2. Physics 102: Lecture 23, Slide 1 De Broglie Waves, Uncertainty, and Atoms Today’s Lecture will include material from textbook sections 27.5, 28.2, 4 Physics 102: Lecture 23

3. Outgoing photon has momentum p and 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 Energy of a photon

4. Physics 102: Lecture 23, Slide 3 ACT: Photon Collisions Photons with equal energy and momentum hit both sides of a metal 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

5. Physics 102: Lecture 23, Slide 4 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 Photon that sticks has an impulse p Photon that bounces has an impulse 2p!

6. Physics 102: Lecture 23, Slide 5 Black side (absorbs) Shiny side (reflects) 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

7. Physics 102: Lecture 23, Slide 6 Black side (absorbs) Shiny side (reflects) 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

8. Physics 102: Lecture 23, Slide 7 So far only for 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

9. Physics 102: Lecture 23, Slide 8 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 23.5

10. Physics 102: Lecture 23, Slide 9 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 23.5 Lower momentum gives higher wavelength. p=mv, so slower ball has smaller p.

11. Physics 102: Lecture 23, Slide 10 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?

12. Physics 102: Lecture 23, Slide 11 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? Speed, v, and momentum, p=mv, increase.

13. Photon with 1 eV energy: 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. Electron with 1 eV kinetic energy: Solve for Equations are different - be careful! = =

14. Photon with 1 eV energy: 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. Electron with 1 eV kinetic energy: Solve for Big difference! Equations are different - be careful!

15. 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

16. 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 andso double p then quadruple E double p then double E

17. Physics 102: Lecture 23, Slide 16 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

18. Physics 102: Lecture 23, Slide 17 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

19. Physics 102: Lecture 23, Slide 18 Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa. If we know the momentum p, then we know the wavelength, and that means we’re not sure where along the wave the particle is actually located! y Heisenberg Uncertainty Principle

20. Physics 102: Lecture 23, Slide 19 Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa. This seems weird but… If we know the momentum p, then we know the wavelength, and that means we’re not sure where along the wave the particle is actually located! y Heisenberg Uncertainty Principle OK this is weird but…… it is also true. Java

21. Physics 102: Lecture 23, Slide 20 Number of electrons arriving at screen screen w x y  p  p y = p sin  p  Heisenberg Test  y = w= /sin  electron beam

22. Physics 102: Lecture 23, Slide 21 Number of electrons arriving at screen screen w x y  p  p y = p sin  p  Heisenberg Test  y = w= /sin  Use de Broglie electron beam

23. Physics 102: Lecture 23, Slide 22 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 diffraction electron beam screen Number of electrons arriving at screen w x y pypy

24. Physics 102: Lecture 23, Slide 23 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.” Remember earlier we saw that a particle whose momentum (and therefore wavelength) is known precisely is very uncertain in position.

25. Physics 102: Lecture 23, Slide 24 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

26. Physics 102: Lecture 23, Slide 25 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

27. Physics 102: Lecture 23, Slide 26 Early Model for Atom But how can you look inside an atom 10 -10 m across? Light(visible) = 10 -7 m Electron (1 eV) = 10 -9 m Helium atom = 10 -11 m - - - - + + + + Plum Pudding –positive and negative charges uniformly distributed throughout the atom like plums in pudding

28. Physics 102: Lecture 23, Slide 27 Rutherford Scattering Scattering He ++ atoms off of gold. Mostly go through, some scattered back! Atom is mostly empty space with a small (r = 10 -15 m) positively charged nucleus surrounded by cloud of electrons (r = 10 -10 m) If nucleus was baseball in Memorial Stadium, electrons would be where? (Alpha particles = He ++ ) Only something really small (i.e. nucleus) could scatter the particles back!

29. Physics 102: Lecture 23, Slide 28 Rutherford Scattering Scattering He ++ atoms off of gold. Mostly go through, some scattered back! Atom is mostly empty space with a small (r = 10 -15 m) positively charged nucleus surrounded by cloud of electrons (r = 10 -10 m) Flash If nucleus was baseball in Memorial Stadium, electrons would be in Savoy (Alpha particles = He ++ ) Only something really small (i.e. nucleus) could scatter the particles back!

30. Physics 102: Lecture 23, Slide 29 Nuclear Atom (Rutherford) Classic nuclear atom is not stable! Electrons will radiate and spiral into nucleus Need quantum theory Large angle scatteringsnuclear atom More Black Body RadiationRadiation

31. Physics 102: Lecture 23, Slide 30 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

32. Physics 102: Lecture 23, Slide 31 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

33. Physics 102: Lecture 23, Slide 32 Recap Photons carry momentum p=h/ Everything has wavelength =h/p Uncertainty Principle  p  x > h/(2  Atom –Positive nucleus 10 -15 m –Electrons “orbit” 10 -10 m –Classical E+M doesn’t give stable orbit –Need Quantum Mechanics!

34. Physics 102: Lecture 23, Slide 33 See you next lecture! Read Textbook Sections 28.1-28.7