Final ExamPhysics 208 Exit surveyRadioactive nucleiRadioactive decayBiological effects of radiationRadioactive tracersA random processRadioactive half-lifeRadioactive decay questionSlide 10Quantifying radioactivityDifferent types of radioactivityExample of decayDecay sequence of 238URadonActivity of RadonSlide 17Beta decaySlide 19Changing particlesbeta decay exampleRadiocarbon datingCarbon-dating questionOther carbon decaysGamma decayDecay summaryThurs, 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 and protonsThurs, 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)Geiger counterThurs, 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 radioactivity as student with Ernest Rutherford. Lodged in nearby boarding home.Suspected his landlady was serving meals later in week ‘recycled’ from the Sunday meat pie. His landlady denied this!deHevesy described his first foray into nuclear medicine:George de HevesyGeorge 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.”Thurs, 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 N = N x Prob(decay) =rNt–# decays / s = N/t =rN € Prob decay in Δt( )= rΔt€ ⇒ 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 yrt=2 yrt=3 yrEvery half-life, half the atoms decayUndecayed nucleiThurs, Dec 11, 2008 Phy208 Lect299Radioactive decay questionA piece of radioactive material is initially observed to 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 observed to have 1,000 decays/sec. It’s half life is 2 days.Four days later, you measure A. 1,000 decays / secB. 500 decays / secC. 250 decays / secD. 125 decays / secThurs, Dec 11, 2008 Phy208 Lect2911Decay rate r (Units of s-1) Prob( nucleus decays in time t ) = r tActivity R (Units of becquerel (1 Bq=1 s-1) orcurie (1 Ci=3.7x1010 s-1)Mean # decays / s = rN, N=# nuclei in sampleHalf-life t1/2 (Units of s) time for half of nuclei to decay = t1/2 Quantifying 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 uranium radiation is complex and that there are present at least two distinct types of radiation - one that is very readily absorbed, which will be termed for convenience the alpha-radiation, and the other of more penetrative character which will be termed the beta-radiation."Thurs, Dec 11, 2008 Phy208 Lect2913Heavy nucleus spontaneously emits alpha particleExample of 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 protons decayThurs, Dec 11, 2008 Phy208 Lect2915RadonQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.Zone 1 Highest Potential (greater than 4 pCi/L)QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.Zone 2 Moderate Potential (from 2 to 4 pCi/L) http://www.radonwisconsin.com/ •Radon is in the 238U decay series•Radon is an emitter that presents an environmental hazard •Inhalation of radon and its daughters can ionize lung cells increasing 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 nuclei in 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 protons decayBut what are these?Thurs, Dec 11, 2008 Phy208
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