Diffraction of electrons

Calculate the de Broglie wavelength associated with a helium-4 atom 

2 What is the de Broglie mass of a (Aioton of light with X = 122 nm (The velocity of a photon is the speed of light, c.) 

1 Calculate the de Broglie wavelength associated with a helium-4 atom (4.00 amu) moving at 3.0 X 10 m/s. 

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C. J. Davisson (New York) and G. P. Thomson (London) experimental discovery of the diffraction of electrons by crystals. 

Cowley, J.M. (1992) Scattering factors for the diffraction of electrons by crystalline solids, In International Tables for Crystallography, Wilson, A.J.C. (Ed.), Volume C. Kluwer Academic Publishers, Dordrecht/Boston/London. 

K. Kuchitsu and L. S. Bartell, Effects of Anharmonicity of Molecular Vibrations on The Diffraction of Electrons. II. Interpretation of Experimental Structural Parameters, J. Chem. Phys., 35 (1961) 1945-1949. 

I believe that this contribution, the discovery of the technique of determining the structure of gas molecules by the diffraction of electrons, constitutes Mark s most important contribution to... 

Conclusion. This book is concerned with optical and X-ray methods but there are of course other methods of studying the structures of crystals and molecules. The diffraction of electrons and of neutrons depends on the same general principles as that of X-rays or visible light but there are important theoretical differences, and the expert mental arrangements are very different. It is not proposed to deal with either of these subjects here, but a few remarks will be made on their relation to the X-ray diffraction method. 

Modem structural chemistry differs from classical structural chemistry with respect to the detailed picture of molecules and crystals that it presents. By various physical methods, including the study of the structure of crystals by the diffraction of x-rays and of gas molecules by the diffraction of electron waves, the measurement of electric and magnetic dipole moments, the interpretation of band spectra, Raman spectra, microwave spectra, and nuclear magnetic resonance spectra, and the determination of entropy values, a great amount of information has been obtained about the atomic configurations of molecules and crystals and even their electronic structures a discussion of valence and the chemical bond now must take into account this information as well as the facts of chemistry. 

Louis de Broglie discussed the relations between energy, momentum, and wavelength for photons as well as for electrons and examined the results of the Davisson-Germer experiment on the diffraction of electrons by crystals, which were in perfect agreement with theory. 

Joyce-Loebel MK III C flat-bed microdensitometer. The structure factor magnitudes were derived from the integrated intensities according to F(hk ) 2 = I(hk ). The largest errors in the intensity measurements were for the darkest spots. The scattering factors of C, 0 H for the diffraction of electrons were taken from the International Tables for X-Ray Crystallography, vol. IV (7). No correction for multiple scattering and n-beam dynamical interactions were applied because the thickness of the crystals was of the order of 100 X (6). 

The diffraction of electrons photoemitted from core levels gives structural information on the surface. 

Aggarwal, E. H., and S. H. Bauer The Structure of Hexamethylcyclo-trisiloxane as Determined by the Diffraction of Electrons on the Vapour. 

This relation found a direct experimental confirmation in the experiments of Davisson and Germer and of Thomson already mentioned on the diffraction of electron beams by crystal lattices. In fact for electrons which have traversed a potential difference P, the energy eP = 1/2 mv2 the kinetic energy, or (mv)2 = 2 meP thus ... 

Bartell LS (1955) Effects of anharmonicity of vibration on the diffraction of electrons by free molecules. J Chem Phys 23 1219-1222... 

Kuchitsu K, Bartell LS (1961) Effects of anharmonicity of molecular vibrations on the diffraction of electrons. II. Interpretation of experimental structural parameters. J Chem Phys 35 1945-1949... 

The diffraction of electrons with high energies (30-70 keV) incident at very low angles (0.5°-4 ) to a crystal surface such that they are reflected from it... 

We now consider the diffraction of electrons by a single crystal in terms of the so-called kinematical theory. Although this theory has serious limitations, it is useful in practice under certain conditions, and it also provides an introduction to the more satisfactory dynamical theory, which we develop in Chapter 4. 

The diffraction of electrons by gaseous diborane has been studied by Bauer who originally interpreted the data in terms of the ethane model and obtained the following values for the interatomic distances B—B = 1 86 A and B—H = 1 27 A. More recently , however, it has been shown that the data agree equally well with distribution of atoms in the bridge model, the values for the distances being as foUows ... 

Ti 3p core level, distinct increases in ion current also correlated with increases of the secondary electron emission as shown Fig. 3. As no core levels for O and Ti atoms exists at this energy it can be concluded that the sharp increases are due to an enhancement of the ion yield produced by secondary electrons from the Ti02 sublayer. It was also observed that these thresholds are very sensitive to the azimuth angle of the incident electron at the surface. It would appear that this phenomena could be related with the work of Maschhoff, Pan and Madey on the backscattered diffraction of electrons by the Ti02 sublayer [105]. 

Davisson C, Germer LH (1927) Diffraction of electrons by a crystal of nickel. Phys Rev 30 705... 

In order to subject the diffraction of electrons by crystal lattices to calculation, it is natural to begin by combining the simple de Broglie equation... 

Experiments on the diffraction of electrons below 500 volts, however, show that here the ordinary interference equations no longer suffice. The first experiments on metals f showed that the wave-length calculated theoretically is greater than that found by experiment, and that the slower the electron, the greater the discrepancy. 

Two years after de Broglie s prediction, C. Davisson (1882-1958) and L. H. Germer (1896-1971) at the Bell Telephone Laboratories demonstrated diffraction of electrons by a crystal of nickel. This behavior is an important characteristic of waves. It shows conclusively that electrons do have wave properties. Davisson and Germer found that the wavelength associated with electrons of known energy is exactly that predicted by de Broglie. Similar diffraction experiments have been successfully performed with other particles, such as neutrons. 

G.24 J. B. Cohen. Diffraction Methods in Materials Science (New York Macmillan, 1966). Includes material on the diffraction of electrons and neutrons, as well as x-rays. Studies of crystal imperfections. 

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