P301 Lecture 10 “X-Rays”

1. P301 Lecture 10“X-Rays” Typical early x-ray tube, the anode cut at an angle to aid heat flow and emission of x-rays. • Coolidge tube from ca 1917 • http://en.wikipedia.org/wiki/X-ray_tube More modern design typical of medical diagnostic use (except that this figure does not show the filters typically put in place to limit the low-energy x-rays that add to the dose but don’t contribute to the image) • http://medical-dictionary.thefreedictionary.com/x-ray+tube

2. P301 Lecture 10“X-Rays” • Experimental results on the absorption of x-rays from C. G. Barkla Phil. Mag. 17 (1909) • He used secondary radiation from the “radiators” on the left and investigated absorption in many different elements (table)

3. P301 Lecture 10“X-Rays” http://www2.rgu.ac.uk/life_SEMWEB/xray.html • Bremsstrahlung (or breaking) radiation comes from the direct deceleration of the incident electron and can produce x-rays of energy up to the incident electron’s energy. • Characteristic (and secondary) radiation, comes from the incident electron (or photon) knocking out an inner electron and the resulting hole being filled by a higher lying electron with the consequent emission of a photon.

4. P301 Lecture 10“X-Rays” http://www2.rgu.ac.uk/life_SEMWEB/xray.html For characteristic x-rays the notation is K, L, M … for holes in the lowest, second lowest, third lowest etc. shell. a,b,g for filling that hole from 1 higher, 2 higher, 3 higher etc. shells above the hole. MoKaelement Mo hole in n=1 shell filled from n=2 • Bremsstrahlung (or breaking) radiation comes from the direct deceleration of the incident electron and can produce x-rays of energy up to the incident electron’s energy. • Characteristic (and secondary) radiation, comes from the incident electron (or photon) knocking out an inner electron and the resulting hole being filled by a higher lying electron with the consequent emission of a photon.

5. P301 Lecture 10“X-Rays” • Coolidge tube from ca 1917 • http://en.wikipedia.org/wiki/X-ray_tube • http://medical-dictionary.thefreedictionary.com/x-ray+tube

6. P301 Lecture 10“X-Rays” http://en.wikipedia.org/wiki/File:Bragg_diffraction.png http://en.wikipedia.org/wiki/Moseley%27s_law • Ka and Kb lines from various elements (Mosely, 1913). He realized that he could use Bragg’s recent discovery of x-ray diffraction by crystals to analyse characteristic x-rays more quantitatively than had Barkla.

7. P301 Lecture 10“Compton scattering” A. H. Compton Phys. Rev. 21 p483 (1923) Phys. Rev. 22 p409 (1923)

8. P301 Lecture 10“Compton scattering ” Dl = l’- l = lC[1-cos(q)] where lC = h/mc http://universe-review.ca/I15-72-Compton1.jpg

9. P301 Lecture 9“CALM” • What is the wavelength of Mo Ka radiation (based on this figure)?

10. P301 Lecture 9“CALM” • What is the wavelength of Mo Ka radiation (based on this figure)? • We know from Compton’s formula that the difference in wavelength at a scattering angle of 135 deg must be: Dl = lC(1-cos(135o))= 4.1pm • But from the figure we can see that: Dl/l ~ 0.35o/6.75o = 0.052 • So from this we conclude that l=4.15pm/0.052 = 0.08 nm • The correct wavelength for Mo Ka is actually 0.071 nm, so this is not too bad.

11. P301 Lecture 9 • The birth of quantum mechanics is typically traced to THREE key experimental results and the success of a quantum theory of QED to describe them: • The EM spectrum from a Black body and the success of Planck’s law • The photo-electric effect and the success of Einstein’s explanation of it • The Compton effect, which shows that light must be treated as a particle with the properties Planck attributed to it to describe how high-frequency light scatters off electrons.

12. P301 Lecture 10“JITT question” • Explain briefly why there must be two photons emitted (back-to-back) when a particle and its anti-particle annihilate at rest? • No answer: 16 • 5 answered to conserve energy or particle number • 18 said to conserve energy and momentum (and energy) (that is the key) • What do you suppose would happen if the pair annihilated while their center of mass was moving at high speed (say 0.8c) w.r.t. the observer? • Energy would be Doppler shift up (3) (and different for the two photons, 5) • Angle between would not be 180o (3) • Confused or confusing answers: 10 • In fact, the energies of the two would be different (just how different will depend on the angle between the “boost” and the CoM frame direction of the photons), the angle between them will not be 180 degrees (unless the boost is directly lined up with the decay line), and at least one of the photons (and most likely both) will have energies greater than 511keV

13. P301 Lecture 9“Discovery of the position” Fig 1 from C. Anderson “The Positive Electron” Phys. Rev. 43 p491 (1933) Note how the curvature increases as the particle passes through the lead plate in the cloud chamber, this provides conclusive evidence for the direction of travel (upward in the figure). By looking at the ionization, and the reduction in momentum due to traverse of the lead, Anderson was able to put limits on the charge and mass of the particle (q<2e m<20 me) Track of interest 6 mm Lead plate

14. P301 Lecture 11“Facts” about atoms ca. 1900 • Elemental character was associated with atoms (in order to explain chemistry) • Atoms were small, and their size was on the order of 0.2-0.4 nm in diameter (from density and kinetic theory estimates of Avagadro’s number). • Atoms had smaller constituents • Cathode rays came from materials. • electron’s very large e/m ratio, compared to that of atoms • Photo-electric effect • Atoms had some internal dynamics • Characteristic spectra • Chemical properties • Radioactivity • X-rays

15. P301 Lecture 11Possible models for Atoms • Planetary model like the solar system (all the mass in the center, lighter electrons orbiting it)? • Thomson quickly figured out that this was inconsistent with the known physics of EM radiation emitted from accelerated charges. http://www.vias.org/physics/bk4_03_01b.html • Plum pudding model of Thomson Phil Mag. Ser 6 vol 7 p 237-65 (1904) http://www.uk-astronomy.com/atom.htm

16. P301 Lecture 11“JITT question” • Explain briefly why the planetary model of the atom was rejected by Thomson prior to the results of the Geiger and Marsden experiment. • Negative charges repel rather than attract (like gravity) (5 responses) This is a concern, and represents a complicated problem (the “many-body” problem), but it only applies to multi-electron atoms (since you could hypothesise a positively charged central mass) and is not fundamental. • Need a neutral atom, so you need positive charges somewhere (5) True, but why a pudding not a nucleus? • Accelerating charges emit radiation, hence the electrons would quickly crash into any central mass (3) This applies even to hydrogen, and requires completely new physics to avoid. • Other (5 responses)

17. P301 Lecture 11“Geiger-Marsden experiment” Ra source (a emitter) From Geiger and Marsden PRSL A82 495 (1909) Pt Reflector Pb shield Pb shield ZnS screen Reflector ZnS screen

18. P301 Lecture 11“Geiger-Marsden experiment” http://www.antonine-education.co.uk/Physics%20A%20level/Unit_1/Radioactivity/Structure/Rutherford_1.gif From Geiger and Marsden Phil Mag. 25 p 604 (193)

19. P301 Lecture 11“Scattering experiments” b = [Z1Z2e2cot(q/2)]/[8peoK]=(4.6) in T&R, [this form holds only for Coulomb forces] • NOTES: • The scattering angle is related to the “momentum transfer” Dp • Smaller impact parameter -> larger angle • If the ‘target’ is small, then most projectiles’ will not get scattered. • Typically we know how many particles are incident on the sample per unit area and time, multiplying this by a “cross-section” gives the rate of scattering. http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/imgnuc/ruthgeo.gif

20. P301 Lecture 12“Bohr’s Hypotheses” Bohr formulated the following ad hoc model: • Atoms exist only in certain stable “stationary states” • The dynamic equilibrium of these stationary states is determined by the laws of classical physics, but the way the atoms interact with the electromagnetic field of light waves (and therefore how they transit between the stationary states) is not • The emission and absorption of EM waves by atoms takes place ONLY in conjunction with a transition between two stationary states, with the frequency of the emitted light being determined according to the Planck hypothesis: |Ei – Ef|= hf • The (orbital) angular momentum of the electron in a stationary state can only take on values given by integral multiples of Planck’s constant divided by 2pLn = nh/2p It is this last hypothesis that is the truly new (revolutionary) idea from Bohr himself, the other three are pretty much inescapable and/or had been provided by someone else already.

21. Periodic Table circa 1905(Werner) Quam and Quam, J. Chem. Ed. P217 (1934) http://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=64 Places where the chemical properties suggested a different order than the atomic weights. People did not understand this. Why are there gaps? What is the physical meaning of the sequence number that had up to this point been assigned to atoms?

22. P301 Lecture 12“Moseley’s Law” http://chimie.scola.ac-paris.fr/sitedechimie/hist_chi/text_origin/moseley/Moseley-article.htm Lb La • NOTES: • Moseley started to catalogue characteristic x-ray energies (and therefore frequencies) using a technique we’ll discuss next week. • He developed the above empirical relations for the frequencies, determined that atomic number, not weight, was the relevant parameter to explain the periodicity of the periodic table (e.g. he explained the reversed positions of Ni and Fe; K and Ar), and predicted the existence of (only) three as yet undiscovered elements (Z=43, 61, and 75; later: Tc, Pm, and Re) “between Al and Au” Lg Ka Kb

23. P301 Lecture 12“Characteristic X-ray production” • NOTES: • Barkla first discovered “characteristic x-rays” in 1909, several years before Bohr, the Braggs, and Moseley did their work. • The “shell” model of the atom, which is foreshadowed by Bohr’s model for H, is very useful even when considering multi-electron atoms • The various “shells” (K, L, M, N, etc., corresponding to increasing values for “n” in the Bohr model) are typically split into a few (or several) individual energy levels that are much more closely spaced than the separation between the shells. • We will start to explore the smaller splittings later in the course.

24. P301 Lecture 10“X-Rays” http://en.wikipedia.org/wiki/File:Bragg_diffraction.png http://en.wikipedia.org/wiki/Moseley%27s_law • Ka and Kb lines from various elements (Mosely, 1913). He realized that he could use Bragg’s recent discovery of x-ray diffraction by crystals to analyse characteristic x-rays more quantitatively than had Barkla.

25. It's electrons are easier to excite than the other two It's electrons are easier to excite than the other two It's electrons are easier to excite than the other two It's electrons are easier to excite than the other two P301 Lecture 12“JITT question” • Look back at figure 3-19 (page 113 of the text). Why is it that in this figure only the curve for the molybdenum (Mo) anode displays characteristic x-rays? • Several said it had something to do with valence electrons or simple described how x-rays are made. • Some suggested only Mo could be excited at 35kV • Some suggested that the W and Cr x-rays simply fell in a different range of wavelengths.