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The Electron Diffraction
 
Quantum physics maintains a dual view of all material objects, claiming that they have both wave- and particle- properties. According to de Broglie's hypothesis that was postulated in 1924, every body with mass m and moving at velocity v should have a wavelength of
λ = h/mv = h/p,
Where h = 6.63?10-34 J s is Planck's constant.
The wave aspects are most pronounced in elementary particles, also known as the microscopic particles. Due to their small masses, the de Broglie wavelength appears to be comparable with distances between the adjacent atoms in crystals. Diffraction phenomena appear if an electron beam interacts with the crystal lattice. Electrons with the energy 150 eV have a wavelength of λ = 10-10 m. Distances between atoms in crystals are of the same order. If a beam of electrons is directed at a crystal, the electrons scatter in accordance with the laws of diffraction. A diffraction pattern that is fixed on film contains information about the structure of a three-dimensional crystal lattice.
Electron scattering in crystals can be illustrated by an experiment pertaining to electron diffraction on one - dimensional grating. From the wave point of view, this model is completely equivalent to the optical experiment with diffraction grating. The positions of the maxima are determined by
dsinΘm = mλ,
Where d is the grating spacing, Θm is the angle of diffraction, m is an integer (the order of diffraction maximum), and λ is de Broglie wavelength.
At smaller angles of diffraction,
Θm = mλ/d.
If a photographic film is placed at distance L from the grating, a diffraction pattern with thin fringes will appear. The fringes? positions for small angles of diffraction are given by
xm = L?Θm = mL(λ/d) .
In quantum physics, the intensity distribution in the diffraction pattern is interpreted as a distribution of probability of an electron striking different points of the screen. Each electron interacts with the grating as a wave (interacting with the entire grating), but on the screen, its interaction is localized in a definite point. Thus, the appearance of diffraction pattern reaffirms the theory of probability.
 
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