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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.
Most of the algebraic properties of the Christoffel symbols follow from their relationship to the affine connection; only a few follow from the fact that the structure group is the orthogonal group O(m, n) (or the Lorentz group O(3, 1) for general relativity). Christoffel symbols are used for performing practical calculations.
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.
Hence, the calculator is of great importance for those working in numerical areas of experimental mathematics. The ISC contains 54 million mathematical constants. Plouffe's Inverter (opened in 1998) contains 214 million. A newer version of the tables with 3.702 billion entries (as of June 19, 2010) exists.
The size of Ln 3+ ions regularly decreases with atomic number. According to Fajans' rules , decrease in size of Ln 3+ ions increases the covalent character and decreases the basic character between Ln 3+ and OH − ions in Ln(OH) 3 , to the point that Yb(OH) 3 and Lu(OH) 3 can dissolve with difficulty in hot concentrated NaOH.
In atomic physics, the effective nuclear charge of an electron in a multi-electron atom or ion is the number of elementary charges an electron experiences by the nucleus. It is denoted by Z eff . The term "effective" is used because the shielding effect of negatively charged electrons prevent higher energy electrons from experiencing the full ...
In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction (half-cell or full cell reaction) from the standard electrode potential, absolute temperature, the number of electrons involved in the redox reaction, and activities (often approximated by concentrations) of the chemical species undergoing ...
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