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Slide 2 12 Slide 3 Sections Photon and Matter Waves Compton Effect Light as a Probability Wave Electrons and Matter Waves Schrodinger s Equation Waves on Strings and Matter Waves Trapping an Electron Three Electron Traps The Hydrogen Atom Slide 4 12-1 Photon and Matter Waves ( ) Light Waves and Photons Slide 5 The Photoelectric Effect Slide 6 First Experiment (adjusting V) the stopping potential V stop Second Experiment (adjusting f) the cutoff frequency f 0 The experiment Slide 7 The plot of V stop against f Slide 8 The Photoelectric Equation Work function Slide 9 12-2 Compton Effect Slide 10 Slide 11 Slide 12 Energy and momentum conservation Slide 13 Frequency shift Compton wavelength Slide 14 12-3 Light as a Probability Wave The standard version Slide 15 The single-photon, double-slit experiment is a phenomenon which is impossible, absolutely impossible to explain in any classical way, and which has in it the heart of quantum mechanics - Richard Feynman The Single-Photon Version First by Taylor in 1909 Slide 16 The Single-Photon, Wide- Angle Version (1992) 50m Slide 17 Light is generated in the source as photons Light is absorbed in the detector as photons Light travels between source and detector as a probability wave The postulate Slide 18 12-4 Electrons and Matter Waves The de Broglie wave length Experimental verification in 1927 Iodine molecule beam in 1994 Slide 19 1989 double-slit experiment 7,100,3000, 20,000 and 70,000 electrons Slide 20 Experimental Verifications X-ray Electron beam Slide 21 Slide 22 12-5 Schrodinger s Equation Matter waves and the wave function The probability (per unit time) is Complex conjugate Slide 23 The Schrodinger Equation from A Simple Wave Function (1D) Slide 24 1D Time-independent SE Slide 25 3D Time-dependent SE Slide 26 12-6 Waves on Strings and Matter Waves Slide 27 Confinement of a Wave leads to Quantization discrete states and discrete energies Quantization Slide 28 12-7 Trapping an Electron For a string Slide 29 Finding the Quantized Energies of an infinitely deep potential energy well Slide 30 The ground state and excited states The ground state and excited states The Zero-Point Energy The Zero-Point Energy n cant be 0 n cant be 0 The Energy Levels Slide 31 The Wave Function and Probability Density For a string Slide 32 The Probability Density Slide 33 Normalization ( ) Correspondence principle ( ) At large enough quantum numbers, the predictions of quantum mechanics merge smoothly with those of classical physics Slide 34 A Finite Well Slide 35 The probability densities and energy levels Slide 36 Barrier Tunneling Transmission coefficient Slide 37 STM Piezoelectricity of quartz Slide 38 12-8 Three Electron Traps Nanocrystallites Nanocrystallites Slide 39 A Quantum Dot An Artificial Atom The number of electrons can be controlled Slide 40 Quantum Corral Slide 41 12-1.9 The Hydrogen Atom The Energies Slide 42 41 The Bohr Model of the Hydrogen Atom 39- Fig. 39-16 Balmers empirical (based only on observation) formula on absorption/emission of visible light for H Bohrs assumptions to explain Balmer formula 1)Electron orbits nucleus 2)The magnitude of the electrons angular momentum L is quantized Slide 43 42 Coulomb force attracting electron toward nucleus Orbital Radius is Quantized in the Bohr Model 39- Quantize angular momentum l : Substitute v into force equation : Where the smallest possible orbital radius ( n =1) is called the Bohr radius a : Slide 44 43 The total mechanical energy of the electron in H is: Orbital Energy is Quantized 39- Solving the F=ma equation for mv 2 and substituting into the energy equation above: Substituting the quantized form for r : Slide 45 44 Energy Changes 39- Substituting f=c/ and using the energies E n allowed for H: This is precisely the formula Balmer used to model experimental emission and absorption measurements in hydrogen! However, the premise that the electron orbits the nucleus is incorrect! Must treat electron as matter wave. Where the Rydberg constant Slide 46 Slide 47 Schrdingers Equation and the Hydrogen Atom Fig. 39-17 Slide 48 The Ground State Wave Function Slide 49 Quantum Numbers for the Hydrogen Atom For ground state, since n=1 l=0 and m l =0 Slide 50 The Ground State Dot Plot Slide 51 50 Fig. 39-21 Wave Function of the Hydrogen Atoms Ground State 39- Fig. 39-20 Probability of finding electron within a small volume at a given position Probability of finding electron within a within a small distance from a given radius Slide 52 Slide 53 N=2, l=0, m l =0 Slide 54 N=2, l=1 Slide 55 54 As the principal quantum number increases, electronic states appear more like classical orbits. Hydrogen Atom States with n>>1 39- Fig. 39-25 Slide 56