Lecture 25 (Ch 11.5, 29.1-29.2)

# Lecture 25 (Ch 11.5, 29.1-29.2) - Lecture 25 Quantum...

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Lecture 25 Quantum Physics IV "What we observe is not nature itself, but nature exposed to our method of questioning." --Werner Heisenberg

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Review o Light travels like a wave It Refracts Shows Interference Exhibits the Doppler effect o Light “hits” like a particle! Photo-electric effect Compton Scattering This particle-wave “duality” is intimately linked to the theory of Quantum Mechanics Matter – Particle and Wave? o de Broglie’s idea:
What’s Your Wavelength? o In principle, even macroscopic objects have a deBroglie wavelength. For a 60.0 kg person, walking at 2.00 m/s: λ = h/p = h/mv λ = (6.63 × 10 -34 J s)/(60.0 kg)(2.00 m/s) λ = 5.52 × 10 -36 m o Because Planck’s constant is so small, quantum effects are not observable in macroscopic objects o For an electron moving at 2.00 m/s: λ = 3.64 × 10 -4 m (1/3 mm)

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Two-Slit Experiment with Electrons o If we shoot electrons with de Broglie wavelength comparable to slit spacing, we get a two-slit interference pattern o The interference pattern persists even if only one electron at a time is fired The electron somehow interferes “with itself”
Double Slit The number m is called the order number of the fringe. Use:

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2 slit electron pattern Pattern builds up slowly, ~1 electron at a time! How do electrons interfere with themselves?…
Electrons with speed 400 m/s pass through a double slit experiment. The first bright spot occurs at an angle of 1 degree above horizontal. What is the spacing between the slits?

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Electrons with speed 400 m/s pass through a double slit experiment. The first bright spot occurs at an angle of 1 degree above horizontal. What is the spacing between the slits? What wavelength of light would be required to produce the same diffraction pattern?
Electrons with speed 400 m/s pass through a double slit experiment. The first bright spot occurs at an angle of 1 degree above horizontal. What is the spacing between the slits? What wavelength of light would be required to produce the same diffraction pattern? The same:

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Green light of 546nm hits a metal surface. The work function of the metal is 1.77 eV. What is the deBroglie wavelength of the fastest electrons that emerge from the metal? (use p = mv for the electrons and E = mv^2/2) h = 6.626 × 10 -34 J s = 4.14 x 10 -15 eV s hc = 1240 eV nm
Green light of 546nm hits a metal surface. The work function of the metal is 1.77 eV. What is the deBroglie wavelength of the fastest electrons that emerge from the metal? h = 6.626 × 10 -34 J s = 4.14 x 10 -15 eV s hc = 1240 eV nm Determine speed of e’s:

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Electron Microscopes o Electron microscopes use de Broglie’s principle Speed electrons up to very high momenta to get very small de Broglie wavelengths. Magnifications of up to x300,000! Resolution up to 0.1 nm (~ wavelength of electron)
The resolving power of a microscope depends on the wavelength used. If one wished to “see” an atom, a resolution of 10^ -11 m would be required. If electrons are used, what is the minimum kinetic energy required to “see” an atom?

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