Wavelength for electrons

In fact, the wavelength depends on the electron density. The wavelength for electrons in metals is typically around 10 nm, but in semiconductors it may vary between 10 nm and 1 p,m. 

For improved magnification, one exploits the dual nature of matter, that particles also behave as waves. The wavelengths are obtained from the momentum as mV = TjihlX, where m is the mass of the particle, Vis its velocity, h is Planck s constant, and k is the resulting wavelength. For electrons, the wavelength works out to be about 0.005 nm, calculated resolution 0.003 nm, and the aetual resolution more like 2 nm. Since electric and magnetic fields can be used like lenses, unlike... 

What is the wavelength for electrons accelerated by 1.00 X 10" volts When an electron is accelerated by a voltage difference, the kinetic energy acquired by the electron equals the voltage times the charge on the electron. Thus, one volt imparts a kinetic energy of 1.602 X 10 volt-coulombs, or... 

The first and the most fundamental effect is the radiative broadening due to the spontaneous decay of an excited state (the half-width of the spectral line is r = 7rad = 7). A spectral line due to spontaneous decay has a Lorentzian shape (eqn 2.5). The lifetime of an excited atomic or molecular state depends on the oscillator strength of the transition and the radiation wavelength. For electronic transitions of atoms and molecules in the visible region of the spectrum, l/7rad — s. For metastable atomic and vibrational molecular levels, the radiative lifetime may be much longer, namely... 

Fig. 21. Representative nonionic photoacid generators. A variety of photochemical mechanisms for acid production ate represented. In each case a sulfonic acid derivative is produced (25,56,58—60). (a) PAG that generates acid via 0-nitrobenzyl rearrangement (b) PAG that generates acid via electron transfer with phenohc matrix (c) PAG that is active at long wavelengths via electron-transfer sensitization (d) PAG that generates both carboxylic acid and...

Many sources of energy are used to excite samples to emit characteristic wavelengths for chemical identification and assay (91,92). Very high temperature sources can be employed but are not necessary. AH materials can be vaporized and excited with temperatures of only a few electron volts. The introduction of samples to be analyzed into high temperature or high density plasmas and thek uniform excitation often are problematic. 

Fig. 8. Dichroism of electronic absorption spectra of oriented and nonoriented PAN films after IR irradiation, (a) Dependence of optical density ( >) on the wavelength for various values of (angle between film orientation axis and light polarization plane).

Wavelength shift of K absorption edge of sulfur, 37, 38 Weight-fraction , use, 164, 171 Window absorption, 45 Windowless counter tube, 55, 222 Windows, for electron beam, 177 for proportional counter, 55... 

A number of investigations of the copper-group oxides and dioxygen complexes have been reported. The electronic spectra of CuO, AgO, and AuO were recorded in rare-gas matrices (9), and it was found that the three oxides could be formed effectively by cocondensation of the metal atoms with a dilute, oxygen matrix, followed by near-ultraviolet excitation. The effective wavelengths for CuO or AgO formation were X > 300 nm and for AuO was X > 200 nm. In addition, the laser fluorescence spectrum of CuO in solid Ar has been recorded (97). 

The treatment presented so far is quite general and formally exact. It combines the eikonal representation for nuclear motions and the time-dependent density matrix in an approach which could be named as the Eik/TDDM approach. The following section reviews how the formalism can be implemented in the eikonal approximation of short wavelengths for the nuclear motions, and for specific choices of electronic states leading to the TDHF equations for the one-electron density matrix, and to extensions of TDHF. 

Approximations have been reviewed in the case of short deBroglie wavelengths for the nuclei to derive coupled quantal-semiclassical computational procedures, by choosing different types of many-electron wavefunctions. Time-dependent Hartree-Fock and time-dependent multiconfiguration Hartree-Fock formulations are possible, and lead to the Eik/TDHF and Eik/TDMCHF approximations, respectively. More generally, these can be considered special cases of an Eik/TDDM approach, in terms of a general density matrix for many-electron systems. 

In this case, the output from a group of adjacent diodes is electronically suauMd or averaged to produce one signal output. Practically, this is accomplished by defining a central wavelength for detection and an associated effective bandwidth. These parameters, however, must be set carefully to avoid nonlinearity in the calibration plots [80]. 

Tables 15 and 16 show the absorption maxima of some metal complexes of benzothiazolyl-substituted formazans 230 and 231.283 The wavelengths are metal ion dependent, making formazans useful reagents for the identification of specific metal ions or the simultaneous determination of two ions. The wavelengths are much longer than those of the formazan anion (Table 14). The general trend for electron-rich substituents is toward a larger shift this is to be expected as it tends to enhance the aromatic character of the ring and increase the covalent character of the metal — nitrogen bond. The sharpness of the absorption band has been attributed to coordination to the heterocyclic nitrogen as in 232.57S...

The UV-spectra of azolides have already been discussed in the context of hydrolysis kinetics in Chapter 1. Specific infrared absorptions of azolides were mentioned there as well increased reactivity of azolides in nucleophilic reactions involving the carbonyl group is paralleled by a marked shift in the infrared absorption of the corresponding carbonyl bond toward shorter wavelength. For example, for the highly reactive N-acetyl-tetrazole this absorption is found in a frequency range (1780 cm-1) that is very unusual for amides obviously the effect is due to electron attraction by the heterocyclic sys-tem.[40] As mentioned previously in the context of hydrolysis kinetics of both imidazo-... 

X-rays are electromagnetic radiation with short wavelengths of about 0.01 to 10 nm. X 0.15 nm is the typical wavelength for the study of soft condensed matter. Whenever X-rays are interacting with matter, their main partners are the electrons in the studied sample. Thus X-ray scattering is probing the distribution of electron density, p (r), inside the material. 

Fig. 21. Top The general Jablonski diagram for the flavin chromophore. The given wavelengths for absorption and luminescence represent crude average values derived from the actual spectra shown below. Due to the Franck-Condon principle the maxima of the peak positions generally do not represent so-called 0 — 0 transitions, but transitions between vibrational sublevels of the different electronically excited states (drawn schematically). Bottom Synopsis of spectra representing the different electronic transitions of the flavin nucleus. Differently substituted flavins show slightly modified spectra. Absorption (So- - S2, 345 nm S0 -> Si,450nm 1561) fluorescence (Sj — S0) 530 nm 156)) phosphorescence (Ty Sq, 605 nm 1051) triplet absorption (Tj ->Tn,...

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