Chapter 1 Basic Radiation Physics - IRSN
Chapter 1Basic Radiation PhysicsThis set of 194 slides is based on Chapter 1 authored byE.B. Podgorsakof the IAEA publication (ISBN 92-0-107304-6):Radiation Oncology Physics:A Handbook for Teachers and StudentsObjective:To familiarize students with basic principles of radiation physics andmodern physics used in radiotherapy.Slide set prepared in 2006 (updated Aug2007)by E.B. Podgorsak (McGill University, Montreal)Comments to S. Vatnitsky:dosimetry@iaea.orgIAEAInternational Atomic Energy AgencyCHAPTER 1.TABLE OF CONTENTS1.1. Introduction1.2. Atomic and nuclear structure1.3. Electron interactions1.4. Photon interactionsIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.(2/194)1
1.1 INTRODUCTION1.1.1 Fundamental physical constants Avogadro’s number:NA 6.022 10 23 atom/g-atomSpeed of light in vacuum: c 3 108 m/se 1.6 1019 AsElectron charge:me 0.511 MeV/c 2Electron rest mass:Proton rest mass:mp 938.2 MeV/c 2Neutron rest mass:mn 939.3 MeV/c 2Atomic mass unit:u 931.5 MeV/c 2IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.1 Slide 1 (3/194)1.1 INTRODUCTION1.1.2 Derived physical constants Reduced Planck’s constant speed of light in vacuum c 197 MeV fm 200 MeV fm Fine structure constante2 11 4 o c 137 Classical electron radius1e2re 2.818 MeV4 o mec 2 IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.2 Slide 1 (4/194)2
1.1 INTRODUCTION1.1.2 Derived physical constants Bohr radius:ao 4 o ( c)2 c 0.529 Å mec 2e 2 mec 2 Rydberg energy:2211 e 2 mecER mec 2 2 13.61 eV 22 4 o ( c)2 Rydberg constant:ERm c 2 2R e 109 737 cm 12 c4 cIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.2 Slide 2 (5/194)1.1 INTRODUCTION1.1.3 Physical quantities and units Physical quantities are characterized by their numericalvalue (magnitude) and associated unit. Symbols for physical quantities are set in italic type, whilesymbols for units are set in roman type.For example: m 21 kg; E 15 MeVIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.3 Slide 1 (6/194)3
1.1 INTRODUCTION1.1.3 Physical quantities and units The numerical value and the unit of a physical quantitymust be separated by space.For example:21 kg and NOT 21kg; 15 MeV and NOT 15MeV Currently used metric system of units is known as theSystéme International d’Unités (International system ofunits) or the SI system.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.3 Slide 2 (7/194)1.1 INTRODUCTION1.1.3 Physical quantities and unitsThe SI system of units is founded on base units for sevenphysical quantities:QuantitySI unitLengthMass mTime tElectric current (I)Temperature (T)Amount of substanceLuminous intensityIAEAmeter (m)kilogram (kg)second (s)ampère (A)kelvin (K)mole (mol)candela (cd)Review of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.3 Slide 3 (8/194)4
1.1 INTRODUCTION1.1.4 Classification of forces in natureThere are four distinct forces observed in interaction betweenvarious types of particlesForceSourceTransmitted particle Relative strengthStrongStrong chargeGluon1EMElectric chargePhoton1/13710-6WeakWeak chargeW , W-, and ZoGravitational EnergyGraviton10-39IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.4 Slide 1 (9/194)1.1 INTRODUCTION1.1.5 Classification of fundamental particlesTwo classes of fundamental particles are known: Quarks are particles that exhibit strong interactionsQuarks are constituents of hadrons with a fractional electriccharge (2/3 or -1/3) and are characterized by one of threetypes of strong charge called color (red, blue, green). Leptons are particles that do not interact strongly.Electron, muon, tau, and their corresponding neutrinos.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.5 Slide 1 (10/194)5
1.1 INTRODUCTION1.1.6 Classification of radiationRadiation is classified into two main categories: Non-ionizing radiation (cannot ionize matter). Ionizing radiation (can ionize matter). Directly ionizing radiation (charged particles)electron, proton, alpha particle, heavy ion Indirectly ionizing radiation (neutral particles)photon (x ray, gamma ray), neutronIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.6 Slide 1 (11/194)1.1 INTRODUCTION1.1.6 Classification of radiationRadiation is classified into two main categories:IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.6 Slide 2 (12/194)6
1.1 INTRODUCTION1.1.7 Classification of ionizing photon radiationIonizing photon radiation is classified into four categories: Characteristic x rayResults from electronic transitions between atomic shells. BremsstrahlungResults mainly from electron-nucleus Coulomb interactions. Gamma rayResults from nuclear transitions. Annihilation quantum (annihilation radiation)Results from positron-electron annihilation.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.7 Slide 1 (13/194)1.1 INTRODUCTION1.1.8 Einstein’s relativistic mass, energy, and momentum Mass:m( ) Normalized mass:m( ) mowhereIAEA cmo 1 c21 1 cand2 mo mo1 211 2 11 2Review of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.8 Slide 1 (14/194)7
1.1 INTRODUCTION1.1.8 Einstein’s relativistic mass, energy, and momentumm( ) m( ) momo 1 c21 1 cIAEA2 mo1 211 2 mo c11 2Review of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.8 Slide 2 (15/194)1.1 INTRODUCTION1.1.8 Einstein’s relativistic mass, energy, and momentum Total energy:E m( )c 2 Rest energy:Eo moc 2 Kinetic energy: EK E Eo ( 1)Eo Momentum:withIAEAp 1E 2 Eo2c cand 11 2Review of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.8 Slide 3 (16/194)8
1.1 INTRODUCTION1.1.9 Radiation quantities and unitsIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.1.9 Slide 1 (17/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structure The constituent particles forming an atom are: Proton Neutron ElectronProtons and neutrons are known as nucleons and they form thenucleus. Atomic number ZNumber of protons and number of electrons in an atom.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 1 (18/194)9
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structure Atomic mass number ANumber of nucleons A Z N in an atom,where Z is the number of protons (atomic number) in an atom. N is the number of neutrons in an atom.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 2 (19/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structure There is no basic relation between the atomic massnumber A and atomic number Z of a nucleus but theempirical relationship:Z A1.98 0.0155A2/3furnishes a good approximation for stable nuclei.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 3 (20/194)10
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structure Atomic gram-atom is defined as the number of grams ofan atomic compound that contains a number of atomsexactly equal to one Avogadro’s number, i.e.,NA 6.022 10 23 atom/g-atom Atomic mass number A of all elements is defined suchthat A grams of every element contain exactly NA atoms. For example: 1 gram-atom of cobalt-60 is 60 g of cobalt-60. 1 gram-atom of radium-226 is 226 g of radium-226.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 4 (21/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structure Molecular gram-mole is defined as the number of gramsof a molecular compound that contains exactly oneAvogadro’s number of molecules, i.e.,NA 6.022 10 23 molecule/g-mole The mass of a molecule is the sum of the masses of theatoms that make up the molecule. For example: 1 gram-mole of water is 18 g of water. 1 gram-mole of carbon dioxide is 44 g of carbon dioxide.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 5 (22/194)11
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definition for atomic structure Atomic mass M is expressed in atomic mass units u 1 u is equal to 1/12th of the mass of the carbon-12 atom orto 931.5 MeV/c2. The atomic massMis smaller than the sum of theindividual masses of constituent particles because of theintrinsic energy associated with binding the particles(nucleons) within the nucleus.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 6 (23/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definition for atomic structure Nuclear mass M is defined as the atomic mass with themass of atomic orbital electrons subtracted, i.e.,M M ZmeThe binding energy of orbital electrons to the nucleus isneglected.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 7 (24/194)12
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structureIn nuclear physics the convention is to designate a nucleusX as AZ X ,whereA is the atomic mass numberZ is the atomic numberFor example: Cobalt-60 nucleus with Z 27 protons and N 33 neutrons isidentified as 60Co .27 Radium-226 nucleus with Z 88 protons and N 138 neutrons isRa .identified as 22688IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 8 (25/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structure Number of atoms Na per mass m of an element:Na NA mA Number of electrons Ne per mass m of an element:NNNe Z a Z AmmA Number of electrons Ne per volume V of an element:NNNe Z a Z AVmAIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 9 (26/194)13
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.1 Basic definitions for atomic structure For all elements Z /A 0.5 with two notable exceptions: Hydrogen-1 for which Z /A 1.0 Helium-3 for which Z /A 0.67 . Actually, Z /A gradually decreases: from 0.5 for low atomic number Z elements. to 0.4 for high atomic number Z elements. For example: Z /A 0.50 for 42 HeIAEAZ /A 0.45 for6027Z /A 0.39 for23592CoUReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.1 Slide 10 (27/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom Rutherford’s atomic model is based on results of theGeiger-Marsden experiment of 1909 with 5.5 MeV alphaparticles scattered on thin gold foils with a thickness ofthe order of 10-6 m.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 1 (28/194)14
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom At the time of the Geiger-Marsden experiment Thomsonatomic model was the prevailing atomic model. The model was based on anassumption that the positiveand the negative (electron)charges of the atom weredistributed uniformly overthe atomic volume(“plum-pudding model”).IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 2 (29/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom Geiger and Marsden found that: More than 99% of the alpha particles incident on the gold foilwere scattered at scattering angles less than 3o. Distribution of scattered alpha particles followed Gaussian shape. Roughly one in 104 alpha particles was scattered with a scattering angle exceeding 90o (probability 10-4). This finding (one in 104) was in drastic disagreement withthe theoretical prediction of one in 103500 resulting fromthe Thomson’s atomic model (probability 10-3500).IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 3 (30/194)15
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom Ernest Rutherford concluded that the peculiar results ofthe Geiger-Marsden experiment did not support theThomson’s atomic model and proposed the currentlyaccepted atomic model in which: Mass and positive charge of theatom are concentrated in thenucleus the size of which isof the order of 10-15 m. Negatively charged electronsrevolve about the nucleus ina spherical cloud on the peripheryof the Rutherford atom with aradius of the order of 10-10 m.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 4 (31/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom Based on his model and four additional assumptions,Rutherford derived the kinematics for the scattering ofalpha particles on gold nuclei using basic principles ofclassical mechanics. The four assumptions are related to: Mass of the gold nucleus. Scattering of alpha particles. Penetration of the nucleus. Kinetic energy of the alpha particles.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 5 (32/194)16
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom The four assumptions are: Mass of the gold nucleus mass of the alpha particle. Scattering of alpha particles on atomic electrons is negligible. Alpha particle does not penetrate the nucleus, i.e., there are nonuclear reactions occurring. Alpha particles with kinetic energies of the order of a few MeVare non-relativistic and the simple classical relationship for thekinetic energy EK of the alpha particle is valid:EK IAEAm 22Review of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 6 (33/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atomAs a result of the repulsive Coulomb interaction between thealpha particle (charge 2e) and the nucleus (charge Ze) thealpha particle follows a hyperbolic trajectory.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 7 (34/194)17
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom The shape of the hyperbolic trajectory and the scatteringangle depend on the impact parameter b.The limiting case is a direct hit with b 0 and (backscattering)that, assuming conservation of energy, determines the distance ofclosest approach D N in a direct hit (backscattering) interaction.EK IAEA2ZNe 24 o D N D N 2ZNe 24 o EKReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 8 (35/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom The shape of the hyperbolic trajectory and the scatteringangle are a function of the impact parameter b. The repulsive Coulomb force between the alpha particle(charge ze, atomic number 2) and the nucleus (chargeZe) is governed by 1/ r 2 dependence:Fcoul2Ze 2 4 or 2where r is the separation between the two charged particles.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 9 (36/194)18
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atom The relationship between the impact parameter b andthe scattering angle follows from the conservation ofenergy and momentum considerations:b 1D N cot22 This expression is derived using: The classical relationship for the kinetic energy of the particle:EK m 2 / 2. The definition of D N in a direct hit head-on collision for whichthe impact parameter b 0 and the scattering angle .IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 10 (37/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.2 Rutherford’s model of the atomDifferential Rutherford scattering cross section is given asd Ruth D N d 421sin ( / 2)4where D N is the distanceof closest approachD N 2ZNe 24 o EKIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.2 Slide 11 (38/194)19
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.3 Bohr’s model of the hydrogen atom Niels Bohr in 1913 combined: Rutherford’s concept of the nuclear atom with Planck’s idea of quantized nature of the radiation process anddeveloped an atomic model that successfully deals withone-electron structures, such as the hydrogen atom,singly ionized helium, etc. Mnucleus with mass M me electron with mass me rnradius of electron orbitIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.3 Slide 1 (39/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.3 Bohr’s model of the hydrogen atom Bohr’s atomic model is based on four postulates: Postulate 1: Electrons revolve about the Rutherford nucleus inwell-defined, allowed orbits (planetary-like motion). Postulate 2: While in orbit, the electron does not lose anyenergy despite being constantly accelerated (no energy loss whileelectron is in allowed orbit). Postulate 3: The angular momentum of the electron in anallowed orbit is quantized (quantization of angular momentum). Postulate 4: An atom emits radiation only when an electronmakes a transition from one orbit to another (energy emissionduring orbital transitions).IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.3 Slide 2 (40/194)20
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.3 Bohr’s model of the hydrogen atomBohr’s atomic model is based on four postulates:Postulate 1: Planetary motion of electrons Electrons revolve about the Rutherford nucleus in welldefined, allowed orbits. The Coulomb force of attraction between the electronand the positively charged nucleus is balanced by thecentrifugal force.Fcoul IAEAme e21 Ze 2 F centre4 o re2Review of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.3 Slide 3 (41/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.3 Bohr’s model of the hydrogen atomBohr’s atomic model is based on four postulates:Postulate 2: No energy loss while electron is in orbit. While in orbit, the electron does not lose any energydespite being constantly accelerated. This is a direct contravention of the basic law ofnature (Larmor’s law) which states that:“Any time a charged particle is accelerated or decelerated part of its energy is emitted in the form ofphotons (bremsstrahlung)”.IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.3 Slide 4 (42/194)21
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.3 Bohr’s model of the hydrogen atomBohr’s atomic model is based on four postulates:Postulate 3: Quantization of angular momentum The angular momentum L me rof the electron in anallowed orbit is quantized and given as L n ,where n is an integer referred to as the principalquantum number and h / 2 . The lowest possible angular momentum of electron inan allowed orbit isL . All angular momenta of atomic orbital electrons areinteger multiples of .IAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.3 Slide 5 (43/194)1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.3 Bohr’s model of the hydrogen atomBohr’s atomic model is based on four postulates:Postulate 4: Emission of photon during atomic transition. An atom emits radiation only when an electron makesa transition from an initial allowed orbit with quantumnumber ni to a final orbit with quantum number nf. Energy of the emitted photon equals the difference inenergy between the two atomic orbits.h Ei E fIAEAReview of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.2.3 Slide 6 (44/194)22
1.2 ATOMIC AND NUCLEAR STRUCTURE1.2.3 Bohr’s model of the hydrogen atom Radius rn of a one-electron Bohr atom is:o 2 n2 nrn ao 0.53 A Z Z Velocity
Chapter 1 Basic Radiation Physics Slide set prepared in 2006 (updated Aug2007) by E.B. Podgorsak (McGill University, Montreal) Comments to S. Vatnitsky: dosimetry@iaea.org IAEA Review of Radiation Oncology Physics: A Handbook for Teachers and Students - 1.(2/194) CHAPTER 1. TABLE OF CONTENTS 1.1. Introduction 1.2. Atomic and nuclear structure 1.3.File Size: 1MB
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
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DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
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