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Actually, we need not speak of particles at all. For many experiments it is more convenient to speak of matter waves... The two pictures are of course mutually exclusive, because a certain thing cannot at the same time be a particle... and a wave... but the two complement each other. By playing with both pictures, by going from the one picture to the other and back again, we finally get the right impression of the strange kind of reality behind our quantum experiments.” ~ Werner Heisenberg (If you thought Special Relativity was strange…)

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I read Chapter 15 before coming to class 1. Yes, the whole thing. 2. Nope, essentially none. 3. Well some, more than ½. 4. A little only. 0 of 250 10

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Light is 1. Just a wave that transports energy through space. 2. Just a stream of particles that carries energy with it. 3. A unique entity that exhibits both wave and particle properties. 10 0 250

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In the Bohr model of the atom, electrons 1. orbit only at specific distances from the nucleus. 2. can have any sized orbit just like planets orbiting the sun. 3. are embedded into a positively charged “pudding” like substance. 0 of 250 10

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Laser diffraction demo vs. photo electric effect How does the photoelectric effect imply that light is made up of particles? How does a diffraction experiment tell us light is a wave?

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Matter Models continued… Two puzzles remain at this point: The wave-particle duality of light. The physical basis for the Bohr model.

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In 1923 a struggling graduate student named Louis deBroglie proposed that moving matter also has a wave-particle duality defined from wavelength = h/(mass×speed) where h = Plank’s constant = 6 x 10 -34

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Examples Wavelength = 10 -38 m (nonsense?) Wavelength = 10 -34 m (again nonsense?) Wavelength = 10 -10 m which is the diameter of an atom. Now we are getting somewhere… 60 mph 100 mph - 2,000 mps

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But are electrons really waves? See if they diffract. We need slits about the size of the electron wavelength (10 -10 m) to witness it. How do you make a slit that small? You don’t. You use the space between atoms in a crystal. Fire an electron beam at a crystal and we DO get diffraction rings! Electrons ARE waves?!?!

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Double slits again… OK. The Millikan oil drop experiment says that electrons are particles. Or at least they are picked up in discrete chunks by oil drops. But electrons clearly diffract like waves. Let’s turn to our old friend, the double slit experiment, and see if electrons interfere! particles waves

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Davisson-Germer Experiment Do a “double slit” experiment using the spaces between atoms in a crystal. An interference pattern is clearly seen. Electrons ARE waves!

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Harnessing the Wavelength of Electrons Diffraction is bad if you want to see things clearly. Large hole Small hole Sharp image Fuzzy image See this

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Electron Microscopes Microscopic things diffract light and limit how clearly we can see small items using light. Electron wavelengths are 1/1000 th the size of optical wavelengths. Using electron beams we can see 1000 times smaller with the same clarity.

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Wave-Particle Duality Experiments done with neutrons and even whole atoms show that they, too, have a wave nature. But experiments also show that all atomic matter clearly has a particle aspect to it. How can we reconcile this into a single model?

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What is Waving? For starters, having a “wave nature” does NOT mean that electrons move up and down or back and forth as they move through space like the waves of chapter 10. The “wave” is interpreted as being the probability of locating the particle. Let’s ask someone really smart…

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Huh? “Electrons or photons arrive in lumps, like particles, but the probability of arrival of these lumps is determined as the intensity of waves would be. It is in this sense that the electron behaves sometimes like a particle and sometimes like a wave.” Richard Feynman Nobel Prize, 1965

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Probability Laws of probability predict the overall distribution of many results. These laws do not predict what any specific result will be before it is tabulated, just the range in which it will fall.

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Moving Electrons Look at a single electron moving though space. Its position is given by a probability distribution. We know the range of positions it may have and the most likely position it may have but not the exact position is has.

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When we detect it, it does have a specific position but not necessarily the middle of the probability distribution. Repeat the experiment a million times and the entire curve will be filled. Reconciling Wave and Particle

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Electron Double-Slit Diffraction The electrons arrive as particles. They arrive in locations determined by the interference pattern of a wave with wavelength equal to h/(mass×speed)

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Heisenberg Uncertainty Principle The wave nature makes it impossible to know with infinite precision how atomic matter moves. Specifically: To know a particle’s motion we must know its position and velocity at the same time. But how do you locate the position of a wave/particle electron? The wave nature makes it impossible to know with infinite precision how atomic matter moves. Specifically: To know a particle’s motion we must know its position and velocity at the same time. But how do you locate the position of a wave/particle electron? Pure sine wave no position but clear wave properties. Sharp pulse clear position but unclear wave properties.

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Heisenberg Uncertainty Principle Electrons: fuzzy position and fuzzy wave properties. How fuzzy?....The uncertainty in position times the uncertainty in momentum (mass x velocity) is greater than Planck’s constant. Or ∆x ∆(mv) > h This is the Heisenberg Uncertainty Principle

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Consequences The more we know about where an electron is, the less we know about where it is going. Measuring position more accurately makes uncertainty in momentum larger. This is an alternative explanation for electron diffraction.

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In other words… We can predict this interaction perfectly using Newton’s Laws of motion. We cannot predict the results of an interaction between electrons perfectly. We can only say what will probably happen. 8 ? ? ? ?

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Important Tie-in to atoms! An electron orbiting a nucleus has its position determined to within the diameter of the atom. But its momentum is therefore made so uncertain we CANNOT know how it orbits! More in chapter 16…

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Philosophy Is probability all there is to electron motions? Does God really “play at dice” with the universe? Do we determine reality by our interactions with it? Or does it just seem that way? Bear in mind that these effects are only noticeable for sizes on the order of an atomic diameter.

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Heisenberg: Mathematics is sense! That’s what sense is! Bohr: But in the end, in the end, remember, we have to be able to explain it all to Margrethe!

Heisenberg: Mathematics is sense! That’s what sense is! Bohr: But in the end, in the end, remember, we have to be able to explain it all to Margrethe!

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