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The "lanthanoid contraction" refers to a phenomenon observed in the periodic table involving the contraction in atomic and ionic radii as you move across the lanthanide series (also known as the rare earth elements) from left to right.
This contraction occurs due to the poor shielding effect of f-electrons in the lanthanoid series. As electrons are added to the f-orbitals, they are not very effective at shielding the increasing nuclear charge from the outermost s- and p-electrons. As a result, the effective nuclear charge experienced by the outer electrons increases, leading to a contraction in the size of the atoms and ions as you move across the lanthanide series.
The lanthanoid contraction has significant consequences in various chemical properties, including ionization energy, atomic and ionic radii, and complex formation.
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