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I0I0 I 0 V 0 V0V0 f f 0 1)Current depends on potential; max current I 0 (saturation) for high voltages. I 0 reached when all electrons are collected 2)Positive current even for (small) negative potential up to V 0 (stopping potential). V 0 corresponds to max. E kin : eV 0 = E kin, max 3)I 0 (= # of electrons per time) depends on light intensity but NOT on frequency 4)V 0 depends on the material and frequency, but not on intensity. 5)Emission only occurs for frequencies f > f 0 (V 0 (f 0 ) = 0 ) 6)The current is always observed immediately with begin of irradiation. A Light e –e – 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 > w 0 Kinetic energy of electron: E kin, max = h f – w 0 stopping potential: eV 0 = E kin, max = h f – w 0 ; threshold frequency (E kin = 0) : f 0 = w 0 /h -V0-V0 Photoelectric Effect

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Roentgens original tube Very first medical x-ray exposure: Berta Roentgens hand, December 22, 1895 Cathode Anode Vacuum tube – + cathode rays Wilhelm Röntgen – X-rays /

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d d sin Wave front Crystal lattice Bragg condition: 2d sin = n Crystal x-ray Bragg reflection of x-rays

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Single crystal Polycrystalline powder Bragg reflection of x-rays

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E i, p i E f, p f E e, p e Conservation of energy E i + m e c 2 = E f + E e Conservation of momentum x: p i = p f cos + p e cos y: 0= p f sin + p e sin E e 2 = p e 2 c 2 + m e 2 c 4 ; E i,f = p i,f c Compton Scattering Change in wavelength: = C (1-cos ) with C = h/m e c = 2.43× m

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Temperature [K] Energy [eV] Wavelength [nm] Visible Wavelength [m] Frequency [Hz] infraredγ-rays x-rays micro- wave radio ultra- violet Electromagnetic Spectrum

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Thermal radiation – continuous spectrum Radiation of gases (e.g. H) – discrete spectrum Source: Source: Light emission Spectra

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Bremsstrahlung + characteristic emission Source: X-ray emission

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Target, r t Projectile, r p Cross section: (r p +r t )² Number of interactions N: N = n t n: number of targets per area : (total) cross section [ n : fraction of total area covered with disks] : flux of projectiles (# of projectiles/time) [ t: total number of projectiles] Interaction probability per projectile P: P = n Cross section and Interaction Probability

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Cross section for the interaction of photons with C atoms (1 barn = m²) Photo effect Pair production (momentum transfer to nucleus) Thomson scattering Compton scattering Pair production (momentum transfer to electron) Cross section and Interaction Probability 41

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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( ) Probability for interaction (Number of interactions N = n t, n: targets per area, : 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) n = I(x) – I(x) dx ( : atoms per volume) dI/dx = (I(x+dx) – I(x))/dx = – I(x) I(x) = I 0 exp( – x)

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