De Broglie Waves, Uncertainty, and Atoms

1. Physics 102: Lecture 23 De Broglie Waves, Uncertainty, and Atoms

2. Three Early Indications of Problems with Classical Physics • Blackbody radiation • Photoelectric effect • Wave-particle duality Lecture 22: Quantum Mechanics • Compton scattering • DeBroglie • Heisenberg Uncertainty Principle Today

3. Electron at rest 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 Photon energy Photon momentum  E = pc

4. 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

5. 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

6. 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

7. Radiometer Incident photons Black side (absorbs) Shiny side (reflects) 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

8. 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

9. 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

10. Electrons are Particles and Waves! • Depending on the experiment electron can behave like • wave (interference) • particle (localized mass and charge) • Recall Young’s double slit experiment: • If we measure which slit the electron went through, then there is no interference pattern!!

11. 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!!

12. Preflight 23.3 Which baseball has the longest De Broglie wavelength? (1) A fastball (100 mph) (2) A knuckleball (60 mph) (3) Neither - only curveballs have a wavelength

13. 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

14. Some Numerology Standard units (m, kg, s) are not convenient for talking about photons & electrons • 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

15. Equations are different - be careful! Big difference! Solve for Example Comparison:Wavelength of Photon vs. Electron 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:

16. X-ray vs. electron diffraction X-ray diffraction e– diffraction Demo Identical pattern emerges if de Broglie wavelength of e– equals the X-ray wavelength! From College Physics, Vol. Two

17. 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 Electron A has twice as much momentum as Electron B. Compare their energies. • EA = EB • EA = 2 EB • EA = 4 EB

18. 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

19. Heisenberg Uncertainty Principle Recall: Quantum Mechanics tells us nothing is certain, everything is probability Uncertainty in momentum (along y) Uncertainty in position (along y) Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa.

20. Electron diffraction Number of electrons arriving at screen p electron beam p Dpy = p sinq q screen Example Electron beam traveling through slit will diffract Single slit diffraction pattern w q y x Recall single-slit diffraction 1st minimum: sinq = l/w w = l/sinq = Dy Using de Broglie l

21. 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.

22. 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.”

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.