I 0

1. Light e– A I V0 I0 V 0 f 0 f 0 Photoelectric Effect -V0 1) Current depends on potential; max current I0 (saturation) for high voltages.  I0 reached when all electrons are collected 2) Positive current even for (small) negative potential up to V0 (“stopping potential”).  V0 corresponds to max. Ekin: eV0 = Ekin, max 3) I0 (= # of electrons per time) depends on light intensity but NOT on frequency 4) V0 depends on the material and frequency, but not on intensity. 5) Emission only occurs for frequencies f > f 0(V0(f 0) = 0 ) 6) The current is always observed immediately with begin of irradiation. Interpretation: Light comes in bundles (photons) with energy E = hf, each photon is absorbed by a single electron.  # of electrons  # of incident photons  e– emitted only if photon energy is larger than e– separation energy (“work function”): hf> w0  Kinetic energy of electron: Ekin, max= h f– w0 stopping potential: eV0 = Ekin, max= h f– w0 ; threshold frequency (Ekin = 0) : f 0= w0/h

2. Vacuum tube Cathode Anode – + Wilhelm Röntgen – X-rays Roentgen’s original tube cathode rays Very first “medical” x-ray exposure: Berta Roentgen’s hand, December 22, 1895 http://www.deutsches-museum.de/sammlungen/ausgewaehlte-objekte/meisterwerke-ii/roentgen/

3. Wave front d q d sin q Crystal lattice Bragg reflection of x-rays Bragg condition: 2d sin q = nl Crystal x-ray www.unl.edu/ncmn/facilities/images/Lauebkg_sm.gif

4. Bragg reflection of x-rays Polycrystalline powder Single crystal

5. Compton Scattering Conservation of energy Ei + mec2 = Ef + Ee Conservation of momentum x: pi = pfcosq + pecosj y: 0 = pf sin q + pe sin j Ee2 = pe2c2 + me2c4; Ei,f = pi,f c Ee, pe Ei, pi j q Ef, pf Change in wavelength: Dl = lC (1-cosq) with lC = h/mec = 2.43×10-12 m

6. Temperature [K] Energy [eV] ultra- violet micro- wave x-rays γ-rays infrared radio Frequency [Hz] 1010 10-16 1014 1024 10-14 108 1022 1012 1020 10-12 106 1010 1018 108 104 10-10 1016 106 102 10-8 1014 100 10-6 104 10-2 102 10-4 1012 1010 10-2 10-4 100 108 100 10-6 10-2 10-8 10-4 102 106 10-10 104 104 10-6 Wavelength [m] Visible Wavelength [nm] 400 450 500 550 600 650 700 750 Electromagnetic Spectrum

7. Light emission Spectra Source: http://library.tedankara.k12.tr Thermal radiation – continuous spectrum Radiation of gases (e.g. H) – discrete spectrum Source: http://mo-www.harvard.edu/Java/MiniSpectroscopy.html

8. X-ray emission Bremsstrahlung + characteristic emission Source: http://www.uni-koeln.de/math-nat-fak/geomin/images/ausstattung/xerzeug.gif

9. Cross section and Interaction Probability Target, rt Projectile, rp Cross section: p(rp+rt)² Number of interactions N: N = nsfDt n: number of targets per area s: (total) cross section [ ns: fraction of total area covered with “disks”] f: flux of projectiles (# of projectiles/time) [ fDt: total number of projectiles] Interaction probability per projectile P: P = ns

10. Cross section and Interaction Probability Photo effect Cross section for the interaction of photons with C atoms (1 barn = 10-28 m²) http://xdb.lbl.gov/Section3/Sec_3-1.html 41 Pair production (momentum transfer to nucleus) Thomson scattering Pair production (momentum transfer to electron) Compton scattering

11. Matter and Radiation Energy from matter to radiation: emission - Continuous: thermal radiation, bremsstrahlung - Discrete: atomic spectra, characteristic x-rays - Radioactive decay (gamma radiation, but also other radiation) Energy from radiation to matter: absorption, scattering - Photoelectric effect - Compton scattering - Pair production Cross section(s) Probability for interaction (Number of interactions N = nsfDt, n: targets per area, f : flux of projectiles) Attenuation Beam of photons propagating through material Intensity at position x: I(x) Intensity at x+dx: I(x) – probability that something happens in dx  I(x+dx) = I(x) – I(x)sn = I(x) – I(x)srdx (r : atoms per volume)  dI/dx = (I(x+dx) – I(x))/dx = – srI(x)  I(x) = I0 exp( – sr x)