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Chapter 28: Quantum Physics

Chapter 28: Quantum Physics. Wave-Particle Duality Matter Waves The Electron Microscope The Heisenberg Uncertainty Principle Wave Functions for a Confined Particle The Hydrogen Atom The Pauli Exclusion Principle Electron Energy Levels in a Solid The Laser

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Chapter 28: Quantum Physics

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  1. Chapter 28: Quantum Physics • Wave-Particle Duality • Matter Waves • The Electron Microscope • The Heisenberg Uncertainty Principle • Wave Functions for a Confined Particle • The Hydrogen Atom • The Pauli Exclusion Principle • Electron Energy Levels in a Solid • The Laser • Quantum Mechanical Tunneling • For Wed recitation: • Online Qs • Practice Problems: • # 3, 6, 13, 21, 25 • Lab: 2.16 (Atomic Spectra) • Do Pre-Lab & turn in • Next week optional 2.03 • Final Exam: Tue Dec 11 3:30-5:30 pm @220 MSC • 200 pts: Chs.25,27,28,(26) • 200 pts: OQ-like on 12,16-24

  2. §28.1 Wave-Particle Duality Light is both wave-like (interference & diffraction) and particle-like (photoelectric effect). • Double slit experiment: allow only 1 photon at a time, but: • still makes interference pattern! • can’t determine which slit it will pass thru • can’t determine where it will hit screen • can calculate probability: • higher probability  higher intensity • IE2, so E2 probability of striking at a given location; E represents the wave function.

  3. §28.2 Matter Waves If a wave (light) can behave like a particle, can a particle act like a wave? • Double slit experiment w/ electrons: •  interference pattern! Wave-like! • Allow only 1 e– at a time: • still makes interference pattern • can still calculate probabilities • Add detector to see which slit used: • one slit or other, not both • interference pattern goes away! • wave function “collapses” to particle!!

  4. Diffraction (waves incident on a crystal sample) X-rays: Electrons:

  5. Like photons, “matter waves” have a wavelength: “de Broglie wavelength” Momentum: Electron beam defined by accelerating potential, gives them Kinetic Energy: Note: need a relativistic correction if v~c (Ch.26)

  6. Example (PP 28.8): What are the de Broglie wavelengths of electrons with kinetic energy of (a) 1.0 eV and (b) 1.0 keV?

  7. §28.3 Electron Microscope • Resolution (see fine detail): • • visible light microscope limited by diffraction to Dq~1/2 l (~200 nm). • • much smaller (0.2-10 nm) using a beam of electrons (smaller l).

  8. Fig. 28.06 Scanning Electr. Micr. Transmission Electr. Micr.

  9. Example: We want to image a biological sample at a resolution of 15 nm using an electron microscope. • What is the kinetic energy of a beam of electrons with a de Broglie wavelength of 15.0 nm? • (b) Through what potential difference should the electrons be accelerated to have this wavelength? -

  10. §28.4 Heisenberg’s Uncertainty Principle Sets limits on how precise measurements of a particle’s position (x) and momentum (px) can be: Uncertainty in position & momentum where Superposition wave packet The energy-time uncertainty principle:

  11. Example: We send an electron through a very narrow slit of width 2.010-8 m. What is the uncertainty in the electron’s y-component momentum?

  12. Example: An electron is confined to a “quantum wire” of length 150 nm. • What is the minimum uncertainty in the electron’s component of momentum along the wire? • In its velocity?

  13. §28.5 Wave Functions for a Confined Particle Analogy: standing wave on a string: Same for electron in a quantum wire (particle in a 1D box), so & particle’s KE is Conclude: A confined particle has quantized energy levels

  14. Electron cloud represents the electron probability density for an H atom (the electron is confined to its orbit): Energy states and durations are “blurred”

  15. Example: We want to image a biological sample at a resolution of 15 nm using an electron microscope. • What is the kinetic energy of a beam of electrons with a de Broglie wavelength of 15.0 nm? • (b) Through what potential difference should the electrons be accelerated to have this wavelength? - Square both sides, solve for K: =1.07x10-21 J = 0.0067 eV (low E!) (b) so = 0.0067 V (low Voltage, easy desktop machine!)

  16. Example: We send an electron through a very narrow slit of width 2.010-8 m. What is the uncertainty in the electron’s y-component momentum? Key idea:electron goes through slit; maybe through center, or ±a/2 above/below it, so use Dy = a/2! Then H.E.P. says so Notice: This uncertainty in the electron’s vertical momentum means it can veer off its straight-line course; many veered electrons  diffraction pattern!!

  17. Example: An electron is confined to a “quantum wire” of length 150 nm. • What is the minimum uncertainty in the electron’s component of momentum along the wire? • In its velocity? Key idea:electron w/in wire; maybe at center, or ±l/2 from center, so use Dx = l/2! Then use H.E.P. (b) Solve for the velocity:

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