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De Broglie Waves, Uncertainty, and Atoms

Physics 102: Lecture 23. De Broglie Waves, Uncertainty, and Atoms. Hour Exam 3. Monday, April 14 Covers lectures through Lecture 20 (last Monday’s lecture) homework through HW 10 discussions through Disc 10 Review, Sunday April 13, 3 PM, 141 LLP. Hour Exam 3 Review.

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De Broglie Waves, Uncertainty, and Atoms

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  1. Physics 102: Lecture 23 De Broglie Waves, Uncertainty, and Atoms Hour Exam 3 • Monday, April 14 • Covers • lectures through Lecture 20 (last Monday’s lecture) • homework through HW 10 • discussions through Disc 10 • Review, Sunday April 13, 3 PM, 141 LLP

  2. Hour Exam 3 Review • Fall 2007, HE2, problems 18-25 • Fall 2007, HE3, all except 22,27

  3. Photoelectric Effect Summary • Each metal has “Work Function” (W0) which is the minimum energy needed to free electron from atom. • Light comes in packets called Photons • E = h f h=6.626 X 10-34 Joule sec • Maximum kinetic energy of released electrons • K.E. = hf – W0 30

  4. KE hf W0 Photoelectric Effect Summary • Maximum kinetic energy of released electrons • K.E. = hf – W0 30

  5. Electron at rest Energy of a photon Compton Scattering This experiment reallyshowsphoton momentum! Pincoming photon+ 0 =Poutgoing photon+ Pelectron Outgoing photon has momentum p and wavelength  Incoming photonhas momentum, p, and wavelengthl Recoil electron carries some momentum and KE 5

  6. Is Light a Wave or a Particle? • Wave • Electric and Magnetic fields act like waves • Superposition, Interference, and Diffraction • Particle • Photons • Collision with electrons in photo-electric effect • Compton scattering from electrons BOTH Particle AND Wave

  7. ACT: Photon Collisions Photons with equal energy and momentum hit both sides of the plate. The photon from the left sticks to the plate, the photon from the right bounces off the plate. What is the direction of the net impulse on the plate? 1) Left 2) Right 3) Zero Photon that sticks has an impulse p Photon that bounces has an impulse 2p! 10

  8. Incident photons Black side (absorbs) Shiny side (reflects) Radiometer Preflight 23.1 Photon A strikes a black surface and is absorbed. Photon B strikes a shiny surface and is reflected back. Which photon imparts more momentum to the surface? Photon A Photon B 38% 63% 11

  9. Ideal Radiometer Photons bouncing off shiny side and sticking to black side. Shiny side gets more momentum so it should rotate with the black side leading 12

  10. Our Radiometer Black side is hotter:gas molecules bounce off it with more momentum than on shiny side-this is a bigger effect than the photon momentum 13

  11. Are Electrons Particles or Waves? • Particles, definitely particles. • You can “see them”. • You can “bounce” things off them. • You can put them on an electroscope. • How would know if electron was a wave? Look for interference!

  12. d 2 slits-separated by d Young’s Double Slit w/ electron • JAVA Source of monoenergetic electrons L Screen a distance L from slits 41

  13. Electrons are Waves? • Electrons produce interference pattern just like light waves. • Need electrons to go through both slits. • What if we send 1 electron at a time? • Does a single electron go through both slits? 43

  14. Electrons are Particles and Waves! • Depending on the experiment electron can behave like • wave (interference) • particle (localized mass and charge) • If we don’t look, electron goes through both slits. If we do look it chooses 1. 46

  15. De Broglie Waves So far only photons have wavelength, but De Broglie postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,…... Explains why we can see interference and diffraction for material particles like electrons!! 15

  16. Preflight 23.3 Which baseball has the longest De Broglie wavelength? 31% 60% 8% (1) A fastball (100 mph) (2) A knuckleball (60 mph) (3) Neither - only curveballs have a wavelength Lower momentum gives higher wavelength. p=mv, so slower ball has smaller p. 18

  17. ACT: De Broglie Wavelength A stone is dropped from the top of a building. What happens to the de Broglie wavelength of the stone as it falls? 1. It decreases 2. It stays the same 3. It increases Speed, v, KE=mv2/2, and momentum, p=mv, increase. 20

  18. Example Equations are different - be careful! Big difference! Solve for Comparison:Wavelength of Photon vs. Electron Say you have a photon and an electron, both with 1 eV of energy. Find the de Broglie wavelength of each. • Photon with 1 eV energy: • Electron with 1 eV kinetic energy: 23

  19. and so double p then double E double p then quadruple E Preflights 23.4, 23.5 Photon A has twice as much momentum as Photon B. Compare their energies. • EA = EB • EA = 2 EB • EA = 4 EB 21% 47% 33% Electron A has twice as much momentum as Electron B. Compare their energies. 22% 40% 38% • EA = EB • EA = 2 EB • EA = 4 EB 25

  20. ACT: De Broglie Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy. (1) lbowling > lgolf (2) lbowling = lgolf (3) lbowling < lgolf 27

  21. Heisenberg Uncertainty Principle Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa. This seems weird but… OK this is weird but…… it is also true. 29

  22. Number of electrons arriving at screen p electron beam screen p Dpy = p sinq q Use de Broglie l Heisenberg Uncertainty Principle:A Consequence of the Wave Nature of Particles w q Dy = w = l/sinq y x 33

  23. Preflight 23.7 According to the H.U.P., if we know the x-position of a particle, we can not know its: (1) y-position (2) x-momentum (3) y-momentum (4) Energy to be precise... Of course if we try to locate the position of the particle along the x axis to Dx we will not know its x component of momentum better than Dpx, where and the same for z. 35

  24. + + - - - - + + Early Model for Atom • Plum Pudding • positive and negative charges uniformly distributed throughout the atom like plums in pudding But how can you look inside an atom 10-10 m across? Light (visible) l = 10-7 m Electron (1 eV) l = 10-9 m Helium atom l = 10-11 m 38

  25. (Alpha particles = He++) Rutherford Scattering Scattering He++ atoms off of gold. Mostly go through, some scattered back! Flash Only something really big (i.e. nucleus) could scatter the particles back! If nucleus was baseball in Memorial Stadium, electrons would be A) Front Row B) Back Row B) Quad C) Savoy D) Moon Atom is mostly empty space with a small (r = 10-15 m) positively charged nucleus surrounded by cloud of electrons (r = 10-10 m) 42

  26. Large angle scatterings nuclear atom Need quantum theory Classic nuclear atom is not stable! Electrons will radiate and spiral into nucleus Nuclear Atom (Rutherford) 45

  27. Recap • Photons carry momentum p=h/l • Everything has wavelength l=h/p • Uncertainty Principle DpDx > h/(2p) • Atom • Positive nucleus 10-15 m • Electrons “orbit” 10-10 m • Classical E+M doesn’t give stable orbit • Need Quantum Mechanics! 50

  28. Reminder: Review Sunday

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