Lecture 22-1 Beyond Bohr Model Unfortunately, the classical visualization of the orbiting electron turns out to be wrong even though it still gives us a simple way to think of the atom. Quantum Mechanics is needed to truly understand and describe the atom. Wave-particle duality, Probabilistic formulation of quantum physics Chap. 28
Lecture 22-2 Electron Energy Levels in Solids When great many (order of Avogadro s number) atoms come together to form a solid, the individual atom s energy levels split up into dense groups of levels for the combined solid, called energy bands. These bands span essentially continuous range of energies.
Lecture 22-3 Energy Bands for Solids holes Dark regions are filled (i.e., there are electrons occupying there). Electrons can only move to available (unoccupied) states. There are many unoccupied states nearby in a conductor but there is none in an insulator. Small number of electrons can make a transition in semiconductors.
Lecture 22-4 Stimulated Emission of Light Incident photon with hf = ΔE stimulates emission of photon of the same frequency. So more photons come out as have gone in. Cascading effect can occur! Emitted photon in phase with incident photon. Coherent amplification. laser
Lecture 22-5 Laser Light amplification by stimulated emission of radiation Coherent, narrow, and intense Monochromatic (can be tunable as in liquid dye lasers) Can be continuous or pulsed Can be made using solid, liquid, gas, or even free electrons. Sustained population inversion is required.
Lecture 22-6 Examples of Lasers He-Ne Laser (continuous) Little populated, thus population inversion easy.
Lecture 22-7 Compton Scattering (Compton Effect) When X-ray strikes matter, EM radiation is found to scatter with longer wavelength than in the incident ray. Classically, the incident ray should vibrate charges in the target with the target reradiating with the same frequency/wavelength as in the incident ray. In quantum physics, we view this as the collision of a photon and an electron instead. Some of the energy of the incident photon is transferred to the electron. Thus the energy of the photon is reduced, or the frequency decreases.
Lecture 22-8 Compton Scattering (continued) c c Photon: In vacuum, always travels with speed c. Energy: hf = cp Momentum: p = hf/c = h/λ
Lecture 22-9 Compton Scattering with a free electron c c Energy conservation: E = K + E γi e γ f hf = K + hf i i e hc hc = Ke + λ λ f f Momentum conservation: p = p + p γ i e γ f h h = pe cosφ + cosθ λ λ i h 0= sinθ pe sinφ λ f f h λ f λi = θ mc K + mc = ( mc ) + ( cp ) ( 1 cos ) 2 2 2 e e e e e Compton Wavelength 2.43 pm
Lecture 22-10 Photoelectric Effect vs Compton Scattering Photoelectric effect An incident photon knocks out an electron. No photon comes out. Compton scattering (from an atom) An incident, high-energy photon scatters off of an electron, knocking it out of the atom as well as itself getting scattered into smaller frequency. The term Compton scattering is also used to describe more general photonelectron scattering events as well.
Lecture 22-11 Physics 219 Question 1 April 06, 2011. Which of the following is a property of the photoelectric effect but not one of Compton scattering? A. Photon (EM radiation) is an incident particle. B. Photon of lower frequency comes out. C. Electron gains energy and emerges from atom(s). D. Photon of higher frequency comes out. E. Photon is completely absorbed.
Lecture 22-12 Wave-Particle Duality 1 In quantum physics, the wave-nature and particle-nature of an object are closely linked. They turn out to be two aspects of the same reality. Consider again the two-slit interference pattern for light, where the part of the wave passing through one slit interferes with the part of the wave passing through the other slit, producing an interference pattern of intensity. Wave nature!
Lecture 22-13 Wave-Particle Duality 2 From a particle-like point of view, the intensity is proportional to the number of photons. So the fringe pattern can be viewed as a map of how many photons landed where. (A photomultiplier can count them.) Now what if we turn down the light intensity enough so that one photon at a time leaves the source? (a) Initially, photons seem to land at random places. Not just at the places expected for ballistic trajectories but no apparent interference pattern. (b) Gradually, bands of preferred landing areas emerge. (c) Eventually, clear interference pattern forms. Interference pattern like one from waves! Somehow, ONE photon knows about BOTH slits and interferes with itself!?
Lecture 22-14 Wave-Particle Duality 3 Even one photon evidently diffracts i.e., they do not always travel ballistically. Even one photon knows about both slits and interferes with itself. It is impossible to predict where a given photon will land, but there is evidently a well-defined pattern on average. Not only that, but also There is a well-defined probability for a photon to land at a place. ( wave function) 2 If we put a detector on each slit to find out which slit a photon has gone through, then no interference pattern any more!!
Lecture 22-15 Wave-Particle Duality 4 If we place detectors on the slits, we can determine which slit each photon goes through. Then, no more interference. By measuring the location of the photon at the slits, we somehow make the photon act more like a particle and less like a wave. Measurements affect what is being measured. In this case, if we don t find out which slit the photon has gone through, then it is as if it has gone through both slits and the part which has gone through one slit interferes with itself which has gone through the other slit, so to speak. As soon as you try to find out which slit it really goes through, though, it really does go through one but not the other, and thus no interference!! I am going to tell you what nature behaves like. Do not keep saying to yourself, if you can possibly avoid it, but how can it be like that? Nobody knows how it can be like that. R. P. Feynman
Lecture 22-16 De Broglie s Theory of Matter Waves If a photon can behave as either a particle or a wave, what about an electron, proton, atom, etc? Other particles, such as electrons, do have a wave nature also. The wavelength λ of a particle depends on its momentum p, and is called the de Broglie wavelength: λ = h p hc A photon: E = hf =, E = cp λ h λ = p de Broglie proposed that the same holds for any particle!
Lecture 22-17 Examples What is the wavelength of an electron that is moving at a speed of 4 m/s? h λ = = p h m v e 34 6.63 10 Js = = 1.82 10 31 9.11 10 kg 4 m / s What is the wavelength of a 0.25 kg rock that is moving at 4 m/s? 4 m h h λ = = p m v rock 34 6.63 10 Js = = 6.63 10 0.25kg 4 m / s 34 m Much maller than any known length!! No wave nature shows up.
Lecture 22-18 Physics 219 Question 2 April 06, 2011. According to de Broglie s theory, every particle behaves also like a wave with a wavelength related to its momentum. Now consider a baseball thrown at a batter at 50 miles/hr. The batter hits the ball and it travels to the outfield at 100 miles/hr. If the de Broglie wavelength of the ball was λ just before being hit by the batter, what is it just afterward (when it is traveling with 100 miles/hr)? A. 0.25 λ B. 0.5 λ C. λ D. 1.5 λ E. 2 λ