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Unformatted text preview: Wave character: Quantum Interference MatterWave de Broglie relation λ= h / p λ the wave length, h= 6.62×1034 Js Planck’s constant, p the momentum of particle • Xrays λ ( Å) = 12.4 / E (keV) Generated by the deceleration of electrons (Synchrotron) or by the excitation of core electrons in metals (Cu K α 1.5418 Å) • Neutrons λ ( Å) = 0.28 / [ E (eV)] 1/2 Interact with magnetic electrons and nuclei. • Electrons λ ( Å) = 12 / [ E (eV)] 1/2 Interact strongly with atoms and penetrate a relatively short distance into the crystal Interference of Two Wave Two plane waves starting with a same phase travel through distances L 1 and L 2 , and, finally, overlap with each other on a screen. The wave intensity on the screen depends on the phase difference, ∆φ , between the two waves, , where L ∆ 1 ψ 1 L 2 L screen k 2 k L L π φ λ ∆ = ∆ = ∆ 2 2 1 2 1 2     2    cos( ) I ψ ψ ψ ψ φ = + + ∆ The phase difference 1 2 L L L ∆ =  2 ψ the difference between traveling distances Interference of Two Wave (Cont’d) 2 2 1 2 1 2     2    cos( ) I ψ ψ ψ ψ φ = + + ∆ If L n λ ∆ = is an integer, then 2 2 1 2 1 2     2    I ψ ψ ψ ψ = + + Constructive Interference If 1 2 L n λ ∆ = + is half of an odd integer, 2 2 1 2 1 2     2    I ψ ψ ψ ψ = +  Deconstructive Interference 2 n φ π ∆ = 2 n φ π π ∆ = + and the intensity 2 n φ π ∆ = 1 ψ 2 ψ 1 2 ψ ψ + and the intensity (2 1) n φ π ∆ = + 1 ψ 2 ψ 1 2 ψ ψ + Interference of Multiple Waves 1 2  e  N in n I φ ∆ = = ∑ N is the number of atoms, and ∆φ = k ∆ L , is the phase difference. L ∆ The intensity k n 1 2 3 3 … N 8 N = 4 N = • The intensity has maximum at ∆φ = 2 m π , m is an arbitrary integer. • When N increases, the peak becomes narrower, the peak height increases, H 2 H N ∝ Interference of Multiple Waves (cont’d) ∆φ = 2 m π L ∆ k n 1 2 3 3 … N a θ sin L a θ ∆ = 2 sin k L a π φ θ λ ∆ = ∆ = Constructive interference condition sin a m θ λ = 1 sin θ Diffraction pattern tells the distance between atoms 1 sin d λ θ = A 1D lattice has...
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This note was uploaded on 09/28/2009 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at Berkeley.
 Spring '07
 Whaley
 Physical chemistry, Electron, pH

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