i.e. Cerium ( $ Z=58 $ ) having electronic configuration $ [Xe]4{{f}^{1}},5{{d}^{1}},6{{s}^{2}} $ . It has $ 4 $ valence electrons in the outermost shell.

Complete Step By Step Answer:
The $ Ce $ forms $ 3 $ different oxidation states i.e. $ +2,+3,+4 $ but $ +3 $ and $ +4 $ are the most common oxidation states.
Electronic configuration of $ +2,+3,+4 $ oxidation states are $ [Xe]4{{f}^{1}}5{{d}^{1}},[Xe]4{{f}^{1}},[Xe]4{{f}^{0}} $ . $ C{{e}^{+4}} $ is favoured as by losing $ 4 $ electrons it attains noble gas configuration.
 $ C{{e}^{+3}} $ is favoured due to the penetrating power of $ 4f $ electrons. The $ 4f $ electrons in the antepenultimate shell are held tightly by the nucleus due to which stability of $ 4f $ is more than $ 5d,6s $ electrons. Due to this it doesn’t take part in bonding. That’s why $ C{{e}^{+4}} $ acts as an oxidizing agent.
Likewise Cerium, other lanthanide metals like Praseodymium $ (\Pr ) $ ,Neodymium $ (Nb) $ ,Terbium $ (Tb) $ ,Dysprosium $ (Dy) $ also exist on $ +4 $ oxidation state.
Cerium is soft, ductile, silvery white metal. It is the second most active Lanthanide after Europium. It readily reacts with oxygen that can be set on fire by simply scraping the surface with a knife. It also reacts with water, acids, halogens, other elements like sulphur and nitrogen.
Cerium reacts with water to form $ Ce{{(OH)}_{3}} $ {cerium hydroxide} and Hydrogen gas.
 $ Ce\xrightarrow{with-{{H}_{2}}O}Ce{{(OH)}_{3}}+{{H}_{2}} $
Cerium with all halogens i.e. $ {{F}_{2}},C{{l}_{2}},B{{r}_{2}},{{I}_{2}} $ to form cerium trihalide i.e. $ Ce{{X}_{3}} $
 $ Ce\xrightarrow{With-Halogens}Ce{{X}_{3}} $
Cerium reacts with acid to liberate hydrogen gas.
 $ Ce\xrightarrow{With-Acids}{{H}_{2}} $
Cerium heated with sulphur to form cerium sulfide i.e. $ C{{e}_{2}}{{S}_{3}} $ . Likewise is heated in the presence of nitrogen gas to form cerium nitride
 $ \begin{align}
  & Ce\xrightarrow{Heated-with-Sulphur}C{{e}_{2}}{{S}_{3}} \\
 & Ce\xrightarrow{Heated-with-Nitrogen}CeN \\
\end{align} $

Note :
Mischmetal is an alloy of cerium along with magnesium which is used in production of bullets, shells and lighter flint. Cerium has $ 4 $ Naturally occurring Isotope( elements having same atomic number but different mass number) $ Ce-136,Ce-138,Ce-140,Ce-142 $ .