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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 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.
This is the energy per mole necessary to remove electrons from gaseous atoms or atomic ions. The first molar ionization energy applies to the neutral atoms. The second, third, etc., molar ionization energy applies to the further removal of an electron from a singly, doubly, etc., charged ion.
Another example is incandescent light bulbs, which emit only around 10% of their energy as visible light and the remainder as infrared. A common thermal light source in history is the glowing solid particles in flames, but these also emit most of their radiation in the infrared and only a fraction in the visible spectrum.
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
The most common lanthanide ions used in photon upconversion are the pairs erbium-ytterbium (Er 3+,Yb 3+) or thulium-ytterbium (Tm 3+, Yb 3+). In such combinations ytterbium ions are added as antennas, to absorb light at around 980 nm and transfer it to the upconverter ion.
An FM radio station transmitting at 100 MHz emits photons with an energy of about 4.1357 × 10 −7 eV. This minuscule amount of energy is approximately 8 × 10 −13 times the electron's mass (via mass–energy equivalence). Very-high-energy gamma rays have photon energies of 100 GeV to over 1 PeV (10 11 to 10 15 electronvolts) or 16 nJ to 160 ...
The electrostatic potential energy, E pair, between a pair of ions of equal and opposite charge is: = where z = magnitude of charge on one ion e = elementary charge, 1.6022 × 10 −19 C ε 0 = permittivity of free space 4 π ε 0 = 1.112 × 10 −10 C 2 /(J·m)