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 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  E 2, so E 2  probability of striking at a given location; E represents the wave function.

3 If a wave (light) can behave like a particle, can a particle act like a wave? Double slit experiment 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!! §28.2 Matter Waves

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

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  ~1/2 (~200 nm). much smaller ( nm) using a beam of electrons (smaller ).

Fig Transmission Electr. Micr. Scanning Electr. Micr.

9 Example: We want to image a biological sample at a resolution of 15 nm using an electron microscope. (a)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 (p x ) can be: where The energy-time uncertainty principle: wave packet Uncertainty in position & momentum Superposition

11 Example: We send an electron through a very narrow slit of width 2.0  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. (a)What is the minimum uncertainty in the electron’s component of momentum along the wire? (b)In its velocity?

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

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. (a)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: =1.07x J = eV (low E!) (b) so = V (low Voltage, easy desktop machine!)

16 Example: We send an electron through a very narrow slit of width 2.0  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  y = 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. (a)What is the minimum uncertainty in the electron’s component of momentum along the wire? (b)In its velocity? Key idea: electron w/in wire; maybe at center, or ±l/2 from center, so use  x = l/2! Then use H.E.P. (b) Solve for the velocity: