William Hunter-NM Lectures-Fall 2011
Main points from last week's lecture: “Decay of Radioactivity” Mathematics description nly yields probabilities and averages -λ t -0.693 t /T Interactions of Radiation Decay equation: N(t) = N(0) × e = N(0) × e 1/2 Activity: A(t) = -dN(t)/dt = λ N(t) with Matter Decay constant λ = A(t)/N(t) Half-life: T1/2 = ln(2) / λ = 0.693 / λ Average lifetime: = 1 / λ -λ t -0.693 t / T William Hunter, PhD Decay factor (DF): e = e 1/2 Image frame decay correction - effective decay factors
[email protected] Approximation for short frame times relative to isotope half-life: e.g., DFeff ≈ ½ [DF(t)+DF(t+Dt)] Nuclear Medicine Basic Science Lectures Specific Activity 18 http://www.rad.washington.edu/research/our-research/groups/irl/education/ CFSA [Bq/g] = max SA ≈ 4.8 x 10 /(A x T1/2) for T1/2 given in days, A: atomic weight basic-science-resident-lectures Mixed radionuclide samples
September 20, 2011 Atotal(t) always eventually follows the slope of the longest half-life nuclide. Parent-daughter decay rates
1. Secular equilibrium: T½,parent >> T½,daughter daughter activity quickly asymptotes to parent’s 2. Transient equilibrium: T½,parent ≥ T½,daughter daughter activity slowly asymptotes to parent’s
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Passage of radiation through matter Types of Radiation depends on … Particles ejected from an unstable nucleus: • Alpha radiation = 2p+2n (same as a He nucleus). Usually from a heavy element 1. Type of radiation • Beta radiation = β- or β+ (electron or positron) • charged particle (e.g., electron, proton, etc.) For example: neutron conversion inside the nucleus: • electromagnetic (e.g., high energy photon (n → p + e- + … or other permutations) such as x-ray or -ray) e • Heavy Ions and Neutrons! 2. Energy of radiation (e.g., in keV or MeV) Electromagnetic energy (photons): • Gamma radiation = 3. Nature of matter traversed (atomic number & density) De-excitation of a nucleus following another nuclear decay • Other electromagnetic radiation All photons from sources other than nuclear decay (e.g., atomic electron-orbital transitions)!
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[email protected] William Hunter-NM Lectures-Fall 2011
I. Interactions of Interactions of Charged Particles with Matter Charged Particles with Matter Description of Passage
Types of charged particle radiation relevant to Nuclear Medicine Gradual loss of particleʼs energy Particle Symbol Mass Charge Energy Imparted (amu) (relative) Energy transferred to nearby atoms and molecules Electron e-, - 0.000548 -1 kinetic
Positron e+, + 0.000548 +1 kinetic + 2 × 0.511MeV
Alpha 4.0028 +2 kinetic (can be large)
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Interactions of Charged Particles with Matter Interactions of Charged Particles with Matter Interaction mechanisms Excitation • Energy is transferred to an orbital electron, but not enough to free it.
• Electron is left in an excited state and energy is 1. Excitation dissipated in molecular vibrations or in atomic emission of infrared, visible or uv radiation, etc. 2. Ionization