In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system of benzene.

This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.

* The Small-angle X-ray scattering intensity of a nanostructured system is the Fourier transform of the spatial autocorrelation function of the electron density.

The reaction works because the high electron density at the double bond causes a temporary shift of electrons in the Br-Br bond causing a temporary induced dipole.

This deformation of the lattice causes another electron, with opposite spin, to move into the region of higher positive charge density.

Arrows indicate chain direction, and electron density contours outline the non-H atoms.

Even if the particles do not have a permanent dipole, fluctuations of the electron density gives rise to a temporary dipole in a particle.

The Thomas-Fermi theory, developed in the 1920s, was used to estimate electronic energy levels by treating the local electron density as a variational parameter.

X-rays have energies of the order of 10 keV and hence are able to probe atomic length scales, and are used to measure variations in electron charge density.

Coulomb and Mott scattering measurements can be made by using electron beams as scattering probes, and similarly, positron annihilation can be used as an indirect measurement of local electron density.

In this type of calculation, there is an approximate Hamiltonian and an approximate expression for the total electron density.

with being the elementary charge and the electron density.

If the carriers are holes, replace electron density by the negative of the hole density.

The latter have high electron density and enter nucleophilic aromatic substitution only with very strong electron withdrawing groups.

Electrophilic substitution is the counterpart of the nucleophilic substitution in that the attacking atom or molecule, an electrophile, has low electron density and thus a positive charge.

In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form, where P is the pressure, is the mass density, and is a constant.

For more massive stars, electron degeneracy pressure will not keep the iron core from collapsing to very great density, leading to formation of a neutron star, black hole, or, speculatively, a quark star.

In the anode, the converse applies: It features a high density of free " holes " and consequently fixed negative dopants which have captured an electron ( hence the origin of the holes ).

Electron gas can undergo plasma oscillation, which is waves caused by synchronized variations in electron density, and these produce energy emissions that can be detected by using radio telescopes.

Electronegativity, symbol < span class =" nounderlines "> χ </ span >, is a chemical property that describes the tendency of an atom or a functional group to attract electrons ( or electron density ) towards itself.

C < sub > 60 </ sub > with isosurface of ground state electron density as calculated with Density functional theory | DFT

Af is paramagnetic, and electron paramagnetic dipole as well as nuclear dipole effects lead to line broadening.

Indeed it is possible to separate electron paramagnetic from nuclear effects.

The information provided by the electron paramagnetic effects is then discussed, and finally the nuclear effects are interpreted in terms of various motional-modified models of the Af bond in Af.

The approximate equation is Af, where N is the number of Af with electron line-density greater than or equal to Af, and Q is proportional to the mass of the meteorite.

Radiopasteurization by either the electron accelerator or cesium-137 source is in the range of freezing costs.

Irradiation using the nuclide source is more expensive than use of an electron accelerator.

It should be noted, however, that the paraxial resolution is quite similar for both electron optical systems.

The electron optical system ( see fig. 14-1 ) is based in principle on the focusing action of concentric spherical cathode and anode surfaces.

The charges of the electron and proton are believed to be exactly equal and opposite, but Dr. Lyttleton is not so sure.

Suppose, says Dr. Lyttleton, the proton has a slightly greater charge than the electron ( so slight it is presently immeasurable ).

A Lewis acid is a species that accepts a pair of electrons from another species ; in other words, it is an electron pair acceptor.

BF < sub > 3 </ sub > is a Lewis acid because it accepts the electron pair from fluoride.

The species that gains the electron pair is the Lewis acid ; for example, the oxygen atom in H < sub > 3 </ sub > O < sup >+</ sup > gains a pair of electrons when one of the H — O bonds is broken and the electrons shared in the bond become localized on oxygen.

The number of electrons in each element's electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior.

An atom containing an equal number of protons and electrons is electrically neutral, otherwise it has a positive charge if there are fewer electrons ( electron deficiency ) or negative charge if there are more electrons ( electron excess ).

Over 99. 94 % of an atom's mass is concentrated in the nucleus ,< ref group = note > In the case of hydrogen-1, with a single electron and nucleon, the proton is, or 99. 95 % of the total atomic mass.

Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.

The electron is by far the least massive of these particles at, with a negative electrical charge and a size that is too small to be measured using available techniques.

During the period from 1 July 1960 through 31 January 1961, additional research affiliations were effected with the U. S. Army Medical Research and Development Command to conduct research in procedures for quantitative electron microscopy, and for the study of biophysical and biological studies of the structure and function of ocular tissue.

An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.

This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus.

# The electrons are never in a single point location, although the probability of interacting with the electron at a single point can be found from the wave function of the electron.

) A state is actually a function of the coordinates of all the electrons, so that their motion is correlated, but this is often approximated by this independent-particle model of products of single electron wave functions.

With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen like atom, a Bohr electron " wavelength " could be seen to be a function of its momentum, and thus a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength ( this historically incorrect Bohr model is still occasionally taught to students ).

Auger electron spectroscopy involves the emission of Auger electrons by bombarding a sample with either X-rays or energetic electrons and measures the intensity of Auger electrons as a function of the Auger electron energy.

In his article entitled " Criticism and Counterproposals to the Copenhagen Interpretation of Quantum Theory ," countering the view of Alexandrov that ( in Heisenberg's paraphrase ) " the wave function in configuration space characterizes the objective state of the electron.

Thermionic emission occurs when the thermal energy exceeds the metal's work function, while field electron emission occurs when the electric field at the surface of the metal is high enough to cause tunneling, which results in the ejection of free electrons from the metal into the vacuum.

Transmission electron microscopes function in a manner similar to overhead projector, with a beam of electrons passing through a slice of material then being projected by lenses on a photographic slide or a charge-coupled device.

In chemistry, a molecular orbital ( or MO ) is a mathematical function describing the wave-like behavior of an electron in a molecule.

This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region.

At the plasmon frequency, the frequency-dependent dielectric function of the free electron gas goes from negative ( reflecting ) to positive ( transmitting ); higher frequency photons are not reflected at the surface, and do not contribute to the color of the metal.

Schrödinger himself initially did not understand the fundamental probabilistic nature of quantum mechanics, as he thought that the absolute square of the wave function of an electron should be interpreted as the charge density of an object smeared out over an extended, possibly infinite, volume of space.

In the photoemission process, if an electron within some material absorbs the energy of one photon and acquires more energy than the work function ( the electron binding energy ) of the material, it is ejected.

The number of electrons also changes because the probability that each photon results in an emitted electron is a function of photon energy.

The term ' is the work function ( sometimes denoted, or ), which gives the minimum energy required to remove a delocalised electron from the surface of the metal.

Probability clouds are approximate, but better than the Bohr model, whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.