PHY138Y Nuclear and Radiation Professor Tony Key MP401 key@physics.utoronto.ca Announcements Next and last Representative Assembly, Friday of next week (23 rd ) MP713 me 12:10 FRIDAY 23 rd FREE COOKIES AND DRINKS! Please come! you Announcements E = mc 2 ; see an excellent explanation at : http://www.upscale.utoronto.ca/pvb/harrison/specrel/massenergy.html MP problems set #4 due Sunday at midnight NB correction to question 1; (HVL, TVL) Replace Energy Attenuation Coefficient by Energy Absorption Coefficient...thanks Liana! PS#5 WRITTEN now posted! - do teams, no Lone Wolves!! Today Quick Review SNIV Biological Effects (Readg this week) Derivation Worked Example Review of SNIII RADIOACTIVITY Discovery Becquerel, Curies, Joliot Alpha transmission through forbidden region Beta contuous spectrum led to discovery of neutro Gamma decay of excited nuclei by jumpg from nuclear energy levels EC verse beta decay Energetics of radioactive Decay Q VALUE is the energy available for the decay Parent Daughter + Decay Products Q/c 2 = Mass(Parent) {Mass(Daughter) + Mass(decay products)} nuclear masses (Atomic Masses Knight) Converted to Ketic Energy of Daughter and decay products 1
Important Parameters of Radioactive Decay 1.dN = - λ N dt N(t) = N 0 exp(- λt) 2.Activity: R(t) = dn/dt = R 0 exp(- λt) = λ N(t) 3.Half Life T ½ = ln2/ λ = 0.693/ λ = 1/1.44 λ A(t) = A(0) e -γt Decay of 66 Cu Decay of 66 Cu AT 3 MINS, COUNT IS 166 (CORRECTED, 166-16 = 150) AT 8 MINS, COUNT IS 91 (CORRECTED 91 16 =75) HALF-LIFE = 5 MINS (APROX) BACKGROUND = 16 C/MIN BACKGROUND = 16 C/MIN WORKED PROBLEM Calculate the half-life for this decay ATTENUATION AND ABSORPTION Total Energy Out = Total Energy In 2
electron electron Total Energy Out = Total Energy In Total Energy Out < Total Energy In Attenuation and Absorption Attenuation refers to an process which the s lose their origal direction and momentum lear attenuation coefficient - μ (important X-ray images) Absorption refers to any process which the s lose energy the material energy absorption coefficient - μ en (important dose calculations) Attenuation and Absorption µ - lear attenuation coefficient: measures attenuation of s any loss of origal s a beam by change energy or direction (after even one teraction with an atom) µ en energy absorption coefficient: measures absorption of energy of beam -loss of energy of beam deposited material -(often several teractions) Exposure, Dose review SNII Exposure, Dose: Review SNII 1 Roentgen a measure of EXPOSURE 1 R produces a 2.58 certa x 10 number -4 C of Coulombs of +ve charge / of ion pairs 1 kg of dry air at STP Given by D air = 8.69 x 10-3 Gy X R 1 Gray the ABSORBED DOSE 1 Gray deposits one J of energy per kg of matter : 1 Gy = 1 J.kg -1 1 rad = 0.01 Gy : 1 Gy = 100 rad this constant contas units 3
Fluence of a Beam of Photons (SNII & SNIV) Dose, Fluence, Exposure Photon Fluence no. of s crossg one square metre Φ = N/S (phi) Photon Fluence Rate no. of s crossg one square metre per second φ = Δ Φ /Δt Energy Fluence ~ Φ (hf) (psi) Energy Fluence Rate = Δ /Δt Dose, Fluence, Exposure D air = 8.69 x10-3 X (Gy to R) (x) = (0) exp(-µ en x) D m (x) = (µ en /ρ) m (x) (cludg D air = (µ en /ρ) air ) REMEMBER AND UNDERSTAND THESE THREE RELATIONSHIPS! A person is exposed to a beam of X-rays. Which quantities do you thk will be the same on both sides of the air-sk boundary? A. the exposure B. the dose C. the energy fluence of the beam D. none of the above E. all of the above air = body 4
ASSUMPTIONS, CONSTANTS 1. Effective X-ray energy is 120/3 = 40 kev 2. No loss of energy between mache and chest - μ en is VERY small 3. Energy fluence at sk = energy fluence enterg body 4. Chest has surface area S = 25 x 25 cm 2 = 625 cm 2 5. Tissue Bone Lung x t = 5cm x b = 5 cm x lung = 15 cm Thus, chest has depth d = x t + x b + x lung = 25 cm ( ) e -4.63 = 0.0098 1- e -4.63 = 0.990 5