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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.
The number of ways to link an X to two external lines is 4 × 3, and either X could link up to either pair, giving an additional factor of 2. The remaining two half-lines in the two X s can be linked to each other in two ways, so that the total number of ways to form the diagram is 4 × 3 × 4 × 3 × 2 × 2, while the denominator is 4! × 4 ...
In condensed-matter physics, channelling (or channeling) is the process that constrains the path of a charged particle in a crystalline solid. [1] [2] [3]Many physical phenomena can occur when a charged particle is incident upon a solid target, e.g., elastic scattering, inelastic energy-loss processes, secondary-electron emission, electromagnetic radiation, nuclear reactions, etc.
The time-integral of the Wiener process ():= is called integrated Brownian motion or integrated Wiener process. It arises in many applications and can be shown to have the distribution N (0, t 3 /3), [ 12 ] calculated using the fact that the covariance of the Wiener process is t ∧ s = min ( t , s ) {\displaystyle t\wedge s=\min(t,s)} .
Besides the well-known Pitzer-like equations, there is a simple and easy-to-use semi-empirical model, which is called the three-characteristic-parameter correlation (TCPC) model. It was first proposed by Lin et al. [22] It is a combination of the Pitzer long-range interaction and short-range solvation effect: ln γ = ln γ PDH + ln γ SV
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 ...
A metal ion in aqueous solution or aqua ion is a cation, dissolved in water, of chemical formula [M(H 2 O) n] z+.The solvation number, n, determined by a variety of experimental methods is 4 for Li + and Be 2+ and 6 for most elements in periods 3 and 4 of the periodic table.