Physics 222

1. Physics 222 D.S. Durfee

2. The Physics Revolution of the 20th Century • Relativity – physics of the fast • Quantum Mechanics – law of the small • Atoms: clocks, discharge lamps, lasers • Molecules: chemistry • Nuclei: fission, fusion • Solid State: semiconductors • Degenerate Matter: superconductors • Coherence & Superposition: quantum computing

3. Puzzles at the Beginning of the Twentieth Century • Null result of the Michelson-Morley Experiment • Ultraviolet Catastrophe • Photoelectric Effect • Maxwell’s Equations Spell the Demise of Atoms! • Discrete atomic emission lines

4. Quantum Uncertainty Relations Position – Momentum Energy – Time Other Dimensions Angular Momentum

5. Thought Question Imagine that I measure the location and momentum of an electron. I measure the location with a precision of 1nm. If I make a second measurement one second later, about how well will I be able to predict where I will find the electron with the second measurement? (me ~ 1e-30 kg, h/4¼ ~ 0.5e-34 Js) A : To better than 1 nm B : To within around 1nm C : To within 1 μm D : To within 1 mm E : Not even to within 1 mm

6. Wave-Particle Duality • Things act as wave when propagating • or, in other words, we use waves to make predictions as to what we will find when we make our measurement. • Things act as waves when we measure wave-like properties. • Things act as particles when we measure particle-like properties • Example: BEC interference --- theorists confused about “undefined phase”

7. Postulates of Quantum Mechanics • Every physically-realizable system is described by a state function ψ that contains all accessible physical information about the system in that state • The probability of finding a system within the volume dv at time t is equal to |ψ|2dv • Every observable is represented by an operator which is used to obtain information about the observable from the state function • The time evolution of a state function is determined by Schrödinger’s Equation

8. 4.1 The Nuclear Atom 120 An atom is largely empty space (NOT!) 4.2 Electron Orbits 124 The planetary model of the atom and why it fails 4.3 Atomic Spectra127 Each element has a characteristic line spectrum

9. 4.4 - 4.5 4.4 The Bohr Atom 130 Electron waves in the atom 4.5 Energy Levels and Spectra A photon is emitted when an electron jumps from one energy level to a lower level

10. 4.6 Correspondence Principle 138 The greater the quantum number, the closer quantum physics approaches classical physics 4.7 Nuclear motion 140 The nuclear mass affects the wavelengths of spectral lines 4.8 Atomic Excitation 142 How atoms absorb and emit energy 4.9 The Laser 145 How to produce light waves all in step

11. Reading Quiz Question Which spectral series resulted from a study of the visiblepart of the hydrogen spectrum? • A: The Lyman series B: The Balmer series C: The Paschen series D: The Brackett series E: The Wurald series

12. The Hydrogen Spectrum The Balmer Series

13. Rutherford’s Experiment

14. What would happen if I shot a bullets through a piece of jello?Thought Question A: All of them would come nearly straight through, but with a slightly smaller velocity B: Some of them would be deflected slightly, some would lose a little velocity C: Some would go nearly straight through, some would deflect at large angles, some would ricochet almost straight back D: They would all reflect straight back

15. Thought Question What would happen if I shot a bullets through a piece of jello containing shredded carrots? A: All of them would come nearly straight through, but with a slightly smaller velocity B: Some of them would be deflected slightly, some would lose a little velocity C: Some would go nearly straight through, some would deflect at large angles, some would ricochet almost straight back D: They would all reflect straight back

16. What would happen if I shot a bullets through a piece of jello containing iron anvils?Thought Question A: All of them would come nearly straight through, but with a slightly smaller velocity B: Some of them would be deflected slightly, some would lose a little velocity C: Some would go nearly straight through, some would deflect at large angles, some would ricochet almost straight back D: They would all reflect straight back

17. Johann Jakob Balmer (May 1, 1825 – March 12, 1898) was a Swiss mathematician and an honorary physicist.

18. The Hydrogen Spectrum The Balmer Series

19. Quiz Question In Bohr’s model of the hydrogen atom, what determined the frequency of emitted light? A: The total energy of the orbiting electron B: The energy difference between initial and final electron states C: The frequency of revolution of the orbiting electron D: The difference in revolution frequency between initial and final electron states E: The sum of the initial and final electron revolution frequencies

20. ~ L n = Bohr’s Theory • He did not think in terms of waves • He simply postulated that • There are orbits in which the electron doesn’t radiate. • The light released when an electron changes orbits is a photon with an energy equal to the difference in energy of the two orbits • He further postulated that the orbits were circular, with

21. Results of Bohr Theory

22. Thought Question How many energy levels are there between the hydrogen ground state (-13.6 eV) and the continuum (0 eV)? A: one B: 13 C: 14 D: 1324 E: None of the above

23. Wave Theory of Hydrogen

24. 5th Solvay Conference, Brussels, 23-29 October 1927 Back row: A Piccard, E Henriot, P Ehrenfest, D Durfee, Ed Herzen, Th De Donder, E Schroedinger E Verschaffelt, W Pauli, Waldo, W Heisenberg, R H Fowler, L Brillouin.Middle Row: P Debye, M Knudsen, W L Bragg, H A Kramers, P A M Dirac, A H Compton, L de Broglie, M Born, N Bohr.Front Row: I Langmuir, M Planck, Mme Curie, H A Lorentz, A Einstein, P Langevin, Ch E Guye, C T R Wilson, O W Richardson.

25. Quiz Question “When n gets large, quantum physics should start to look like classical physics” is a somewhat accurate statement of the... A: Equivalence Principle B: Limiting Value Principle C: Legacy Principle D: Completeness Principle E: Correspondence Principle.

26. Thought Question What would happen to the hydrogen spectrum if I replace the electron with a muon (which is like an electron but heavier)? A: No change B: Almost no change C: All of the lines will shift to significantly longer wavelengths D: All of the lines will shift to significantly shorter wavelengths E: I have no idea --- hey, its an honest answer!

27. Thought Question What would happen to the hydrogen spectrum if I replace the nucleus (a proton) with an alpha particle (two protons plus two neutrons… i.e. more charge, more mass)? A: No change B: Almost no change C: All of the lines will shift to significantly longer wavelengths D: All of the lines will shift to significantly shorter wavelengths E: I have no idea

28. Thought Question What would happen to the hydrogen spectrum if I replace the nucleus (a proton) with a deuteron (a proton plus a neutron… i.e. same charge, more mass)? A: No change B: Almost no change C: All of the lines will shift to significantly longer wavelengths D: All of the lines will shift to significantly shorter wavelengths E: I have no idea

29. Frank-Hertz Experiment

31. The Correspondence Principle

32. Quick Writing Assignment • In one minute, write a short, clear, and concise paragraph which explains the correspondence principle.

33. Bohr Theory Successes/Failures • Predicts emission and absorption lines of hydrogen and hydrogen-like ions • Predicts x-ray emissions (Moseley’s law) • Gives an intuitive picture of what goes on in an atom • The correspondence principle is obeyed... sort of • It can’t easily be extended to more complicated atoms • No prediction of rates, linewidths, or line strengths • Fine structure (and hyperfine structure) not accounted for • How do atoms form molecules/solids? • Where did it come from? There must be a more general underlying theory! • It gave hints of a new, underlying theory