Physics 102 Lecture 23 De Broglie Waves Uncertainty

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 • Fall 2007, HE 2, problems 18 -25 • Fall 2007, HE 3, all except 22, 27

Photoelectric Effect Summary • Each metal has “Work Function” (W 0) which is the minimum energy needed to free electron from atom. • Light comes in packets called Photons –E=hf h=6. 626 X 10 -34 Joule sec • Maximum kinetic energy of released electrons – K. E. = hf – W 0 30

Photoelectric Effect Summary • Maximum kinetic energy of released electrons – K. E. = hf – W 0 hf KE W 0 30

Compton Scattering This experiment really shows photon momentum! Pincoming photon + 0 = Poutgoing photon + Pelectron Electron at rest Incoming photon has momentum, p, and wavelength Energy of a photon Outgoing photon has momentum p and wavelength Recoil electron carries some momentum and KE 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

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 Photon that sticks has an impulse p 2) Right 3) Zero Photon that bounces has an impulse 2 p! 10

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 38% Photon B 63% 11

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

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

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!

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

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

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

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

Preflight 23. 3 Which baseball has the longest De Broglie wavelength? 31% (1) A fastball (100 mph) 60%(2) A knuckleball (60 mph) 8% (3) Neither - only curveballs have a wavelength Lower momentum gives higher wavelength. p=mv, so slower ball has smaller p. 18

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=mv 2/2, and momentum, p=mv, increase. 20

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

Preflights 23. 4, 23. 5 Photon A has twice as much momentum as Photon B. Compare their energies. 21% • EA = EB 47% • EA = 2 EB 33% • EA = 4 EB and so double p then double E Electron A has twice as much momentum as Electron B. Compare their energies. 22% • EA = EB 40% • EA = 2 EB 38% • EA = 4 EB double p then quadruple E 25

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

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

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

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. 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 35

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 e. V) Helium atom l = 10 -9 m l = 10 -11 m 38

Rutherford Scattering He++ atoms off of gold. Mostly go through, some scattered back! Flash (Alpha particles = He++) 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

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

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

Reminder: Review Sunday