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What are \[f\]-block elements \[?\] Distinguish between lanthanoid and actinoid?

Answer
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Hint: First we know that the elements in the periodic table are arranged into four blocks associated with the four sublevels \[s,p,d,\] and \[f\]. This periodic table consists of groups and periods. Lanthanoid and actinoid are \[f\]-block elements in the periodic table.

Complete answer:
\[f\]-block elements are placed separately at the bottom of the periodic table and they are a subset of \[{6^{th}}\] and \[{7^{th}}\] periods. \[f\]-block elements are the elements in the periodic table in which last electrons enters into \[f\] orbitals or simply, the elements whose \[f\] orbital getting filled up by electrons are called \[f\]-block elements. These block elements also called as inner transition elements because they provide a transition in the \[{6^{th}}\] and \[{7^{th}}\] row of the periodic table which separates the \[s\] block and the \[d\] block elements.
Difference between lanthanoid and actinoid
LanthanoidActinoid
Lanthanoids are non-radioactive except promethiumActinides are radioactive elements.
Lanthanoid include the elements with atomic numbers starting from \[57\] and ending at \[71\]Actinoids include elements with atomic numbers starting from \[89\] and ending at \[103\]. 
Lanthanoids have a low tendency to form complexes.Actinoids have a greater tendency to form complexes.
In lanthanoid, the last electrons enter into \[4f\] orbitals.In actinoid, the last electrons enter into \[5f\] orbitals.
Binding energy of \[4f\] orbital is higher.Binding energy of \[5f\] orbital is lower.


Note:
\[f\]-block elements are divided into two series corresponding to the filling up of \[4f\] and \[5f\] orbitals. The elements from \[Ce\] to \[Lu\] are \[4f\] orbital series and \[Th\] to \[Lr\] are \[5f\] orbital series. In each series there are \[14\] elements. The first series of elements are called lanthanides and the second series of elements are called actinides.