De Broglie Waves, Uncertainty, and Atoms

1. Physics 1161: Lecture 29 De Broglie Waves, Uncertainty, and Atoms • sections 30.5 – 30.7

2. Electron at rest Energy of a photon Compton Scattering This experiment reallyshowsphoton momentum! Pincoming photon+ 0 =Poutgoing photon+ Pelectron Outgoing photon has momentum p and wavelength  Incoming photonhas momentum, p, and wavelengthl Recoil electron carries some momentum and KE

3. 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? • Left • Right • Zero

4. 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? • Left • Right • Zero Photon that sticks has an impulse p Photon that bounces has an impulse 2p!

5. De Broglie Waves 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!!

6. Preflight 29.1 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

7. Preflight 29.1 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 Lower momentum gives higher wavelength. p=mv, so slower ball has smaller p.

8. 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. • It increases. • It stays the same.

9. 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. • It increases. • It stays the same. Speed, v, and momentum, p=mv, increase.

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

11. Preflights 28.4, 28.5 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

12. and so double p then double E double p then quadruple E Preflights 28.4, 28.5 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

13. Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy. • lbowling > lgolf • lbowling = lgolf 3. lbowling < lgolf

14. Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy. • lbowling > lgolf • lbowling = lgolf 3. lbowling < lgolf

15. y l Heisenberg Uncertainty Principle 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!

16. Preflight 29.2 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.

17. Preflight 29.7 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.

18. + + - - - - + + 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 eV) l = 10-9 m Helium atom l = 10-11 m

19. (Alpha particles = He++) Rutherford Scattering Scattering He++ nuclei (alpha particles) off of gold. Mostly go through, some scattered back! Only something really small (i.e. nucleus) could scatter the particles 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)

20. Atomic Scale • Kia – Sun Chips Model • Nucleons (protons and neutrons) are like Kia Souls (2000 lb cars) • Electrons are like bags of Sun Chips (1 lb objects) • Sun Chips are orbiting the cars at a distance of a few miles • (Nucleus) BB on the 50 yard line with the electrons at a distance of about 50 yards from the BB • Atom is mostly empty space • Size is electronic

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