Chem120A+Notes+-+Wave+Character

Chem120A+Notes+-+Wave+Character - Wave character Quantum...

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Wave character: Quantum Interference
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Matter-Wave de Broglie relation λ = h / p λ the wave length, h= 6.62×10 -34 Js Planck’s constant, p the momentum of particle X-rays 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
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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
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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 +
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Interference of Multiple Waves 1 2 0 | 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
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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 =
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A 1D lattice has as its lattice constant; the incident wave vector is normal to the 1D lattice; and
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