Chem120A+Notes+-+Wave+Character

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

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Unformatted text preview: Wave character: Quantum Interference Matter-Wave de Broglie relation = h / p the wave length, h= 6.6210-34 Js Plancks constant, p the momentum of particle X-rays ( ) = 12.4 / E (keV) Generated by the deceleration of electrons (Synchrotron) or by the excitation of core electrons in metals (Cu K 1.5418 ) Neutrons ( ) = 0.28 / [ E (eV)] 1/2 Interact with magnetic electrons and nuclei. Electrons ( ) = 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, , between the two waves, , where L 1 1 L 2 L screen k 2 k L L = = 2 2 1 2 1 2 | | | | 2 | || | cos( ) I = + + The phase difference 1 2 L L L = - 2 the difference between traveling distances Interference of Two Wave (Contd) 2 2 1 2 1 2 | | | | 2 | || | cos( ) I = + + If L n = is an integer, then 2 2 1 2 1 2 | | | | 2 | || | I = + + Constructive Interference If 1 2 L n = + is half of an odd integer, 2 2 1 2 1 2 | | | | 2 | || | I = + - Deconstructive Interference 2 n = 2 n = + and the intensity 2 n = 1 2 1 2 + and the intensity (2 1) n = + 1 2 1 2 + Interference of Multiple Waves 1 2 | e | N in n I - = = N is the number of atoms, and = 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 = 2 m , m is an arbitrary integer. When N increases, the peak becomes narrower, the peak height increases, H 2 H N Interference of Multiple Waves (contd) = 2 m L k n 1 2 3 3 N a sin L a = 2 sin k L a = = Constructive interference condition sin a m = 1 sin Diffraction pattern tells the distance between atoms 1 sin d = A 1D lattice has...
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Chem120A+Notes+-+Wave+Character - Wave character: Quantum...

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