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De Broglie Waves, Uncertainty, and Atoms

Physics 102: Lecture 23. De Broglie Waves, Uncertainty, and Atoms. Hour Exam 3. Monday, Apr 19 Covers Lectures through Lecture 21 (no single-slit diffraction!) Homework through HW 10 Discussions through Disc 10 Review session Sunday, Apr 18 Sunday, Apr 18, 3pm, 141 Loomis

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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

  2. Hour Exam 3 • Monday, Apr 19 • Covers • Lectures through Lecture 21 (no single-slit diffraction!) • Homework through HW 10 • Discussions through Disc 10 • Review session Sunday, Apr 18 • Sunday, Apr 18, 3pm, 141 Loomis • Will cover Fall ’09 exam 3

  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 Momentum of a photon Compton Scattering This experiment reallyshowsphoton momentum! Pincoming photon+ 0 =Poutgoing photon+ Pelectron Experiment: Outgoing photon has longer wavelength  Incoming photonhas momentum, p, and wavelengthl Recoil electron carries some momentum and KE 5

  6. Compton Scattering • Incident photon loses momentum, since it transfers momentum to the electron • Lower momentum means longer wavelength • This is proof that a photon has momentum

  7. 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

  8. 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 10

  9. 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 31% 69% 11

  10. 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

  11. 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

  12. 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!

  13. d 2 slits-separated by d Young’s Double Slit w/ electron Electrons produce interference pattern just like light waves. Source of monoenergetic electrons L Screen a distance L from slits 41

  14. Electrons are Particles and Waves! • Depending on the experiment electron can behave like • wave (interference) • particle (localized mass and charge) • If we do an experiment that tells us which slit the electron went through, then there is no interference pattern 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? 25% 66% 9% (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. Some Numerology • 1 eV = energy gained by a charge e when accelerated through a potential difference of 1 Volt e = 1.6 x 10-19 C so 1 eV = 1.6 x 10-19 J • h = 6.626 x 10-34 J-sec • c = 3 x 108 m/s • hc = 1.988 x 10-25 J-m = 1240 eV-nm • Mass of electron m = 9.1 x 10-34 kg • mc2 = 8.2 x 10-13 J = 511,000 eV = 511 keV

  19. 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

  20. 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% 54% 25% Electron A has twice as much momentum as Electron B. Compare their energies. 20% 40% 40% • EA = EB • EA = 2 EB • EA = 4 EB 25

  21. 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

  22. Heisenberg Uncertainty Principle Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa. 29

  23. 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

  24. Electron diffraction py Number of electrons arriving at screen w electron beam screen y x Electron entered slit with momentum along x direction and no momentum in the y direction. When it is diffracted it acquires a py which can be as big as h/w. The “Uncertainty in py” is Dpy h/w. An electron passed through the slit somewhere along the y direction. The “Uncertainty in y” is Dy  w. 35

  25. py Number of electrons arriving at screen w electron beam screen y x If we make the slit narrower (decrease w=Dy) the diffraction peak gets broader (Dpy increases). “If we know location very precisely, we lose knowledge of momentum, and vice versa.” Remember earlier we saw that a particle whose momentum (and therefore wavelength) is known precisely is very uncertain in position. 34

  26. 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

  27. See you Monday

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