Lecture_23

Lecture_23 - Lecture 23-1 Lecture Matter Wave and Bohr...

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Lecture 23 Lecture 23 -1 Matter Wave and Bohr Model ¾ In Bohr model, we assumed the quantization of electron’s orbital angular momentum: / 2 ( 1,2,3,. ..) n LL n h n π = == We can now interpret this in terms of standing waves that fit exactly in the circular orbit of radius r around the nucleus: 2 h r p n λ λ= = 2, 2 2 hn h rn p p r nh Lm v r p r =∴ = = Though the circular orbit idea was wrong, the standing wave idea turns out to be correct. We will see that the quantum mechanical description of the atom is mathematically equivalent to that of standing waves .

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Lecture 23 Lecture 23 -2 Wave Nature of an Electron ¾ J. J. Thomson had discovered the electron as a particle . ¾ His son G. P. Thomson as well as Davisson and Germer performed electron diffraction, establishing the wave nature of the electron . X-ray diffraction from the same sample Electron diffraction pattern from polycrystalline Al
Lecture 23 Lecture 23 -3 Matter Wave Probes ¾ Electron diffraction ¾ Other diffraction probes: neutron, atoms, even molecules Wavelength of an 8 keV electron: 34 31 19 11 2 6.63 10 2 9.11 10 8000 1.6 10 1.37 10 e hh p mK Js kg J m λ −− =≅ × = ×× × × = × X-ray of 1240 0.0137 90.5 hc E eV nm nm keV = = =

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Lecture 23 Lecture 23 -4 Electron Microscope
Lecture 23 Lecture 23 -5 Heisenberg’s Uncertainty Principle ¾ There is an intrinsic uncertainty in nature . (cf. Probabilistic nature associated with the wave-particle duality) As a reflection of this, certain pairs of quantities cannot be measured together beyond certain precision even in principle . ¾ The Position-Momentum Uncertainty Principle states that we cannot know exactly where a particle is, and at the same time know it’s momentum exactly.

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Lecture_23 - Lecture 23-1 Lecture Matter Wave and Bohr...

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