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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.

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Presentation on theme: "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."— Presentation transcript:

1 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

2 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 /

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

4 Single crystal Polycrystalline powder Bragg reflection of x-rays

5 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

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

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

8 Bremsstrahlung + characteristic emission Source: X-ray emission

9 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

10 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

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( ) 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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