Atomic Physics Chapter 6 X ray 11/20/13 24/12/2018 Jinniu Hu 1!1
6.1 The discovery of X ray X-rays were discovered in 1895 by the German physicist Wilhelm Roentgen. He found that a beam of high-speed electrons striking a metal target produced a new and extremely penetrating type of radiation.
6.1 The discovery of X ray X-rays Tube 3.5 THE CO Filament Evacuated glass envelope Metal target Electrons Focusing electrode X rays 50 100 kv +
6.1 The discovery of X ray Electromagnetic wave 24/12/2018 Jinniu Hu
6.1 The discovery of X ray X ray diffraction Bragg equation Ray (1) Ray (2) θ θi D d A θ θ C B θr Reflected rays θ Plane A Plane B n 2d sin n 1, 2, 3, θ Crystal P θ X-ray source Lead collimators Film (a)
6.1 The discovery of X ray Laue diffraction transmission method Sample Incident x rays Photographic plate o from W. Friedrich, P. Knipping, and M. Laue, Sitzungsberichte der
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6.2 X ray production The spectrum of X ray 12 11 10 9 W To 15.2 To 37.2 The continuous spectrum Relative intensity 10 8 6 4 2 50 kv 40 kv 30 kv Tungsten target 20 kv Relative intensity 8 7 6 5 4 3 2 Mo Cr Relative intensity 0 0.02 0.04 0.06 0.08 0.10 Wavelength, nm The characteristic spectrum 12 10 8 Tungsten, 35 kv 6 4 1 3 4 5 6 7 8 9 10 l( 10 2 nm) l min 2 Molybdenum, 35 kv 0 0.02 0.04 0.06 0.08 0.10 Wavelength, nm
6.2 X ray production The continuous spectrum: An energetic electron passing through matter will radiate photons and lose kinetic energy. The process by which photons are emitted by an electron slowing down is called bremsstrahlung, from the German word for braking radiation. Nucleus Electron E i Photon, hf E f
6.2 X ray production The minimum wavelength is due to the inverse photoelectric effect. The conservation of energy requires that the electron kinetic energy equal the maximum photon energy: ev 0 hf max hc l min Therefore, the minimum wavelength (Duane-Hunt rule) is l min hc e 1 V 0 1.240 10 6 V # m V 0
6.2 X ray production The characteristic spectrum: The atom is most stable in its lowest energy state or ground state, so it is likely that N an electron from one of the higher shells will change its state and fill the innershell vacancy at lower energy, emitting radiation as it changes its state. O N M L M a M b M g n 5 n 4 n 3 n 2 L a L b L g L d K K a K b K g K d K e n 1
6.2 X ray production 1 l K a Moseley formula 1 2 1 2 R 1Z 12 2 a 1 1 1 2 2 b 3 R 1Z 2 122 4 1 2 f Ka c l K a 3cR 4 1Z 122 the 1 equation Moseley R 1Z 12 2 a 1 found l K 1 1 describing the K 2 n b R 1Z 2 122 a 1 1 - n b 2 orrectly concluded that the atomic number Z was the d 1 2 1 2 Atomic number 8 79 Au 78 Pt 77 Ir 76 Os 75 74 W 73 Ta 72 Lu 71 Yb 70 TmII 69 Tm I 68 Er 67 Dy 66 Ho 65 Tb 64 Gd 63 Eu 62 Sm 61 60 Nd 59 Pr 58 Ce 57 La 56 Ba 55 Cs 54 Xe 53 I 52 Te 51 Sb 50 Sn 49 In 48 Cd 47 Ag 46 Pd 45 Rh 44 Ru 43 42 Mo 41 Nb 40 Zr 39 Y 38 Sr 37 Rb 36 Kr 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn 29 Cu 28 Ni 27 Co 26 Fe 25 Mn 24 Cr 23 V 22 Ti 21 Sc 20 Ca 19 K 18 Ar 17 Cl 16 S 15 P 14 Si 13 Al Wavelength ( 10 10 m) 6 5 4 3 2 1.5 1 0.9 0.8 0.7 0.6 L a L series K a K series K b 6 8 10 12 14 Square root of frequency ( 10 8 Hz 1/2 ) 16 18 20 22 24
6.2 X ray production Auger electron
6.2 X ray production
6.2 X ray production Auger electron The kinetic energy of Auger electron E ae = E K E L1 E L2,3
6.2 X ray production Synchrotron Radiation In cyclic accelerators, when charged particles are accelerated, they radiate electromagnetic energy called synchrotron radiation.
6.3 Compton scattering At backward-scattering angles, there appeared to be a component of the emitted radiation (called a modified wave) that had a longer wavelength than the original primary (unmodified) wave. Graphite target θ = 90 Rotating crystal Intensity θ = 0 Primary Intensity θ = 90 λ λ 0 λ λ 0 λ λ λ 0 λ θ = 45 θ = 135 X-ray source Ionization chamber λ 0 λ λ λ 0 λ λ (a) (b)
6.3 Compton scattering
The unshifted peak at 0 in Figure 3.23 is caused by x electrons tightly bound to carbon atoms. This unshifted Recoil 6.3 Compton scattering dicted Incident by Equation 3.27 if the electron mass is replaced photon Diagram representing bon atom, which Compton is about scattering 23,000 times of a the photon mass φ of by an elec Let us now turn to the derivation of Equation 3.27 ass an electron. ton exhibits E, p particle-like behavior and collides θ elasticall with a free electron initially at E e, p e rest. Figure 3.24 shows t collision for which energy and Recoiling momentum electron are conserve Incident photon tron typically recoils at high φ speed, we treat the collision Scatter expression for conservation of energy gives E, p θ Scattered photon where E is the energy of the incident E < E, p photon, E is the en photon, m e c 2 is the rest energy of the electron, and E e is Figure 3.24 Diagram representing Compton scattering of electron. energy of The the scattered electron photon after the has collision. less energy Likewise, (or longer from wav m Conservation of we energy have Conservation of momentum incident photon. E m e c 2 E E e E m e c 2 E E e E < E, p p cos p e cos Energy con p sin p e sin
6.3 Compton scattering Therefore p e 2 (p ) 2 p 2 2pp cos With De Broglie relation We have p photon E c hf c h E e hf hf m e c 2 E 2 e p e 2 c 2 m 2 ec 4 Finally p e 2 hf c 2 hf c 2 2h2 ff c 2 cos 0 h m e c (1 cos ) Compton wavelength λ C = 2.426 10 3 nm
6.4 Photon absorption The three chief ways in which photons of light, x-rays, and gamma rays interact with matter Photoelectric effect Atom hv e Relative probability 1 Compton scattering Carbon Photoelectric effect Pair 0 production 0.01 0.1 1 10 100 Photon energy, MeV Compton scattering Pair production hv hv e e + e hv Relative probability 1 Lead Photoelectric effect Pair production Compton scattering 0 0.01 0.1 1 10 100 Photon energy, MeV
6.4 Photon absorption The intensity I of an x- or gamma-ray beam is equal to the rate at which it transports energy per unit crosssectional area of the beam. Radiation intensity I di I Absorber thickness dx I I 0 e x Linear attenuation coefficient, cm 1 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 Total Photoelectric effect Lead Pair production x ln (I 0 0 5 10 15 20 0 I) Photon energy, MeV Compton scattering 25