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Why is lanthanum in the F-block?

Answer
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Hint: lanthanum has partially filled f-orbitals and so it is an f-block element. The entire group is called lanthanides because lanthanum is their first element, and they all are similar in properties. The general electronic configuration of lanthanides is $[Xe]4{f^{1 - 14}}5{d^{0 - 1}}6{s^2}$.

Complete answer:
The f block elements are the lanthanides and actinides. They are called the inner transition elements. They are placed separately, below the periodic table. They are a subset of \[{6^{th}}\] and \[{7^{th}}\] periods. They are called F-block elements because their extra electron enters in \[\left( {n - {\text{ }}2} \right)f\]orbitals. These elements have electrons, \[\left( {1{\text{ }}to{\text{ }}14} \right)\]in the f orbital, \[\left( {0{\text{ }}to{\text{ }}1} \right)\]in the d orbital of the penultimate energy level and in the outermost orbital.
Lanthanum is the first element of the group lanthanides. It is a rare-earth metal. When we look at the general electronic configuration of lanthanides, it is $[Xe]4{f^{1 - 14}}5{d^{0 - 1}}6{s^2}$. The electrons mostly enter into the $4f$orbitals because the energies of both $5d$orbital and $4f$ orbital are the same. And the $5d$orbitals remain vacant. Lanthanides have partially filled f-orbitals. And the electron shells are filled with \[n - 2\]electrons. That is why lanthanum is placed in f-block elements.
Lanthanides comprise $15$elements, from atomic numbers \[57-71\]that are from lanthanum through the lutetium. They are called lanthanides because the elements in the series are chemically similar to lanthanum. All lanthanide elements form trivalent cations\[L{n^{3 + }}\]. The lanthanides are highly dense elements. Like most metals, these elements have very high melting points and very high boiling points.

Note:
there is a gradual decrease in the size of the lanthanides from lanthanum to lutetium, with an increasing atomic number. This is known as lanthanide contraction. It is caused by a poor shielding effect by the 4f electrons. Due to lanthanide contraction in the lanthanide series of elements, there is a decrease in both atomic and ionic radii.