Particle QM Lecture 2 1 Finish Rutherford scattering - PowerPoint Presentation

1. Particle QM Lecture 21Finish Rutherford scatteringQuizStability of atomsUltraviolet catastropheBohr Model bootcamp

2. PHYS274 Midterm I and related announcementsMidterm I on Oct 16th, MondayProfessor Pui Lam will substitute for me, Oct 6-18, while I am away at KEKIII) There will be a review session before the midterm covering practice problems.

3. “All science is either physics or stamp collecting”

4. Rutherford’s discovery of the nucleus at Manchester“Plum pudding”“It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”1910-1911: Graduate students Geiger and Marsden carried out the experiment.Have you heard of Geiger ?4

5. Simulation: Scatter from a large nucleusQuestion: What is an α particle ? 5What is a β or γ ?

6. Simulation: Hard scatter from a compact nucleusQuestion: Compare to the large nucleus. What is different ?6

7. Rutherford scattering exampleQuestion: An α particle (charge 2e) is aimed directly at a gold nucleus (charge 79e). What minimum initial kinetic energy must the α particle have to approach within 5.0 x 10-14m of the center of the gold nucleus before reversing direction. (Assume that the heavy gold nucleus remains at rest). Potential energy at distance of closest approach. Potential at infinity is zero.7

8. Rutherford scattering example (cont’d)Question: An α particle (charge 2e) is aimed directly at a gold nucleus (charge 79e). What minimum initial kinetic energy must the α particle have to approach within 5.0 x 10-14m of the center of the gold nucleus before reversing direction. (Assume that the heavy gold nucleus remains at rest). Potential energy at distance of closest approach. Potential at infinity is zero.8Remember how to do energy conservation

9. Q19.1In the Rutherford scattering experiment, Ernest Rutherford’s graduate students shot what kind of particles at the gold foil target?ElectronsProtonsNeutronsAlpha particlesUranium nuclei9

10. In the Rutherford scattering experiment, Ernest Rutherford’s students shot what kind of particles at the gold foil target?ElectronsProtonsNeutronsAlpha particlesUranium nuclei10Helium nuclei from a radioactive sourceQ19.1GeigerRutherfordMarsden

11. Q19.2If you increase the kinetic energy of the electrons in an electron microscope, you will Improve the resolution of the microscopeDegrade the resolution of the microscopeThe resolution will remain unchanged.The electrons cannot be captured by the magnetic focus.11

12. Q19.2If you increase the kinetic energy of the electrons in an electron microscope, you will Improve the resolution of the microscopeDegrade the resolution of the microscopeThe resolution will remain unchanged.The electrons cannot be captured by the magnetic focus.12Why?

13. Q19.3If you want to reduce the wavelength of the electron by a factor of two in an electron microscope, youDecrease the accelerating voltage by halfIncrease the accelerating voltage by 2 timesIncrease the accelerating voltage by 4 times 13

14. Q19.3If you want to reduce the wavelength of the electron by a factor of two in an electron microscope, youDecrease the accelerating voltage by halfIncrease the accelerating voltage by 2 timesIncrease the accelerating voltage by 4 times 14

15. Breakdown of classical physics (Crisis)Rutherford’s experiment suggested that electrons orbit around the nucleus like a miniature solar system. However, classical physics predicts that an orbiting electron (accelerating charge) would emit electromagnetic radiation and fall into the nucleus. So classical physics could not explain why atoms are stable.Question: What is the solution to this crisis ?There is a ground state energy level15Why ???

16. Review: Breakdown of classical physics (Crisis)Rutherford’s experiment suggested that electrons orbit around the nucleus like a miniature solar system. However, classical physics predicts that an orbiting electron (accelerating charge) would emit electromagnetic radiation and fall into the nucleus. So classical physics could not explain why atoms are stable.Question: What is the solution to this crisis ?There is a ground state energy level16OK, what does THAT mean?

17. “Ultra-violet catastrophe !”Why doesn’t this happen ?17Something was very wrong in classical physics…Is our universe about to end??

18. Quantization of atomic energy levels (Experimental)Three classes of spectral features: 18

19. Quantization of atomic energy levels (visual evidence)19

20. Quantization of atomic energy levelsNiels Bohr explained atomic line spectra and the stability of atoms by postulating that atoms can only be in certain discrete energy levels. When an atom makes a transition from one energy level to a lower level, it emits a photon whose energy equals that lost by the atom.An atom can also absorb a photon, provided the photon energy equals the difference between two energy levels. Insert Figure 39.1620

21. Quantization of atomic energy levelsAn atom can also absorb a photon, provided the photon energy equals the difference between two energy levels. The master equation for the photon energy in these transitions is 21

22. Are you ready for Bohr Model Bootcamp ?Next exercise22

23. The Bohr model of hydrogen (original argument)Bohr explained the line spectrum of hydrogen with a model in which the single hydrogen electron can only be in certain definite orbits.In the nth allowed orbit, the electron has orbital angular momentum nh/2π (see Figure on the right). Bohr proposed that angular momentum is quantized (this will turn out to be correct in general in quantum mechanics but is not right for the hydrogen atom).Ln=rp=m vn rn23

24. The Bohr model of hydrogenLet’s use a different argument based on deBroglie waves to obtain the same conclusions.Think of a standing wave with wavelength λ that extends around the circle.Q: How is the momentum of the atomic electron related to its wavelength ? (remember the Prince)Same as the Bohr quantization condition24

25. The Bohr model of hydrogenNow let’s use a Newtonian argument for a planetary model of the atom but use the Bohr quantization condition. (A little hokey).(The mass m is that of the electron.)Balance electrostatic and centripetal forcesHere we used the Bohr quantization condition25

26. The Bohr model of hydrogen (Bohr radius)Here n is the “principal quantum number” and a0 is the “Bohr radius”, which is the minimum radius of an electron orbital.26

27. The Bohr model of hydrogen (iClicker Interlude)They rain down continuously (will cover later), and some of them lose energy and slow down near an atom. Will its orbit be ?Further awayNearer to nucleusAccelerate inward, destroy the nucleus and all life as we know it !27A muon is a “heavy electron” (~100 MeV/c^2 vs. 0.5 MeV/c^2) and we are continually bombarded by them

28. The Bohr model of hydrogen (Energy levels, derivation)This expression for the allowed energies can be rewritten and used to predict atomic spectral lines !Note that E and U are negative (1/8-1/4=-1/8)28