BENDING ELECTRONS

Thomson s plum-pudding model of the atom. Thomson proposed that the atom might be made of thousands of tiny, negatively charged particles swarming within a cloud of positive charge, much like plums and raisins in an old-fashioned Christmas plum pudding. 

Was this your answer They are all multiples of 5. In a similar fashion, Millikan noted that all the readings from his electronic equipment were multiples of a very small number, which he calculated to be 1.60 x 10 19 coulomb. 

The cathode ray particle is known today as the electron, a name that comes from the Greek word for amber (electrify, which is a material the early Greeks used to study the effects of static electricity. The electron is a fundamental component of all atoms. All electrons are identical, each having a negative electric charge and an incredibly small mass of 9.1 X 10 31 kilogram. Electrons determine many of a material s properties, including chemical reactivity and such physical attributes as taste, texture, appearance, and color. 

The cathode ray—a stream of electrons—has found a great number of applications. Most notably, a traditional television set (not the modern, thin, LCD screens) is a cathode ray tube with one end widened out into a phosphor-coated screen. Signals from the television station cause electrically charged plates in the tube to control the direction of the ray such that images are traced onto the screen. 

Around 1910, a more accurate picture of the atom came to one of Thomsons former students, the New Zealand physicist Ernest Rutherford (1871—1937). Rutherford oversaw the now-famous gold-foil experiment, which was the first experiment to show that the atom is mostly empty space and that most of its mass is concentrated in a tiny central core called the atomic nucleus. 

Rutherford s gold-foil experiment. A beam of positively charged alpha particles was directed at a piece of gold foil. Most of the particles pas.sed through the foil undeflected, but some were deflected. This result implied that each gold atom was mostly empty space with a concentration of mass at its center -the atomic nucleus. 

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Fig. 6 Comparison of image projection in optical and electron microscopes. In the former, an optical lens focuses and enlarges a beam of light. In the electron microscope, a magnetic coil is used to bend electron rays for focusing and enlargement of the specimen. (Adapted from Ref. 1.)...

Oxygen valence electrons Ox ygen bending electron 0]i cn nonbondingelectrons... 

Fig. 6.2 la) Four cquivulent bending electron PLiirs. (b) Three bonding electron pairs repelled by a nonbording pair of electrons. 

The negative value of CH bending angle indicates inward bending. Electron diffraction data. 

Fig. V-14. Energy level diagram and energy scales for an n-type semiconductor pho-toelectrochemical cell Eg, band gap E, electron affinity work function Vb, band bending Vh, Helmholtz layer potential drop 0ei. electrolyte work function U/b, flat-band potential. (See Section V-9 for discussion of some of these quantities. (From Ref. 181.)...

The observation of a bend progression is particularly significant. In photoelectron spectroscopy, just as in electronic absorption or emission spectroscopy, the extent of vibrational progressions is governed by Franck-Condon factors between the initial and final states, i.e. the transition between the anion vibrational level u" and neutral level u is given by... 

Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Figure Bl.25.12 illustrates the two scattering modes for a hypothetical adsorption system consisting of an atom on a metal [3]. The stretch vibration of the atom perpendicular to the surface is accompanied by a change m dipole moment the bending mode parallel to the surface is not. As explained above, the EELS spectrum of electrons scattered in the specular direction detects only the dipole-active vibration. The more isotropically scattered electrons, however, undergo impact scattering and excite both vibrational modes. Note that the comparison of EELS spectra recorded in specular and off-specular direction yields infomiation about the orientation of an adsorbed molecule.

Figure Bl.25.12. Excitation mechanisms in electron energy loss spectroscopy for a simple adsorbate system Dipole scattering excites only the vibration perpendicular to the surface (v ) in which a dipole moment nonnal to the surface changes the electron wave is reflected by the surface into the specular direction. Impact scattering excites also the bending mode v- in which the atom moves parallel to the surface electrons are scattered over a wide range of angles. The EELS spectra show the higlily intense elastic peak and the relatively weak loss peaks. Off-specular loss peaks are in general one to two orders of magnitude weaker than specular loss peaks.

One reason that the symmetric stretch is favored over the asymmetric one might be the overall process, which is electron transfer. This means that most of the END trajectories show a nonvanishing probability for electron transfer and as a result the dominant forces try to open the bond angle during the collision toward a linear structure of HjO. In this way, the totally symmetric bending mode is dynamically promoted, which couples to the symmetric stretch, but not to the asymmetric one. 

Until now we have implicitly assumed that our problem is formulated in a space-fixed coordinate system. However, electronic wave functions are naturally expressed in the system bound to the molecule otherwise they generally also depend on the rotational coordinate 4>. (This is not the case for E electronic states, for which the wave functions are invariant with respect to (j> ) The eigenfunctions of the electronic Hamiltonian, v / and v , computed in the framework of the BO approximation ( adiabatic electronic wave functions) for two electronic states into which a spatially degenerate state of linear molecule splits upon bending. 

In Table I, 3D stands for three dimensional. The symbol symbol in connection with the bending potentials means that the bending potentials are considered in the lowest order approximation as already realized by Renner [7], the splitting of the adiabatic potentials has a p dependence at small distortions of linearity. With exact fomi of the spin-orbit part of the Hamiltonian we mean the microscopic (i.e., nonphenomenological) many-elecbon counterpart of, for example, The Breit-Pauli two-electron operator [22] (see also [23]). 

Figure 5, Low-eriergy vibronic spectrum in a electronic state of a linear triatomic molecule. The parameter c determines the magnitude of splitting of adiabatic bending potential curves, is the spin-orbit coupling constant, which is assumed to be positive. The zero on the...

Figure 6. Bending potential curves for the X Ai, A B electronic system of BH2 [33,34], Full hotizontal lines K —Q vibronic levels dashed lines /f — I levels dash-dotted lines K — 2 levels dotted lines K — 3 levels. Vibronic levels of the lower electronic state are assigned in benf notation, those of the upper state in linear notation (see text). Zero on the energy scale corresponds to the energy of the lowest vibronic level.

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