1Thurs, Dec 11, 2008 Phy208 Lect291Final Exam• Mon, Dec 15, at 10:05am-12:05 pm, 2103 Chamberlin• 3 equation sheets allowed• About 30% on new material• Rest on topics of exam1, exam2, exam3.Study Tips:Download blank exams and take them.Download blank quizzes and take them.Look through group problems.Look through lab question sheets.Thurs, Dec 11, 2008 Phy208 Lect292Physics 208 Exit survey• Please take web exit survey• Link on course web site• Also will receive an email.• Helps us to understand what was effective(and ineffective!) in the course.Thurs, Dec 11, 2008 Phy208 Lect293Radioactive nuclei~ equal #neutrons andprotonsThurs, Dec 11, 2008 Phy208 Lect294Radioactive decay• Unstable nuclei decay by emitting particle• Can be photon (light particle),or matter particle.• Emitted particle carries away energy– Can strip electrons from atoms (ionizing radiation)– break apart chemical bonds in living cells (radiation damage)GeigercounterThurs, Dec 11, 2008 Phy208 Lect295Biological effects of radiationRadiation type RBEX-rays 1Gamma rays 1Beta particles 1-2Alpha particles 10-20• Radiation damage depends on– Energy deposited / tissue mass (1 Gy (gray) = 1J/kg)– Damaging effect of particle (RBE, relative biological effectiveness)• Dose equivalent = (Energy deposited / tissue mass) x RBE– Units of Sv (sieverts) [older unit = rem, 1 rem=0.01 Sv]– Common units mSv (10-3Sv), mrem (10-3rem)– Common ‘safe’ limit = 500 mrem/yr (5 mSv/yr)Thurs, Dec 11, 2008 Phy208 Lect296Radioactive tracersWorked on radioactivityas student with Ernest Rutherford.Lodged in nearby boarding home.Suspected his landlady was serving meals later inweek ‘recycled’ from the Sunday meat pie.His landlady denied this!deHevesy described his first forayinto nuclear medicine:George de Hevesy“The coming Sunday in an unguarded moment Iadded some radioactive deposit [lead-212] to thefreshly prepared pie and on the following Wednesday,with the aid of an electroscope, I demonstrated to thelandlady the presence of the active deposit in the soufflé.”2Thurs, Dec 11, 2008 Phy208 Lect297A random process• Radioactive decay is a random process– It has some probability of occurring.• For one nucleus,–– r = decay rate• For N nuclei,– # decays ΔN = N x Prob(decay) =rNΔt– # decays / s = ΔN/Δt =rN ! Prob decay in "t( )= r"t! " N = Noe#r tThurs, Dec 11, 2008 Phy208 Lect298Radioactive half-life• Example of random decay.• Start with 8,000 identical radioactive nuclei• After one half-life, half the nuclei have decayed.t=0 t=1 yr t=2 yr t=3 yrEvery half-life,half the atoms decayUndecayednucleiThurs, Dec 11, 2008 Phy208 Lect299Radioactive decay questionA piece of radioactive material is initially observedto have 10,000 radioactive nuclei.3 hours later, you measure 1,250 radiaoctive nuclei.The half-life isA. 1/2 hourB. 1 hourC. 3 hoursD. 8 hoursIn each half-life,the number of radioactive nuclei,and hence the number of decays / second,drops by a factor of two.After 1 half life, 5000 are left undecayed.After 2 half lives, 1/2 of these are left: 2,500After 3 half lives there are 1,250 left.Thurs, Dec 11, 2008 Phy208 Lect2910Radioactive decay questionA piece of radioactive material is initially observedto have 1,000 decays/sec.It’s half life is 2 days.Four days later, you measureA. 1,000 decays / secB. 500 decays / secC. 250 decays / secD. 125 decays / secThurs, Dec 11, 2008 Phy208 Lect2911 Decay rate r (Units of s-1) Prob( nucleus decays in time Δt ) = r Δt Activity R (Units of becquerel (1 Bq=1 s-1) orcurie (1 Ci=3.7x1010 s-1) Mean # decays / s = rN, N=# nuclei in sample Half-life t1/2 (Units of s) time for half of nuclei to decay = t1/2Quantifying radioactivity! =ln2r=0.693r! N = Noe"r tThurs, Dec 11, 2008 Phy208 Lect2912Different types of radioactivity• Three different types of decay observed:Alpha decayBeta decayGamma decay(First three letters of Greek alphabet).Ernest Rutherford (1899): "These experiments show that the uraniumradiation is complex and that there are present at least two distinct typesof radiation - one that is very readily absorbed, which will be termed forconvenience the alpha-radiation, and the other of more penetrativecharacter which will be termed the beta-radiation."3Thurs, Dec 11, 2008 Phy208 Lect2913Heavy nucleus spontaneouslyemits alpha particleExample of α decay• nucleus loses 2 neutrons and 2 protons.• It becomes a different element (Z is changed)• Example: ! 92238U "24He +90234Th92 protons146 neutrons90 protons144 neutrons2 protons2 neutronsAlpha particleThurs, Dec 11, 2008 Phy208 Lect2914Decay sequence of 238UNumber of neutronsNumber of protonsα decayThurs, Dec 11, 2008 Phy208 Lect2915RadonZone 1 Highest Potential (greater than 4 pCi/L)Zone 2 Moderate Potential (from 2 to 4 pCi/L) http://www.radonwisconsin.com/ • Radon is in the 238U decay series• Radon is an α emitter thatpresents an environmentalhazard• Inhalation of radon and itsdaughters can ionize lung cellsincreasing risk of lung cancerThurs, Dec 11, 2008 Phy208 Lect2916Activity of Radon•222Rn has a half-life of 3.83 days.• Suppose your basement has 4.0 x 108 such nucleiin the air. What is the activity?We are trying to find number of decays/sec.So we have to know decay constant to get R=rN! r =0.693t1/ 2=0.6933.83days " 86,400s / day= 2.09 "10#6sR =dNdt= rN = 2.09 "10#6s " 4.0 "108nuclei = 836decays / sR = 836 decays / s "1Ci2.7 "1010decays / s= 0.023µCiThurs, Dec 11, 2008 Phy208 Lect2917Decay sequence of 238UNumber of neutronsNumber of protonsα decayBut what are these?Thurs, Dec 11, 2008 Phy208 Lect2918Beta decayNumber of neutronsNumber of protonsNumber of neutronsdecreases by oneNumber of protonsincreases by oneElectron (beta particle)emittedBut nucleus has only neutrons & protons.4Thurs, Dec 11, 2008 Phy208 Lect2919Beta decay• Nucleus emits an electron(negative charge)• Must be balancedby a positive chargeappearing in the nucleus.This occurs as a neutronchanging into a protonThurs, Dec 11, 2008 Phy208 Lect2920Changing particlesNeutron made up ofquarks.One of the down quarkschanged to an up quark.New combination ofquarks is a proton.Thurs, Dec 11, 2008 Phy208 Lect2921beta decay exampleUsed in radioactive carbon dating.Half-life 5,730 years. ! 614C " 714N + e#8 neutrons6 protons7 neutrons7 protons14 nucleons 14 nucleons6 positivecharges7 positivecharges==+1 electron+1 negative chargeThurs, Dec
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