L03AtomicII145s09

L03AtomicII145s09 - Lecture 3 Atomic Theory II From the...

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Lecture 3, spring 2009 ENGR 145: Chemistry of Materials Case Western Reserve University Lecture 3 – Atomic Theory II From the Bohr model to Schrödinger’s wave equation Reading assignment: OGC §4.4-4.5, 5.1, 5.3-5.4 Learning objectives: Recognize the wave-particle duality of electrons Understand consequences of the Schrödinger equation : the shape of electron orbitals in atoms the electronic configurations of atoms the form of the periodic table of the elements Know how the Heisenberg uncertainty principle limits the precision with which we can know something’s position, momentum, and energy
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Lecture 3, spring 2009 ENGR 145: Chemistry of Materials Case Western Reserve University Wave Nature of Matter (OGC §4.4) Some classical physical systems have quantized states and a wave nature, e.g the standing wave of a vibrating string: DeBroglie: If energy of an e in a Bohr radius has quantized energy, does it also have a wavelength? , 2 L n = λ ,... 3 , 2 , 1 = ν 4.17
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Lecture 3, spring 2009 ENGR 145: Chemistry of Materials Case Western Reserve University Allowed wavelengths: Bohr assumed quantized angular momentum: Comparing (a) and (b) gives: where p = momentum De Broglie Wavelength of Electrons (OGC §4.4) = v m h n r e p 2 n λ=2πρ ,... 3 , 2 , 1 = ν p h v m h e = = λ 4.18 (b) (a)
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Lecture 3, spring 2009 ENGR 145: Chemistry of Materials Case Western Reserve University 4.5 ~mean speed of in Cu (67 mph) (several atomic distances) De Broglie Waves (OGN §4.4)
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Lecture 3, spring 2009 ENGR 145: Chemistry of Materials Case Western Reserve University The standing wave description of the electron implies limits to the precision with which its position and momentum can be known simultaneously Heisenberg’s quantitative statement of this phenomenon places a fundamental limit on the accuracy of the position and momentum
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L03AtomicII145s09 - Lecture 3 Atomic Theory II From the...

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