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4/2003 Rev 2 I.3.4 – slide 1 of 24 Session I.3.4 Part I Review of Fundamentals Module 3Interaction of Radiation with Matter Session 4Photon Interactions IAEA Post Graduate Educational Course Radiation Protection and Safety of Radiation Sources

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4/2003 Rev 2 I.3.4 – slide 2 of 24 In this session we will discuss photon interactions including: In this session we will discuss photon interactions including: Photoelectric effect Photoelectric effect Compton scattering Compton scattering Pair production Pair production Overview

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4/2003 Rev 2 I.3.4 – slide 3 of 24 Photoelectric Effect

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4/2003 Rev 2 I.3.4 – slide 4 of 24 Photoelectric Effect - Example:E incident photon = 80 keV E binding energy = 20 keV E photoelectron = 60 keV E photoelectron = E incident photon – E binding energy

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4/2003 Rev 2 I.3.4 – slide 5 of 24 Photoelectric Effect The photoelectric effect is predominant for: The photoelectric effect is predominant for: Low energy photons Low energy photons High atomic number Z materials High atomic number Z materials Probability is proportional to: Z4Z4Z4Z4 E3E3E3E3

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4/2003 Rev 2 I.3.4 – slide 6 of 24 Photoelectric Effect

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4/2003 Rev 2 I.3.4 – slide 7 of 24 Compton Scattering incident photon (E ip ) scattered photon (E sp ) scattered electron (E se ) loosely bound electron (E ie )

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4/2003 Rev 2 I.3.4 – slide 8 of 24 Compton Scattering E ie = m o c 2 E se = mc 2 E ip = hc ip E* sp = hc sp Conservation of Energy: hc ip + m o c 2 = hc sp + mc 2

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4/2003 Rev 2 I.3.4 – slide 9 of 24 Compton Scattering P se = mv P ip = h ip P* sp = h sp Conservation of Momentum: h ip = h sp cos + mv cos 0 = h sp sin + mv sin horizontal vertical P ie = 0

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4/2003 Rev 2 I.3.4 – slide 10 of 24 Compton Scattering (1 - cos ) = sp - ip = = sp - ip =h mocmocmocmoc Solving both the energy and momentum equations yields: The energy transferred to the scattered electron is: E se = E ip – E sp = - hc ip ip hc sp sp

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4/2003 Rev 2 I.3.4 – slide 11 of 24 Compton Scattering Substituting E = hc into the momentum equations gives the energy of the scattered photon: E sp = 1 + (1 - cos ) E ip moc2moc2moc2moc2 m o c 2 = rest mass energy of the electron = 0.511 MeV

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4/2003 Rev 2 I.3.4 – slide 12 of 24 Compton Scattering E sp = 1 + (1 - cos ) E ip moc2moc2moc2moc2 For simplicity let E ip moc2moc2moc2moc2 = f E sp = 1 + f (1 - cos ) E ip

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4/2003 Rev 2 I.3.4 – slide 13 of 24 Compton Scattering When = 90º, E sp = the energy of the scattered photon is reduced When = 180º, E sp = the energy of the scattered photon is minimum When = 0º, E sp = E ip there is no interaction E ip (1+f) (1+2f)

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4/2003 Rev 2 I.3.4 – slide 14 of 24 Compton Scattering Example 1:A low energy photon (10 keV) scattered by 90º and 180º f = 10 keV/511 keV = 0.02; cos 90º = 0; cos 180º = -1 E sp = 1 + 0.02 (1 - 0) 10 keV = 10/1.02 = 9.8 keV E sp = 1 + 0.02 (1 - -1) 10 keV = 10/1.04 = 9.6 keV the scattered electron receives only 2-4% of the incident energy

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4/2003 Rev 2 I.3.4 – slide 15 of 24 Compton Scattering Example 2:A high energy photon (1000 keV) scattered by 90º and 180º f = 1000 keV/511 keV = 1.96; cos 90º = 0; cos 180º = -1 E sp = 1 + 1.96 (1 - 0) 1000 keV = 1000/2.96 = 340 keV E sp = 1 + 1.96 (1 - -1) 1000 keV = 1000/4.92 = 200 keV the scattered electron receives about 66-80% of the incident energy

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4/2003 Rev 2 I.3.4 – slide 16 of 24 Compton Scattering Example 3:What is the maximum energy of a photon scattered through 90º and 180º for a very high energy incident photon If f = E ip /511 keV >> 1 then (1 + f) f 1 + f E ip f E sp = = 511 keV = = E ip 511 (90º) (180º) 1 + 2f E ip 2f E ip E sp = = = = = 255 keV 511 2 E ip 2E ip 511

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4/2003 Rev 2 I.3.4 – slide 17 of 24 Compton Scattering E = hc h = 6.62 x 10 -34 J-sec c = 3 x 10 8 m/sec E = (6.62 x 10 -34 J-sec)(3 x 10 8 m/sec) (1.6 x 10 -19 J/eV)(10 3 eV/kev) (1.6 x 10 -19 J/eV)(10 3 eV/kev) E = 1.24 x 10 -9 keV-m (m) (m) The energy of a photon relative to its wavelength:

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4/2003 Rev 2 I.3.4 – slide 18 of 24 Pair Production Photon converted into two particles (energy into mass) electron (-) positron (+)

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4/2003 Rev 2 I.3.4 – slide 19 of 24 Pair Production The rest mass energy of a positive or negative electron is 0.511 MeV To create these two particles requires a minimum energy of 2 x 0.511 MeV = 1.02 MeV

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4/2003 Rev 2 I.3.4 – slide 20 of 24 Pair Production A positron cannot exist at rest. It combines with an electron. The two particles annihilate each other converting mass back into energy. Since the rest mass energy of each particle is 0.511 MeV, the two photons created must each possess an energy of 0.511 MeV. Two photons must be created, traveling in opposite directions, to satisfy the Law of Conservation of Momentum.

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4/2003 Rev 2 I.3.4 – slide 21 of 24 Photon Energy (MeV) Pair Production Compton Photoelectric Combined Probability WATER Photon Interactions

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4/2003 Rev 2 I.3.4 – slide 22 of 24 Photon Energy (MeV) Pair Production Compton Photoelectric Combined Probability LEAD K shell Binding Energy Photon Interactions

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4/2003 Rev 2 I.3.4 – slide 23 of 24 Summary We have discussed Photon Interactions including: We have discussed Photon Interactions including: Photoelectric Effect Photoelectric Effect low energy photons low energy photons photon electron photon electron Compton Scattering Compton Scattering medium energy photons medium energy photons photon electron + new photon photon electron + new photon Pair Production Pair Production photon ( 1.02 MeV) photon ( 1.02 MeV) photon e - + e + 2 photons (0.511 MeV each) photon e - + e + 2 photons (0.511 MeV each)

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4/2003 Rev 2 I.3.4 – slide 24 of 24 Where to Get More Information Cember, H., Johnson, T. E., Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2008) Cember, H., Johnson, T. E., Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2008) Martin, A., Harbison, S. A., Beach, K., Cole, P., An Introduction to Radiation Protection, 6 th Edition, Hodder Arnold, London (2012) Martin, A., Harbison, S. A., Beach, K., Cole, P., An Introduction to Radiation Protection, 6 th Edition, Hodder Arnold, London (2012) Jelley, N. A., Fundamentals of Nuclear Physics, Cambridge University Press, Cambridge (1990) Jelley, N. A., Fundamentals of Nuclear Physics, Cambridge University Press, Cambridge (1990) Firestone, R.B., Baglin, C.M., Frank-Chu, S.Y., Eds., Table of Isotopes (8 th Edition, 1999 update), Wiley, New York (1999) Firestone, R.B., Baglin, C.M., Frank-Chu, S.Y., Eds., Table of Isotopes (8 th Edition, 1999 update), Wiley, New York (1999)

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