Midterm 1 summary

1. Midterm 1 summary High score(s) 100 Average 71 Low score 25 I gave lots of partial credit. Please complain if you find a mistake in the grading. Checked with Mike Nassir, head of physics undergraduate education: “exam is fair, looks reasonable”

2. Looking ahead to midterm II Problem I: Chapter 38, Photons/QM (Waves as particles) Problem II: Chapter 39, Particles behaving as Waves Problem III: Chapter 40, Quantum Mechanics (~1/2 half) Problem IV: Conceptual/Short Answer Questions Lots of new material to learn: More details on the exam later For those doing well, please maintain your current pace. For those not doing well, please “buckle down” and contact me for help.

3. v Why do you call this quantum mechanics ? Question: Why do you call this “quantum mechanics”, the photon energies are E= h f, which are not discrete ? Ans: But light is not a wave anymore, it comes in discrete units carrying energy and momentum (called “quanta”) Question: Why does the comet’s tail point away from the sun ? Ans: Radiation pressure from photons from the sun (each photon transfers momentum ?

4. X-ray production • One mechanism of x-ray production is called “bremsstrahlung” from a German word. • Question: What is the meaning of this German word ? • Ans: “braking radiation”. Here “braking” means deceleration.

5. X-ray production via bremsstrahlung • The greater the kinetic energy of the electrons that strike the anode, the shorter the minimum wavelength of the x rays emitted by the anode (see the figure on the lower right). [continuous energy spectrum] • The photon model explains this behavior: Higher-energy electrons can convert their energy into higher-energy photons, which have a shorter wavelength. Notice dependence of energy cutoff on accelerating voltage Does not depend on material !

6. Question: X-ray production via bremsstrahlung • In the x-ray apparatus below, suppose you increase the number of electrons that are emitted from the cathode per second while keeping the potential difference VAC the same. How will this affect the intensity and minimum wavelength λmin of the emitted x-rays ? (i) I and λmin will both increase; (ii) I will increase but λmin will remain the same; (iii) I will increase but λmin will decrease; (iv) I will remain the same but λmin will decrease; (v) none of the above. Each electron produces at most one photon(ii) We use such an apparatus in PHYS481L

7. Example: Applications of x-rays CAT scan= Computerized Axial Tomography Many 2-D images taken around the axis of a patient, combined into a single 3-D result

8. Question: X-ray production via bremsstrahlung • In the x-ray apparatus (and photo-emission via electrons), why is there a maximum photon energy ? Ans: the maximum energy corresponds to an electron giving up all its kinetic energy to the anode when producing a photon. Each electron produces at most one photon(ii)

9. Question: X-ray photoemission example (SI units) • Electrons in an x-ray tube accelerate through a potential difference of 10.0 kV before striking a target. If the electron produces one photon on impact with the target, what is the minimum wavelength of the resulting x-rays ?

10. Question: X-ray photoemission example (in eV units) • Electrons in an x-ray tube accelerate through a potential difference of 10.0 kV before striking a target. If the electron produces one photon on impact with the target, what is the minimum wavelength of the resulting x-rays ? N.B e’s cancel in the expression.

11. X-ray scattering: Compton Scattering Question: Why was the discovery of Compton scattering so important ? The 1927 Nobel Prize in Physics was divided equally between Arthur Holly Compton "for his discovery of the effect named after him" and Charles Thomson Rees Wilson "for his method of making the paths of electrically charged particles visible by condensation of vapor". Ans: In a classical (non-QM) physics picture: light is a wave and the final energy will be the same as the initial. Compton scattering is possible if light is composed of photons (a.k.a quanta).

12. X-ray scattering: Compton Scattering • In the Compton experiment, x rays are scattered from electrons. The scattered x rays have a longer wavelength than the incident x rays, and the scattered wavelength depends on the scattering angle ϕ. • Explanation: When an incident photon collides with an electron, it transfers some of its energy to the electron. The scattered photon has less energy and a longer wavelength than the incident photon.

13. Pair production (Interesting consequence of special relativity) • When gamma rays of sufficiently short wavelength are fired into a metal plate, they can convert into an electron and a positron (positively-charged electron), each of mass m and rest energy mc2. • The photon model explains this: The photon wavelength must be so short (or the energy high enough) so that the photon energy is at least 2mc2.

14. Next exercise Are you ready for Compton Scattering Bootcamp ?

15. X-ray scattering: Compton Scattering (derivation) Let’s write down total energy conservation using special relativity and QM for the photon. Question: what is the initial energy of the electron ? What is the final energy of the electron ? One equation, two unknowns; need another constraint. What should we do ? Conserve vector momentum (relativistic) !

16. X-ray scattering: Compton Scattering (cont’d) Question: Do you remember the law of cosines ? The (mc2)2 terms cancel

17. X-ray scattering: Compton Scattering (nearly there) Divide by c2 Compare Eqn(*) and Eqn(**) Divide by p p’

18. X-ray scattering: Compton Scattering (result) Question: How are the momentum and wavelength of a photon related ? Ans: p=h/λ and p’=h/λ’ Question:What would happen with protons ? Question : What is m (here) ? Which mass ? Ans: the mass of the electron (0.511 MeV)