110.2 Applications of Nuclear PhysicsRadioactive DecayApplications of radioactivity14C DatingSmoke detectorsMedical ApplicationsDecay processes• Alpha decayAA44ZZ22XYHe−−→+example238 234 492 90 2UThHe→+The alpha particle has a high stabilityMost of the kinetic energy is carried away by the alpha particle HeBeta Decay14 1467CNex?−→++A third product must be involved.The electron should carry most of the kinetic energyThe kinetic energy of the electron is not constant.Beta DecayA new particle is involved –Neutrino (ν) or Anti-neutrino ( ) Antiparticlesno chargelow mass interact weakly with matter.ν14 1467CNe−→++νBeta decayPositrons – Anti-particle of the electron were discovered. Mass- same as the electronPositive charge.Positron emission is accompanied by neutrino emission.12 1276NCe+→++νThe electron and positron are anti-particlesThe neutrino and anti-neutrino are anti-particles.Gamma DecayGamma rays are emitted by nuclei that decay to excited states. 12 12 *56BCe−→++ν12 * 1266CC→+γ2Decay rateThe rate of decay, R, for N nuclei is proportional to NNRNt∆==λ∆λ = decay constant (units time-1)Activity – (measure of the rate of radioactive decay) Units Curie,1Ci = 3.7x1010Decays/sRadioactive decayRadioactive decay is a random process the amountof material remaining varies exponentially with time.toNNe−λ=λ is the decay constant ( units 1/time)12t/To1NN2⎛⎞=⎜⎟⎝⎠This can also be expressed aswhere12ln2 0.693T ==λλHalf Life =Example 29.3The half life of radium Ra is 1.6x103yr. If the samplecontains 3.00x1016 nuclei. Find the activity in curies.(1Ci=3.7x1010decays/s) R=λN12ln2 0.693T ==λλ31/ 211 10.693 0.693T 1.6x10 yr(365day/ yr)(24hr /day)(3600s/hr)1.37x10 s−−λ= ==R=1.37x10-11s-1(3.00x1016nuclei) =4.12x105decays/s3.7x1010decays/sCiR=1.1x10-5 Ci or 11µcuriesExample 29.3The half life of radium Ra is 1.6x103yr. If the samplecontains 3.00x1016 nuclei. Find the number of nucleiafter 4.8x103yr. 1/2t/To1NN2⎛⎞=⎜⎟⎝⎠334.8x10 /1.6x10161N3.00x102⎛⎞=⎜⎟⎝⎠N=3.00x1016(1/8)=3.75x1015nucleiExample 29.3The half life of radium Ra is 1.6x103yr. If the samplecontains 3.00x1016 nuclei. Find the activity after 4.8x103yr. R=λNAfter this time since the no. of nuclei is reducedby a factor of 8 the decay rate will also be reduced by a factor of 8.R = 11 µCi/8 =1.4 µCiRadioactive dating14C is continually formed by cosmic rays in the upperatmosphere.n + 14 N -> 14C + pso that the concentration of 14C is relatively constantover long times ( longer than the half life).14C14C decaysThe fraction of 14C decaysexponentially with time.T1//2= 5730 years3Smoke DetectorIonization of air by a radioactive sourceproduces a current.Smoke traps the electronsand reduces the current.setting off the alarm.Medical Applications.Radiation Damage. •Nuclear particles have much higher energies than chemical bonds. •Radiation breaks chemical bonds – forming reactivechemical species – radicals.•Reactive chemicals cause radiation damage to biologicalsystems – often reaction with DNARadiation TherapyRadiation is oftenused in treatingcancer.external radiationRadioimmunotherapyNew methods for can deliver radiationmore specifically totarget cellsTreatment of non-Hodgkins lymphomawith radioimmunotherapyProperties of 131IIodine 131Half-life – 8.07 daysBeta particlemaximum energy- 807 keVaverage energy - 182 keVRange in tissue -2.4 mmCommon clinical applicationsRadioimmunotherapy, thyroid ablation for benign and malignant diseaseMedical Imaging• X-ray Computer axial tomography (CAT)• Positron emission tomography (PET)• Magnetic resonance imaging (MRI)• Contrast • Resolution.4CAT scanContrast – x-ray absorptionmay use heavy elements to increase contrast i.e I, BaA three- dimensional imageis reconstructed from many two dimensional pictures.Computer tomographyabcdincidentx-raydetector 1detector 2detector 3 detector 4at each detector absorbance is due to the sum of theabsorptions from each segment.A (detector) = Ai+AjFor 4 detectors -> 4 linear equationsand 4 segment - > 4 unknowns Solve for each absorbanceHigher resolutionFor higher resolutionthere are more detectorsand the body is rotatedand many picturesare takenx-rayx-raydetectorsdetectorsThe absorbance changefor each segment is calculatewith a computer. Solving ~10,000 linear equations.Computer Axial TomographyAxial Geometry CAT scan of a chest Positron Emission Tomography• Emission of 2 gamma ray photons traveling in opposite direction by Positron-Electron annihilation. (conservation of momentum)• Positrons are produced by decay of short lived radioactive nuclei such as 18F (T1/2=110 min)18 1898FOe+→++νee+−+→γ+γAnnihilationproduces 2 0.51 MeV photonshfhf5PET imaging systemTwo coincident detectors are used to detect the gammarays. The source is in a line directly between the two detectors.PET scan of the human brain15O ( T1/2=2 min) marks the consumption of O2due to brain