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De Broglie Waves, Uncertainty, and Atoms

Physics 1161: Pre- Lecture 29. De Broglie Waves, Uncertainty, and Atoms. Sections 30.1 – 30.7. Electron at rest. Energy of a photon. Compton Scattering. This experiment really shows photon momentum!. P incoming photon + 0 = P outgoing photon + P electron.

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De Broglie Waves, Uncertainty, and Atoms

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  1. Physics 1161: Pre-Lecture 29 De Broglie Waves, Uncertainty, and Atoms • Sections 30.1 – 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. 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!!

  4. 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:

  5. 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!

  6. Number of electrons arriving at screen p electron beam screen p Dpy = p sinq q Use de Broglie l Heisenberg Test w q Dy = w = l/sinq y x

  7. (Alpha particles = He++) Rutherford Scattering Scattering He++ atoms 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)

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

  9. 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!

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