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quantum mechanics

Explore the revolutionary concept of light behavior as particles in quantum mechanics, from cathode rays to diagnostic tests and the quantization of particles and waves.

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quantum mechanics

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  1. quantum mechanics part 1 – waves as particles ch 28

  2. Hmm!?

  3. Light frequecy=f cathode rays Another thing to play with (P.Lenard 1900)key to Cat scans (lets diagnose the problem) • I, f, V, light intensity • I vs f • I vs V • VStop vs f photoelectric

  4. Light frequecy=f cathode rays diagnostic test : I vs f

  5. Light frequecy=f cathode rays diagnostic tests : I vs intensity

  6. Light frequecy=f cathode rays diagnostic test: I vs V

  7. a new test? VStop I=small I=medium VStop I=Big I=zero None of the “cathode rays” make it

  8. Light frequecy=f cathode rays use it- diagnostic test : VStop vs f

  9. summarize the symptoms • cathode ray “current” only for f>f0 • f0 depends on metal of cathode • cathode ray “current” ~ light intensity • No delay in current appearance • for “forward V” , flat current • “backward V”, a VStop • VStop ~ f

  10. Diagnosis • Note: • The WRONG diagnosis when something new is going on is often difficult to understand. • It goes topsy-turvy to try to get it right. • The RIGHT diagnosis may sound crazy but is often simple and straightforward ONCE YOU ACCEPT THE NEW IDEA

  11. Light “heats” up the electrons and makes them more easily jump out of the pool (metal) the WRONG diagnosis I don’t get it….

  12. Symptoms cathode ray “current” only for f>f0 f0 depends on metal of cathode cathode ray “current” ~ light intensity No delay in current appearance for “forward V” , flat current “backward V”, a VStop VStop ~ f Metal – electrons stuck – W=work function characteristic of metal Light – little balls with energy If you don’t hit the electrons in the metal with E>W, the don’t get out. Critical frequncy then using E=hf is f0 =W/h. Lets go back and see…

  13. A CRAZY IDEA - Einstein • LIGHT IS A PARTICLE with energy E=hf • Problems of course • Why does it behave like a wave …. • Note: These things are called photons h a constant – Plank’s constant

  14. Symptoms cathode ray “current” only for f>f0 f0 depends on metal of cathode cathode ray “current” ~ light intensity No delay in current appearance for “forward V” , flat current “backward V”, a VStop VStop ~ f Metal – electrons stuck – W=work function characteristic of metal Light – little balls with energy If you don’t hit the electrons in the metal with E>W, the don’t get out. Critical frequncy then using E=hf is f0 =W/h. Lets go back and see…

  15. Symptoms cathode ray “current” only for f>f0 f0 depends on metal of cathode cathode ray “current” ~ light intensity No delay in current appearance for “forward V” , flat current “backward V”, a VStop VStop ~ f The more light balls “photons” above f0 the more electrons We also don’t need time to “heat up” Lets go back and see…

  16. Symptoms cathode ray “current” only for f>f0 f0 depends on metal of cathode cathode ray “current” ~ light intensity No delay in current appearance for “forward V” , flat current “backward V”, a VStop VStop ~ f Once we are collecting the electrons, we can’t get any more by turning up the voltage, we just make them go faster Lets go back and see…

  17. Symptoms cathode ray “current” only for f>f0 f0 depends on metal of cathode cathode ray “current” ~ light intensity No delay in current appearance for “forward V” , flat current “backward V”, a VStop VStop ~ f If we reverse the voltage though we can make them go backwards. When eV=hf we get nothing so this is VStop Lets go back and see… Voila!

  18. WHY DOES it change the wavelength??? compton

  19. Just do collisions + relativity + f=c/λ It works!

  20. The phototube – the heart of a catscan

  21. Cat Scanning

  22. quantization part 2 –particles as waves ch 28

  23. The world – a) matter - atoms nucleus of tightly packed protons and neutrons. Protons-positive charge electrons orbiting negative charge charges come in bits e=1.602 x 10-19C “quantized”

  24. The World: LightWe have a crazy new idea • LIGHT IS A PARTICLE …. • These things are called photons E=hf h a constant – Plank’s constant h=6.625 x 10-34 J-s 1eV=1.602 x 10-19J

  25. How is light made?absorbed?idea!

  26. Trouble: Why discreet?? Emission spectrum Absorption spectrum Like a Merry go round that can only go 1mph, 3mph, 5mph and NOTHING IN BETWEEN

  27. Why do we exist at all????

  28. Crazy possibility #2 – Bohr: electrons are waves Bohr 1 electron as wave in a circle 2πr=nλelectron

  29. So only certain orbitals are OK, and NOTHING in between. We require 2πr=nλelectron (whatever λelectron is…) States are stationary For orbitals in between, the electron goes around and interferes destructively with itself. Quantization of orbitals 2πr=nλelectron

  30. Starting Stuff Relativity Einstein E=hf Waves c=fλ Mechanics F=ma circular motion _ E&M Now lets see if we can figure out the energies of these orbitals 2πr=nλelectron

  31. But what is λelectron??? • back to light as particle • Relativity • mass of light?? mass of photon?? =0 • E=pc=hf=hc/λ SO p=h/λ or λ=h/p • Now to electron as wave • λelectron=h/pelectron

  32. Now lets see if we can figure out the energies of these orbitals (Hydrogen) here we get • F=ma • 2πr=nλe from here we get L=mvr=nh/2π the quantization of angular momentum

  33. quantization of the energy levels • We get

  34. quantized energy, radius, velocity

  35. What about the spectral lines? Emission spectrum Absorption spectrum Balmer forumla

  36. Only photons with certain energies allowed! bohr photons

  37. Energy of the photonsthe Balmer formula

  38. Binding energy, ionization energy 13.6/n2 eV 13.6 eV

  39. The Davison Germer Experiment • If electrons are really waves, they should diffract. • The Davison Germer Experiment

  40. Quantum MechanicsPart 3 Ch 28

  41. Waves or Particles? • We found out • electrons are particles • light is waves • Later we found out • light is particles • electrons are waves • What gives? • Neither? • Both?

  42. Lets think about the description • Particles • position (x), velocity (v), energy (E), etc • Light • Electric field (E), and magnetic field (B) • Strategy • Let’s First see if we can make Light look like a particle (sort of) • Light has to be like a ball (a small packet) • Then see if we can make electrons like waves • Make a “matter field” thing analogous to the Electric field E(x)~Asin(kx-ωt) • remember k=2π/λ and ω=2πf

  43. Light as particles • How can we make a wave pulse? • Drum beat • turn light on and off; ie make it blink • beats! • Can we add up some waves of different frequency to get little light “particles”? • http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=35 (50,54) • In fact, we can get any shape we want by adding enough waves • http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=33

  44. How many frequencies to make a nice square pulse? • wave f(x)=sin ωnx ωn~n n=1, 3, 5… More square More frequencies 1 frequency 8 frequencies 4 frequencies 1000 frequencies

  45. Heisenberg Uncertainty Principle • So a wave packet or particle is a sum over lots of waves of different frequency • But since E=hf • what is its energy???? • heisenberg uncertainty principle…. • better (more square) position ~smaller Δx  worse Δp= ΔE/c= hΔf/c • HEISENBERG: ΔxΔp h/2 • it will turn out this affects EVERYTHING • Problem with signal transmission

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