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The lanthanide contraction is the greater-than-expected decrease in atomic radii and ionic radii of the elements in the lanthanide series, from left to right. It is caused by the poor shielding effect of nuclear charge by the 4f electrons along with the expected periodic trend of increasing electronegativity and nuclear charge on moving from left to right.
The lanthanide contraction, i.e. the reduction in size of the Ln 3+ ion from La 3+ (103 pm) to Lu 3+ (86.1 pm), is often explained by the poor shielding of the 5s and 5p electrons by the 4f electrons. [18] Lanthanide oxides: clockwise from top center: praseodymium, cerium, lanthanum, neodymium, samarium and gadolinium.
The d-block contraction is less pronounced than the lanthanide contraction but arises from a similar cause. In this case, it is the poor shielding capacity of the 3d-electrons which affects the atomic radii and chemistries of the elements immediately following the first row of the transition metals , from gallium ( Z = 31) to bromine ( Z = 35).
It is the most notable exception to the general trend of the contraction of lanthanide atoms with the increase of their atomic numbers (lanthanide contraction [7]). Many properties of promethium rely on its position among lanthanides and are intermediate between those of neodymium and samarium.
Lanthanide metals react exothermically with hydrogen to form LnH 2, dihydrides. [1] With the exception of Eu and Yb, which resemble the Ba and Ca hydrides (non-conducting, transparent salt-like compounds),they form black pyrophoric, conducting compounds [6] where the metal sub-lattice is face centred cubic and the H atoms occupy tetrahedral sites. [1]
A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x , f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.
The d-block contraction (sometimes called scandide contraction [1]) is a term used in chemistry to describe the effect of having full d orbitals on the period 4 elements. The elements in question are gallium , germanium , arsenic , selenium , bromine , and krypton [ citation needed ] .
About 40-50% of the actinide contraction has been attributed to relativistic effects. [2] A decrease in atomic radii can be observed across the 5f elements from atomic number 89, actinium, to 102, nobelium. This results in smaller than otherwise expected atomic radii and ionic radii for the subsequent d-block elements starting with 103, lawrencium.