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

Physics 102: Lecture 23, Slide 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

Physics 102: Lecture 23, Slide 3 Experiment: Outgoing photon has longer wavelength Recoil electron carries some momentum and KE Incoming photon has momentum p, and wavelength This experiment really shows photon momentum!shows Electron at rest Compton Scattering P incoming photon + 0 = P outgoing photon + P electron Photon energyPhoton momentum  E = pc

Physics 102: Lecture 23, Slide 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

Physics 102: Lecture 23, Slide 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

Physics 102: Lecture 23, Slide 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) Left2) Right3) Zero

Physics 102: Lecture 23, Slide 7 Incident photons 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 APhoton B Black side (absorbs) Shiny side (reflects)

Physics 102: Lecture 23, Slide 8 Photons bouncing off shiny side and sticking to black side. Shiny side gets more momentum so it should rotate with the black side leading Ideal Radiometer

Physics 102: Lecture 23, Slide 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

Physics 102: Lecture 23, Slide 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!!

Physics 102: Lecture 23, Slide 11 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!! De Broglie Waves

Physics 102: Lecture 23, Slide 12 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 Preflight 23.3

Physics 102: Lecture 23, Slide 13 ACT: De Broglie Wavelength A stone is dropped from the top of a building. 1. It decreases 2. It stays the same 3. It increases What happens to the de Broglie wavelength of the stone as it falls?

Physics 102: Lecture 23, Slide 14 Some Numerology 1 eV = energy gained by a charge +e when accelerated through a potential difference of 1 Volt –e = 1.6 x C so 1 eV = 1.6 x J h = x J·sec c = 3 x 10 8 m/s –hc = x J·m = 1240 eV·nm mass of electron m = 9.1 x kg –mc 2 = 8.2 x J = 511,000 eV = 511 keV Standard units (m, kg, s) are not convenient for talking about photons & electrons

Physics 102: Lecture 23, Slide 15 Photon with 1 eV energy: 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. Electron with 1 eV kinetic energy: Solve for Big difference! Equations are different - be careful!

Physics 102: Lecture 23, Slide 16 X-ray diffractione – diffraction From College Physics, Vol. Two Identical pattern emerges if de Broglie wavelength of e – equals the X-ray wavelength! X-ray vs. electron diffraction Demo

Physics 102: Lecture 23, Slide 17 Preflights 23.4, 23.5 Photon A has twice as much momentum as Photon B. Compare their energies. E A = E B E A = 2 E B E A = 4 E B Electron A has twice as much momentum as Electron B. Compare their energies. E A = E B E A = 2 E B E A = 4 E B

Physics 102: Lecture 23, Slide 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) bowling > golf (2) bowling = golf (3) bowling < golf

Physics 102: Lecture 23, Slide 19 Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa. Heisenberg Uncertainty Principle Recall: Quantum Mechanics tells us nothing is certain, everything is probability Uncertainty in position (along y) Uncertainty in momentum (along y)

Physics 102: Lecture 23, Slide 20 Number of electrons arriving at screen screen w x y  p  p y = p sin  p  =  y w = /sin  electron beam Electron diffraction Electron beam traveling through slit will diffract Recall single-slit diffraction 1 st minimum: sin  = /w Using de Broglie Single slit diffraction pattern

Physics 102: Lecture 23, Slide 21 Electron entered slit with momentum along x direction and no momentum in the y direction. When it is diffracted it acquires a p y which can be as big as h/w. The “Uncertainty in p y ” is  p y  h/w. An electron passed through the slit somewhere along the y direction. The “Uncertainty in y” is  y  w. electron beam screen Number of electrons arriving at screen w x y pypy

Physics 102: Lecture 23, Slide 22 electron beam screen Number of electrons arriving at screen w x y pypy If we make the slit narrower (decrease w =  y) the diffraction peak gets broader (  p y increases). “If we know location very precisely, we lose knowledge of momentum, and vice versa.”

Physics 102: Lecture 23, Slide 23 to be precise... Of course if we try to locate the position of the particle along the x axis to  x we will not know its x component of momentum better than  p x, where and the same for z. 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