1. Particle QM Lecture 2 Finish Rutherford scattering Quiz
Stability of atoms
Ultraviolet catastrophe
Bohr Model bootcamp

2. PHYS274 Midterm I and related announcements
Midterm I on Oct 16th, Monday
Professor Pui Lam will substitute for me, Oct 6-18, while I am away at KEK
III) 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
“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.”
“Plum pudding”
: Graduate students Geiger and Marsden carried out the experiment.
Have you heard of Geiger ? 4

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

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

7. Rutherford scattering example
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. 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.
Remember how to do energy conservation 8

9. Q19.1
In the Rutherford scattering experiment, Ernest Rutherford’s graduate students shot what kind of particles at the gold foil target?
Electrons
Protons
Neutrons
Alpha particles
Uranium nuclei
D (Helium nuclei from a radioactive source) 9

10. Q19.1
In the Rutherford scattering experiment, Ernest Rutherford’s students shot what kind of particles at the gold foil target?
Electrons
Protons
Neutrons
Alpha particles
Uranium nuclei
Helium nuclei from a radioactive source
D (Helium nuclei from a radioactive source)
Geiger
Rutherford
Marsden 10

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

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

13. Decrease the accelerating voltage by half
Q19.3
If you want to reduce the wavelength of the electron by a factor of two in an electron microscope, you
Decrease the accelerating voltage by half
Increase the accelerating voltage by 2 times
Increase the accelerating voltage by 4 times
C V_ba = h^2/(2m e lambda^2)lambda^2 = H^2/(2 m e V_ba) 13

14. Decrease the accelerating voltage by half
Q19.3
If you want to reduce the wavelength of the electron by a factor of two in an electron microscope, you
Decrease the accelerating voltage by half
Increase the accelerating voltage by 2 times
Increase the accelerating voltage by 4 times
C V_ba = h^2/(2m e lambda^2)lambda^2 = H^2/(2 m e V_ba) 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.
There is a ground state energy level
Question: What is the solution to this crisis ?
Why ??? 15

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.
There is a ground state energy level
Question: What is the solution to this crisis ?
OK, what does THAT mean? 16

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

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 levels
Niels 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 39.16 20

21. Quantization of atomic energy levels
An 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 exercise
Are you ready for Bohr Model Bootcamp ? 22

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 rn 23

24. The Bohr model of hydrogen
Let’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 condition 24

25. The Bohr model of hydrogen
(The mass m is that of the electron.)
Now let’s use a Newtonian argument for a planetary model of the atom but use the Bohr quantization condition. (A little hokey).
Balance electrostatic and centripetal forces
Balance electrostatic and centripetal forces. Note that the electron and proton have equal and opposite charges.
Here we used the Bohr quantization condition 25

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

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