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Microsoft PowerPoint - resident physics

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    Microsoft PowerPoint - resident physics Microsoft PowerPoint - resident physics Document Transcript

    • Atomic and nuclear physics Atomic and nuclear physics force, energy, and light Textbook: atomic structure and transition Chapters 1 – 7 nuclear structure and transition Cherry SR, Sorenson JA, Phelps ME, interaction between particles and matter “Physics in Nuclear Medicine” 3rd ed photon attenuation in medium (2003) detection of photons production of radioactive nuclides Force Energy and mass Energy closely relates to force. push or pull between two objects higher energy stronger force contacted: mechanical force Energy can be converted to mass or vice over a distance: versa: E = m.C2 gravity force energy and mass unit: electric force electron volt (eV, keV, MeV) magnetic force 1 atomic unit (u) = 1.66 x 10-27 kg = 931.5 MeV nuclear force ≈ 1 GeV Energy is conserved but form can be changed in a process.
    • Electric force Light: electromagnetic wave attractive or repulsive oscillating electric field and perpendicularly oscillating magnetic field propagating stronger than gravity perpendicularly to the electric and magnetic medium range: fields at a speed c = 3 x 108 m/sec inverse square law amplitude electric energy = e.V phase binding the orbital wave length λ electrons to the nucleus frequency ν in an atom λ.ν = c Light: photons Light spectrum e-m wave quantized photons Photons are particles like electrons and protons. Photons carry energy and momentum, so always move, but no mass and no charge. photon energy: E = hν = hc/λ photon momentum: p = E/c Planck constant: h = 6.62 x 10-34 J-sec
    • Atomic structure Atomic force and energy atoms: the smallest part of element How does an atom maintain its stability? size ~ 10-8 cm electric force: attraction between the nucleus mass ~ 1 - 260 u (protons) and electrons charge = 0 n=1 Electric force binding energy n=2 orbital electrons, nucleus a few eV to keV charge -1 electron charge, mass: 511 keV, spin 1/2 decreases with decreasing 1 electron charge = 1.6 x 10-19 Coulomb nuclear charge Pauli exclusion principle: decreases with increasing E= - 1 0 ev E= - 5 ev electrons allowed for an inner shell ≤ 2n2 (n = 1, 2, 3, …) distance (orbits) electrons allowed for an outer shell ≤ 8 Transition of orbital electrons Nuclear structure usually stable: orbital electrons in the low nucleus size ≈ 10-13 cm orbits: minimum energy (ground state) nucleus mass ≈ 1 u (1 GeV) unstable: vacancies on the inner orbits due to nucleus composed of protons (Z, atomic some process (excited state) number) & neutrons (N) back to stable: outer electrons n mass number A = Z + N p jumping to fill the inner hole proton charge: +1 characteristic x-rays p x- ray neutron charge: 0 n Auger electron E= - 1 0 ev E= - 5 ev both spin 1/2 Auger e
    • Nuclear structure Nuclear model AX (Tc-99m) Z isotopes: same Z but different N shell model: 1H and 2H , 15O and 16O similar to the atom 1 1 8 8 isobars: same A but different Z liquid drop model: 14C and 14N 6 7 rotation and vibration isotones: same N but different Z 3H and 4He both can only explain 1 2 part of experimental data isomers: same A and Z but different energy 99mTc43 and 99Tc43 Nuclear force and energy Stability of nucleus for light nuclei (A ≤ 40), N = Z nuclear force: strong and shortly ranged attraction mediated by pions between for heavy nuclei (A > 40), N > Z nucleons The repulsive electric forces N between protons increase with binding energy for a nucleon: ~ 8 MeV increasing number of protons so transition of nucleons between excited that stronger nuclear forces and ground states (< 8 MeV) provided by more neutrons are needed to cancel out the electric Z forces.
    • Nuclear decay β− decay to achieve the stable N/Z ratio by β− decay for neutron rich isotopes − + 1. emitting charged particles ( β , β , α) A neutron decays to a proton, electron and anti- 2. capturing orbital electrons neutrino: n __> p + e- +ν 3. fission 99Mo __ > 99mTc43 + e- +ν 42 to release extra energy by 131I 53 __ > 131Xe - 54 + e +ν e- 1. γ (isomeric) decay ν 2. internal conversion γ-ray emission possible if the child nucleus conservation of energy, mass, charge, is in an excited state. momentum, etc. continuous energy for electrons – energy shared with neutrinos β+ decay Annihilation β+ decay for proton rich isotopes e- + e+ = 2 γ A proton decays to a neutron, positron and neutrino: p n + e+ + ν each γ photon energy: 511 keV due to energy-mass conservation γ 18F __> 18O + e+ + ν 2 γ’s always traveling in opposite 9 8 15O __> 15N + e+ + ν 8 7 e+ directions due to momentum ν e- e+ γ-ray emission possible if the child nucleus is in conversation an excited state. γ continuous energy for electrons – energy PET imaging shared with neutrinos
    • Electron capture α decay proton rich nuclei: p + e- n + ν to absorb orbital electron into nucleus to emit a helium nucleus (α) 226Ra 222Rn + 4He2 7Be + e- 7Li + ν 88 86 4 3 235U 92 231Th 90 + 4He2 α competing process with β+ decay (same product of z-1) usually occurring for heavy nuclei ν often followed by γ-rays successive x-rays and Auger electrons short range ~ 10-6 cm, can be stopped by paper probability increasing with larger Z (closer Unstable Rn-222 gas may cause lung cancer. electron shells). Radon gas Isomeric transition (I.T.) emitting γ photons to release extra energy of relatively short half life: T1/2= 3.825 d the nucleus 99mTc 43 +γ 99Tc 43 α, β and γ decays, decay rate high over occurs when a nucleus transfers from an the first hour and eventually to stable excited state (isomeric state) to ground state Pb-210 (T1/2= 22 y) energy difference passed to γ photons, similar to emission of characteristic x-rays often follows other decays
    • I.T. and I.C. Internal conversion (I.C.) ejecting an orbital electron to release K x-ray extra energy in the nucleus Z conversion e- highest probability for k-shell electrons A but other shells possible Auger e- successive x-rays and Auger electrons competing process with IT γ-ray L Fission Fission breaking a heavy nucleus into two fragments (usual mass ratio: 40:60) a neutron needed to initiate fission but 2 or 3 235U + n __> 92Kr36 + 141Ba56 + 3n + 200 MeV neutrons are created (chain reaction) 92 most energy released as heat, also kinetic energy for fragments and n (~ 1.5 MeV) low probability (e.g. T1/2 = 2×1017y for 235U) controllable in reactor, not controllable in atomic bomb
    • Fusion Nuclear decay rules combining two light nuclei into one heavier based on conservation laws nucleus γ-decay (I.T.) and internal conversion: 2H + 3H __> 4He + n + energy no changes for A & Z 1 1 2 β−-decay: AXZ AY Z+1 + e- + ν naturally occurred in the sun + β -decay: AXZ AY Z-1 + e+ + ν can be initiated artificially but currently uncontrollable in a hydrogen bomb e-capture: AXZ + e- AY Z-1 + ν α-decay: AX Z A-4Y Z-2 + α Nuclear decay scheme Activity ∆N( t ) 99Mo 42 99mTc 43 + e- + ν A( t ) = − = λ ⋅ N( t ) ∆t 9 9 Mo 4 2 ( 6 5 .9 h) 99mTc 43 99Tc 43 +γ λ - decay constant (1/sec, 1/min, 1/hr) 1 6 .4 % β- 9 2 0 .7 keV decay equation: N(t) = N0 exp(-ln2 t/T1/2) 9 9 m Tc 1 .1 % 4 3 (6.01 h) 1 4 2 .7 keV 5 0 9 .1 keV γ1 99% N: number of survived nuclei, ln2 = 0.693 1 4 0 .5 keV 8 1 .8 % γ2 I.C. γ3 half life T1/2 = ln2/λ 1 4 2 .7 keV 89% 11% 1% tradition unit: 1 Ci = 3.7x1010 dps (1 g Ra-226) 1 4 0 .5 keV 0 9 9 Tc 43 (2.111x105 y) SI: 1 Bq = 1 dps 1 mCi = 37 MBq 0 9 9 Tc 43 ( 2 .1 1 1 x1 0 5 y)
    • Parent-child-grandchild decay Parent-child-grandchild decay secular equilibrium: Tc << Tp transient equilibrium: Tc = 0.1 Tp 226Ra __> 222Rn + α (1600 y) 99Mo 99mTc + e- + ν (66 h) A Ap 42 43 222Rn __> 218Po + α (3.8 d) 99mTc 43 99Tc + γ (6 43 h) A Ac  − 0.693 t  A c (t ) Tp Ap  1 − e Tc  Ac = A c ( t ) = A 0p A p ( t ) Tp − Tc     decay with the same halflife after t t m ax Αc(t) = Α0p for large t > 5 Tc tmax: equilibrium t tmax = 24 hr for Mo-Tc equilibrium Parent-child-grandchild decay Effective half life no equilibrium: Tc > Tp 1 1 1 131mTe (30 h) 131I (8 d) = + Teff Tphy Tbio A Tphy × Tbio Teff = Tphy + Tbio Ap Ac if Tph >> Tbi, Teff ≈ Tbi if Tph << Tbi, Teff ≈ Tph t
    • Interaction between particles and matter Electron with matter mainly interact with orbital electrons due to charged particles (electron) with matter the same mass (atoms) ionization free free electron and ion neutrons with matter excited excitation photons with matter excited atom e Bremsstrahlung Neutron with matter bremsstrahlung (braking radiation) x-rays mainly interact with nucleus due to the The electron penetrates the orbital x-rays similar mass electrons and is defected and decelerated by the nucleus. e elastic scattering: kinetic energy unchanged before and after scattering inelastic scattering: kinetic energy Probability increases with greater e- energy and decreased to excite the nucleus n larger atomic number of the medium. neutron capture nucleus n e.g. in W, 10 MeV electrons losing 50% energy n nucleus 100 MeV electrons losing 90% energy
    • Photon with matter Photoelectric process free e photoelectric process no photon after the process (absorption) low photon energy < 60 keV probability decreasing with γ-rays γ- rays Compton scatter greater photon energy (proportional to 1/E3) medium photon energy lower atomic number (proportional to Z3) γ-rays probability 0 when E > 60 keV in tissue pair production followed by characteristic x-ray and free high photon energy > 1.02 MeV electron γ- rays e+ e - Compton scatter Pair production photon changing direction and decreasing energy (minimum E at 180°), but not absorbed E ≥ 1.02 MeV 0° < recoiled electron < 90° no photons after the process dominating at medium energies (60 keV – probability increasing with several MeV) higher photon energy slowly almost same probability for all media (except larger atomic number: proportional to Z for H2) proportional to Z/A dominating when E > 10 MeV in tissue followed possibly by characteristic x-rays or energy deposited locally: E – 1.02 MeV free electron
    • Range of radiation in matter Range of electron and α in matter type of radiation: electron range: charged < n < photon Rair(m) = 4 Emax(MeV) radiation energy: RH2O(cm) = 0.5 Emax(MeV) higher longer range α-particle (4 - 8 MeV) range: composition and density of the medium: Rair (cm) = 0.325 E3/2 (MeV) in air heavier, denser shorter range R = Rair (ρairA1/2/ ρAair1/2) in others Photon attenuation in medium Photon attenuation in medium photon attenuation in medium (absorption and scatter): number of photons (I) decreases with transmission factor: exp(−µl) depth (d) inside the medium according to the attenuation factor: 1 - exp(−µl) exponential function: HVL (l1/2) : I = 0.5 I0 l1/2 = ln2/µ = 0.693/µ I = I 0 e − µd linear attenuation coefficient: µ TVL: I = 0.1 I0 l1/10 = ln10/µ = 2.30/µ mass attenuation coefficient: µm = µ/density mean free path: lm = 1/µ useful in radiation protection, particularly for µ depending on Eγ and medium composition x-ray
    • Inverse square law Photon detection Id = I0/d2 for an isotropic emitting point source gas-filled detectors only detecting number of photons (activity) longer distance Scintillation detectors smaller solid angle detecting both activity and photon energy fewer particles useful in radiation protection, particularly for PET Semi-conductor detectors exposure rate constant for a point source Γ detecting both activity and photon energy (R⋅cm2/(mCi⋅hr)) exposure rate (R/hr) = Γ⋅A/d2 Gas-filled detectors Personnel dosimeter badges ionization chamber (12 a.p. Ar or air) thermoluminescent dosimeter (TLD): To for dose calibrator and accurate survey meter measure cumulative dose over weeks or months Geiger-Muller counter . filled with quenching gas LiF chip: exposed to radiation – heated – for sensitive survey meter emitting light – measured using PMT and area monitor Al2O3 chip: exposed to radiation – optically + stimulated – emitting light e γ h pocket dosimeter: ionization chamber, to _ measure dose for a short period of time
    • Scintillation detectors Scintillation detectors NaI(Tl) for well counter and gamma camera activity: number of the pulses BGO, LSO, GSO, LYSO for dedicated PET energy: number of the blue photons scanner linearity of scintillation: The number blue Tl one γ photon e-h pairs e of blue photons, so the pulse height, is exciting Tl Tl back to g.s. γ linearly proportional to the γ photon blue light (~ 3 eV photons) Na I- h energy. Tl blue e- one electrical pulse Production of radioactive nuclides Nuclear reactor produce neutron-rich nuclides (β− emitters) nuclear reactor for producing neutron- 14N(n,p)14C: 14N + n = 14C + p rich nuclides (β- emitters) 23Na(n,γ)24Na particle accelerator (cyclotron) for 31P(n,γ)32P producing proton-rich nuclides (β+ 32S(n,p)32P 130Te(n,γ)131Te 131I emitters) 99Mo 42 generator for producing Tc-99m and Rb-82 components: uranium, control rods (Cd), moderator (D2O or graphite), coolant
    • Cyclotron Cyclotron accelerate charged particle beam (Ep ~ 10 MeV) to produce proton-rich nuclides (β+ emitters) increase the probability of the (p,n) reaction 11B(p,n)11C : 11B + p = 11C + n components: magnets, high-frequency AC voltage, 12C(d,n)13N Dees, ion source, target chambers ~ 14N(d,n)15O 18O(p,n)18F, 20Ne(d,α)18F 111Cd(p,n)111In 201Hg(d,2n)201Tl Cyclotron The first cyclotron (1930s) magnetic field: keeping charged particle rotating AC: increasing energy of particle in the gap ion source: producing charged particles target chamber: nuclear reaction
    • Medical cyclotron Biosynthesizer (hot cell) attach the cyclotron-produced radionuclide to a biological compound, e.g. F-18 to FDG (2-deoxy-2 [18F]fluoro- D-glucose) Generator Generator components: alumina column, lead shield, air produce Tc-99m or Rb-82 filter, saline eluent parent T1/2 child decay T1/2___ MoO4-- bound to alumina (Al2O3) but 99mTcO4- 82Sr 25 d 82Rb β+,EC 1.3 m not strongly bound 99Mo 66 h 99mTc IT 6h eluted with 5 to 25 ml saline: ~ 80% 99mTc 68Ge 275 d 68Ga β+,EC 68 m extracted in one 113Sn 120 d 113mIn IT 100 m elution