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UW-Madison PHYSICS 208 - LECTURE NOTES

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β and γ decays, Radiation Therapies and Diagnostic, Fusion and FissionFinal ExamNew material not covered by MTE1,2,3Women Nobel PrizesNuclear PhysicsPowerPoint PresentationStable and Unstable IsotopesStability of nucleiRadioactivityPenetrating power of radiationIs the radiation charged?The Decay RateThe half-lifeUnitsAn ExampleRadiocarbon datingCarbon datingDecay processes: α = 4HeA quantum processDisintegration EnergyDecay sequence of 238URadonActivity of RadonRadiation damageSlide 25Radiation LevelsBeta decayExample of β-decayThe Positron and AntimatterDecay Quick QuestionNuclear Medicine: diagnosticPositron Emission Tomography - PETEmission DetectionImage ReconstructionCancer Radiation TherapyGamma decayDecay Question?β and γ decays, Radiation Therapies and Diagnostic, Fusion and FissionThis Lecture: Radioactivity, Nuclear decay Radiation damage, radiation therapies and diagnosticEvaluations for Prof. T. Montaruli todayPrevious lecture: nuclear physicsFinal Exam•Fri, Dec 21, at 7:45-9:45 am in Ch 2103 •About 40% on new material•2 sheets allowed (HAND WRITTEN!)•The rest on previous materials covered by MTE1 MTE2 MTE3.New material not covered by MTE1,2,3•Ch 40.4-5 particle in a box: wave functions, energy levels, photon absorption and emission, 40.10 tunneling•Ch 41.1-3 H-atom quantum numbers and their meaning, wave functions and probabilities, electron spin•Ch 41.4-6 Pauli exclusion principle, multi-electron atoms, periodic table, emission and absorption spectra•Ch 41.8 Stimulated emission and Lasers•Ch 42.1-3 Nuclear structure, atomic mass, isotopes, binding energy, the strong force•Ch 42.5 Radioactivity, Ch 42.6 Nuclear decay, Ch 42.7 Biological applicationsWomen Nobel PrizesThe only 2 female Nobel Prizes in Nuclear Physics!Maria Goeppert-Mayer 1963 Shell Model of Nucleus1903 Marie Curie (with Pierre)in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel5Nuclear Physics•Strong force: attractive force keeping p and n in nucleus (short range) •It is convenient to use atomic mass units to express masses–1 u = 1.660 539 x 10-27 kg–mass of one atom of 12C = 12 u •Mass can also be expressed in MeV/c2– From rest energy of a particle ER = mc2–1 u = 931.494 MeV/c2•Binding energy: mnucleus < Zmp + (A-Z)mn = Zmp + Nmn •The energy you would need to supply to disassemble the nucleus into nucleons Ebinding = (Zmp+Nmn-mnucleus)c2 = (Zmp+Zme+Nmn+ -Zme-mnucleus)c2 =(ZmH + Nmn - matom) c25C1266Fission and FusionStable and Unstable IsotopesIsotope = same ZIsotone = same NIsobar = same AStability of nuclei•Dots: naturally occurring isotopes.•Blue shaded region: isotopes created in the laboratory.•Light nuclei are most stable if N=Z•Heavy nuclei are most stable if N>Z•As # of p increases more neutrons are needed to keep nucleus stable•No nuclei are stable for Z>83Radioactivity•Discovered by Becquerel in 1896 •spontaneous emission of radiation as result of decay or disintegration of unstable nuclei•Unstable nuclei can decay by emitting some form of energy•Three different types of decay observed:Alpha decay ⇒ emission of 4He nuclei (2p+2n)Beta decay⇒ electrons and its anti-particle (positron)Gamma decay⇒ high energy photonsPenetrating power of radiation•Alpha radiation barely penetrate a piece of paper (but dangerous!)•Beta radiation can penetrate a few mm of Al•Gamma radiation can penetrate several cm of leadIs the radiation charged?•Alpha radiation positively charged•Beta radiation negatively charged•Gamma radiation unchargedThe Decay Rate•probability that a nucleus decays during Δt•number of decays (decrease)= NxProb=rNΔt N=number of independent nucleiConstant of proportionality  = decay rate (in s-1)The number of decays per second is the activity# radioactive nuclei at time t# rad. nuclei at t=0€ Prob(in Δt) = rΔt€ ΔNΔt= −rN€ N(t) = N0e−rt€ R =ΔNΔt= rN€ τ =1rtime constantThe half-life•After some amount of time, half the radioactive nuclei will have decayed, and activity decreases by a factor of two.•This time is the half-life€ € N(t1/ 2) =N02= N0e−rt1/2€ t1/ 2=ln2r= τ ln2 = 0.693τUnits•The unit of activity, R, is the curie (Ci)– •The SI unit of activity is the becquerel (Bq)– •Therefore, 1 Ci = 3.7 x 1010 Bq•The most commonly used units of activity are the millicurie and the microcurieAn Example•232Th has a half-life of 14 x109 yr•Sample initially contains: N0 = 106 232Th atoms •Every 14 billion years, the number of 232Th nuclei goes down by a factor of two.N0N0/2N0/4N0/8€ N(t1/ 2) =N02= N0e−rt1/2Radiocarbon dating•14C (Z=6) has a half-life of 5,730 years, continually decaying back into 14N (Z=7).•In atmosphere very small amount! 1 nucleus of 14C each 1012 nuclei of 12CIf material alive, atmospheric carbon mix ingested (as CO2), ratio stays constant.After death, no exchange with atmosphere. Ratio changes as 14C decays So can determine time since the plant or animal died (stopped exchanging 14C with the atmosphere) if not older than 60000 yrCarbon datingA fossil bone is found to contain 1/8 as much 14C as the bone of a living animal. Using T1/2=5,730 yrs, what is the approximate age of the fossil?A. 7,640 yrsB. 17,190 yrsC. 22,900 yrsD. 45,840 yrsFactor of 8 reduction in 14C corresponds to three half-lives.So age is 5,730 x 3 =17,190 yrsHeavy nucleus spontaneously emits alpha particleDecay processes: α = 4He•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 particleA quantum process•This is a quantum-mechanical process–It has some probability for occurring.•For every second of time, there is a probability that the nucleus will decay by emitting an α-particle.•This probability depends on the width of the barrier•The α -particle quantum-mechanically tunnels out of the nucleus even if energy is not > energy barrierPotential energy of αin the daughter nucleus vs distance Coulomb repulsion dominatesNuclear attraction dominatesDisintegration Energy•In decays energy-momentum must be conserved •The disintegration energy appears in the form of kinetic energy of products MXc2 = MYc2 + KY + Mαc2 + Kα⇒ΔEKY Kα= (Mx – My – Mα)c2Textbook: neglect


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UW-Madison PHYSICS 208 - LECTURE NOTES

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