Interference destructive

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

FIGURE 2 2 Interference between waves (a) Constructive interference occurs when two waves combine in phase with each other The amplitude of the resulting wave at each point is the sum of the amplitudes of the original waves (b) Destructive interference decreases the amplitude when two waves are out of phase with each other... 

A wavelength selector that uses either absorption, or constructive and destructive interference to control the range of selected wavelengths. 

The first thing to realize about scattering by liquids is that individual molecules can no longer be viewed as independent scatterers. If a liquid were perfectly uniform in density at the molecular level, its molecules could always be paired in such a way that the light scattered by each member of a pair would be exactly out of phase with the other, resulting in destructive interference. No net scattering results in this case. The second thing to realize, however, is that density is not perfectly uniform at the molecular level. 

Figure 10.10 Interference of light rays scattered by segments j and k in a polymer chain. Destructive interference increases with increasing 6.

Figure 3.12 (a) Constructive and (b) destructive interference between rays 1 and 2 of... 

Figure 2 Molybdenum K-edge X-ray absorption spectrum, ln(i /i ) versus X-ray energy (eV), for molybdenum metal foil (25- jjn thick), obtained by transmission at 77 K with synchrotron radiation. The energy-dependent constructive and destructive interference of outgoing and backscattered photoelectrons at molybdenum produces the EXAFS peaks and valleys, respectively. The preedge and edge structures marked here are known together as X-ray absorption near edge structure, XANES and EXAFS are provided in a new compilation of literature entitled X-rsy Absorption Fine Structure (S.S. Hasain, ed.) Ellis Norwood, New York, 1991.

Figure 3 Schematic illustration of the EXAFS phenomenon (A) outgoing photoelectron (solid curve) from X-ray absorbing atom (B) destructive interference at the absorbing atom between outgoing (solid curve) and backscattered (dashed curve) photoelectron from neighboring atom (C) constructhra interference at the absorbing atom between outgoing (solid curve) and backscat-tared (dashed curve) photoelectron from neighboring atom. Adapted from T. M. Hayes and J. B. Boyce. Solid State Phys. 37.173,1982.

The constructive and destructive interference creates the well known colorful patterns seen when stressed plastic are placed between two polarized filters. Some information about the stress gradients comes from observations of the patterns that provide qualitative analysis. The index of refraction in these directions is different and the difference (or birefringence) is proportional to the stress level. 

In absence of motion the formation of the solid echo is limited by T only, in presence of motions, however, the NMR frequencies in the periods of destructive interference and constructive refocussing, respectively, may be different. The signal following the refocussing pulse is given by27)... 

FIGURE 1.20 (a i Constructive interference. The two component waves (left) are "in phase" in the sense that their peaks and troughs coincide. The resultant (right) has an amplitude that is the sum of the amplitudes of the components. The wavelength of the radiation is not changed by interference, only the amplitude is changed, (b) Destructive interference. The two component waves are "out of phase" in the sense that the troughs of one coincide with the peaks of the other. The resultant has a much lower amplitude than either component. 

When two or more waves pass through the same region of space, the phenomenon of interference is observed as an increase or a decrease in the total amplitude of the wave (recall Fig. 1.20). Constructive interference, an increase in the total amplitude of the wave, occurs when the peaks of one wave coincide with the peaks of another wave. If the waves are electromagnetic radiation, the increased amplitude corresponds to an increased intensity of the radiation. Destructive interference, a decrease in the total amplitude of the waves, occurs when the peaks of one wave coincide with the troughs of the other wave it results in a reduction in intensity. 

This method was developed by Johnston et al. in 1991 and well described in Ref. [10], according to which the method is introduced as follows. The principle of optical interference is shown schematically in Fig. 1. A coating of transparent solid, typically silica, of known thickness, is deposited on top of the semi-reflecting layer. This solid thus permanently augments the thickness of any oil film present and is known as a "spacer layer. The destructive interference now obeys the equation ... 

The phase-twisted peak shapes (or mixed absorption-dispersion peak shape) is shown in Fig. 3.9. Such peak shapes arise by the overlapping of the absorptive and dispersive contributions in the peak. The center of the peak contains mainly the absorptive component, while as we move away from the center there is an increasing dispersive component. Such mixed phases in peaks reduce the signal-to-noise ratio complicated interference effects can arise when such lines lie close to one another. Overlap between positive regions of two different peaks can mutually reinforce the lines (constructive interference), while overlap between positive and negative lobes can mutually cancel the signals in the region of overlap (destructive interference). 

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

Since the wavelength is of the order of lattice distances, electrons that are scattered elastically undergo constructive and destructive interference (as with X-rays in XRD). The back-scattered electrons form a pattern of spots on a fluorescent screen from which the symmetry and structure of the surface may be deduced. 

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