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Lecture 27_1 - Lecture 27 Chapters 38 and 39 Electrons and...

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Lecture 27 April 27, 2010 Chapters 38 and 39
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2 If electromagnetic waves (light) can behave like particles (photons), can particles behave like waves? Electrons and Matter Waves 38- (de Broglie wavelength) h p where p is the momentum of the particle Electrons q 1924 Louis de Broglie
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The wave nature of the electrons and neutrons are used routinely for imaging of microscopic structures of matters. For example: Electron microscopy: TEM and SEM Neutron scattering Fig. 38-9
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38.52 What are (a) the energy of a photon corresponding to wavelength 5.0 nm (in keV), (b) the kinetic energy of an electron with de Broglie wavelength 5.0 nm (in eV), (c) the energy of a photon corresponding to wavelength 5.0 fm (in GeV), and (d) the kinetic energy of an electron with de Broglie wavelength 5.0 fm (in GeV)?
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Calculate the de Broglie wavelength of a 0.20 kg ball moving with speed 15 m/s. 5 1 2 3 4 5 0% 0% 0% 0% 0% 1. 2.2 × 10 -36 m 2. 2.2 × 10 -34 m 3. 2.2 × 10 -32 m 4. 2.2 × 10 -22 m 5. 2.2 × 10 -10 m
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6 Hydrogen (H) is the simplest “natural” atom. Contain +e charge at center surrounded by e charge (electron). Why doesn’t the electrical attraction between the two charges cause them to collapse together? The Bohr Model of the Hydrogen Atom 39- Fig. 39-16 Balmer’s empirical (based only on observation) formula on absorption/emission of visible light for H 2 2 1 1 1 , for 3,4,5, and 6 2 R n n Bohr’s assumptions to explain Balmer formula 1) Electron orbits nucleus 2) The magnitude of the electron’s angular momentum L is quantized , for 1,2,3, L n n
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7 Coulomb force attracting electron toward nucleus Orbital Radius is Quantized in the Bohr Model 39- 1 2 2 q q F k r 2 2 2 0 1 4 e v F ma m r r    Quantize angular momentum l : sin n rmv rmv n v rm Substitute v into force equation : 2 2 0 2 , for 1,2,3, h r n n me 2 , for 1,2,3, r an n Where the smallest possible orbital radius ( n =1) is called the Bohr radius a : 2 10 0 2 5.291772 10 m 52.92 pm h a me Orbital radius r is quantized and r =0 is not allowed (H cannot collapse).
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8 The total mechanical energy of the electron in H is: Orbital Energy is Quantized 39- 2 2 1 2 0 1 4 e E K U
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