Hour Exam 3 Monday, Apr. 18 Review session Conflict exams Lectures 14 – 21 Homework through HW 11 Discussions through Disc 11 Review session Sunday, Apr. 17, 3pm, 141 Loomis Will cover Fall ‘10 exam 3 Conflict exams Make arrangements by Thursday!

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

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

Compton Scattering  E = pc This experiment really shows photon momentum! Pincoming photon + 0 = Poutgoing photon + Pelectron Electron at rest Experiment: Outgoing photon has longer wavelength  Incoming photon has momentum p, and wavelength l Recoil electron carries some momentum and KE Photon energy Photon momentum  E = pc

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

Is Light a Wave or a Particle? 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

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

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 29% 71%

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

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

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!!

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!!

Preflight 23.3 Which baseball has the longest De Broglie wavelength? 27% 61% 12% (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.

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.

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 10-31 kg mc2 = 8.2 x 10-13 J = 511,000 eV = 511 keV

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

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

Preflights 23.4, 23.5 Photon A has twice as much momentum as Photon B. Compare their energies. 18% 64% EA = EB EA = 2 EB EA = 4 EB and so double p then double E Electron A has twice as much momentum as Electron B. Compare their energies. 22% 41% 37% EA = EB EA = 2 EB EA = 4 EB double p then quadruple E

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

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.

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

The “Uncertainty in py” is Dpy  h/w. electron beam screen Number of electrons arriving at screen w x y py 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.

electron beam screen Number of electrons arriving at screen w x y py 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.”

to be precise... ACT/Preflight 23.7 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. ACT/Preflight 23.7 According to the H.U.P., if we know the x-position of a particle, we cannot know its: (1) y-position (2) x-momentum (3) y-momentum (4) Energy 58% correct

See you Monday