A2Physics物理出國英語RadioactivityPart3Radioactivedecay

1.Radioactivedecaylaw

Radioactivedecayisarandomprocess.Theprobabilitythataparticularnucleuswilldecayinagiventimeintervalisconstant.Thenumberofradioactivenuclei$N$inasampleattime$t$followstheexponentialdecaylaw:$N=N_0e^{lambdat}$,where$N_0$istheinitialnumberofradioactivenuclei,$lambda$isthedecayconstantwhichischaracteristicoftheradioactiveisotope.

Forexample,ifwestartwithasampleof1000radioactivenucleiwithadecayconstant$lambda=0.1s^{1}$,after$t=10s$,thenumberofremainingnucleiis$N=1000timese^{(0.1times10)}=1000timese^{1}approx368$.

2.Activity

Theactivity$A$ofaradioactivesampleisdefinedastherateofdecayoftheradioactivenuclei,i.e.,$A=frac{dN}{dt}$.Fromthedecaylaw$N=N_0e^{lambdat}$,wecandifferentiateitwithrespecttotimetoget$A=lambdaN=lambdaN_0e^{lambdat}=A_0e^{lambdat}$,where$A_0=lambdaN_0$istheinitialactivity.TheSIunitofactivityisthebecquerel(Bq),where1Bq=1decaypersecond.

Ifasamplehasaninitialactivityof1000Bqandadecayconstantof$0.02s^{1}$,after$t=20s$,theactivityis$A=1000timese^{(0.02times20)}=1000timese^{0.4}approx670Bq$.

3.Halflife

Thehalflife$T_{1/2}$ofaradioactiveisotopeisthetimetakenforthenumberofradioactivenuclei(ortheactivity)inasampletoreducetohalfofitsinitialvalue.

If$N=frac{N_0}{2}$at$t=T_{1/2}$,then$frac{N_0}{2}=N_0e^{lambdaT_{1/2}}$.Takingthenaturallogarithmofbothsides,weget$ln(frac{1}{2})=lambdaT_{1/2}$,so$T_{1/2}=frac{ln2}{lambda}approxfrac{0.693}{lambda}$.

Foraradioactiveisotopewithadecayconstant$lambda=0.05s^{1}$,thehalflifeis$T_{1/2}=frac{0.693}{0.05}=13.86s$.

4.Carbon14dating

Carbon14isaradioactiveisotopewithahalflifeofabout5730years.Intheatmosphere,theratioofcarbon14tocarbon12isapproximatelyconstant.Livingorganismstakeincarbonfromtheatmosphere,sotheratioofcarbon14tocarbon12intheirbodiesisthesameasintheatmosphere.Whenanorganismdies,itstopstakingincarbon,andtheamountofcarbon14initsbodybeginstodecay.

Bymeasuringtheactivityofcarbon14inasampleofanancientorganismandcomparingitwiththeactivityinalivingorganism,wecanestimatetheageofthesample.

Supposetheactivityofcarbon14inalivingorganismis$A_0$andtheactivityinanancientsampleis$A$.Since$A=A_0e^{lambdat}$,and$lambda=frac{ln2}{T_{1/2}}$,wecansolvefor$t$:$t=frac{T_{1/2}}{ln2}ln(frac{A_0}{A})$.

5.Decayseries

Someradioactiveisotopesdecayintootherradioactiveisotopes,whichinturndecayintofurtherisotopesuntilastableisotopeisreached.Thisiscalledadecayseries.

Forexample,uranium238decaysthroughaseriesofalphaandbetadecaystolead206.Uranium238firstemitsanalphaparticletobecomethorium234.Thorium234thenundergoesbetadecaytobecomeprotactinium234,andsoon.

6.Alphadecay

Inalphadecay,aradioactivenucleusemitsanalphaparticle(aheliumnucleus,$^4_2He$).Thegeneralequationforalphadecayis$^A_ZXrightarrow^{A4}_{Z2}Y+^4_2He$,where$X$istheparentnucleusand$Y$isthedaughternucleus.

Forexample,radium226decaysbyalphaemission:$^{226}_{88}Rarightarrow^{222}_{86}Rn+^4_2He$.Themassnumber$A$oftheparentnucleusdecreasesby4,andtheatomicnumber$Z$decreasesby2.

7.Betaminusdecay

Inbetaminusdecay,aneutroninthenucleusisconvertedintoaproton,andanelectron(betaminusparticle)andanantineutrinoareemitted.Thegeneralequationforbetaminusdecayis$^A_ZXrightarrow^{A}_{Z+1}Y+_{1}^0e+bar{nu}$,where$bar{nu}$istheantineutrino.

Forexample,carbon14decaysbybetaminusemission:$^{14}_6Crightarrow^{14}_7N+_{1}^0e+bar{nu}$.Themassnumber$A$remainsthesame,andtheatomicnumber$Z$increasesby1.

8.Betaplusdecay

Inbetaplusdecay,aprotoninthenucleusisconvertedintoaneutron,andapositron(betaplusparticle)andaneutrinoareemitted.Thegeneralequationforbetaplusdecayis$^A_ZXrightarrow^{A}_{Z1}Y+_{+1}^0e+nu$,where$nu$istheneutrino.

Forexample,fluorine18decaysbybetaplusemission:$^{18}_9Frightarrow^{18}_8O+_{+1}^0e+nu$.Themassnumber$A$remainsthesame,andtheatomicnumber$Z$decreasesby1.

9.Gammadecay

Gammadecayusuallyoccursafteralphaorbetadecaywhenthedaughternucleusisleftinanexcitedstate.Thenucleusthenemitsagammaray(ahighenergyphoton)toreachalowerenergystate.Thegeneralequationforgammadecayis$^A_ZX^rightarrow^A_ZX+gamma$,where$X^$istheexcitednucleusand$X$isthegroundstatenucleus.

10.Energychangesinradioactivedecay

Theenergyreleasedinradioactivedecaycomesfromthemassdefect.AccordingtoEinstein'smassenergyequivalenceprinciple$E=mc^2$,themassoftheproductsofdecayislessthanthemassoftheparentnucleus,andthedifferenceinmass$Deltam$isconvertedintoenergy$E=Deltamc^2$.

Inthealphadecayofradium226,themassofradium226isgreaterthanthesumofthemassesofradon222andthealphaparticle.Themassdefectisconvertedintothekineticenergyofthealphaparticleandtherecoilenergyoftheradonnucleus.

11.Shieldingofradiation

Alphaparticlescanbestoppedbyasheetofpaperorafewcentimetersofair.Betaparticlescanpenetratepaperbutcanbestoppedbyafewmillimetersofaluminum.Gammaraysaremuchmorepenetratingandrequirethickleadorconcreteshielding.

12.Backgroundradiation

Backgroundradiationisthelowlevelradiationthatisalwayspresentintheenvironment.Sourcesofbackgroundradiationincludecosmicraysfromspace,radioactiveisotopesintheEarth'scrust(suchasradongas),andhumanmadesources(suchasnuclearpowerplantsandmedicalXrays).

13.Safetyprecautionsinhandlingradioactivematerials

Whenhandlingradioactivematerials,workersmustwearprotectiveclothing,useshielding,andlimittheirexposuretime.Radioactivewastemustbestoredsafelytopreventcontaminationoftheenvironment.

14.GeigerMullertube

AGeigerMullertubeisadeviceusedtodetectandmeasureradiation.Whenradiationentersthetube,itionizesthegasinside.Theionsandelectronsareacceleratedbyanelectricfield,causingacascadeofionizationandproducinganelectricalpulsethatcanbecounted.

15.Measurementofhalflife

Tomeasurethehalflifeofaradioactiveisotope,wecanmeasuretheactivityofasampleatdifferenttimes.Plotagraphof$lnA$against$t$.Theslopeofthegraphisequalto$lambda$,andthenwecancalculatethehalflifeusing$T_{1/2}=frac{ln2}{lambda}$.

16.Activityandnumberofnucleirelationship

Ifweknowthedecayconstant$lambda$andthenumberofradioactivenuclei$N$inasample,wecancalculatetheactivity$A=lambdaN$.Conversely,ifweknowtheactivity$A$andthedecayconstant$lambda$,wecanfindthenumberofradioactivenuclei$N=frac{A}{lambda}$.

17.Decayprobability

Theprobability$P$thatasinglenucleuswilldecayinatimeinterval$Deltat$isapproximately$P=lambdaDeltat$forasmall$Deltat$.Thisisbasedonthefactthattherateofdecay$frac{dN}{dt}=lambdaN$,andforasinglenucleus($N=1$),theprobabilityofdecayinashorttimeisrelatedtothedecayconstant.

18.Nuclearfissionandradioactivedecay

Nuclearfissionisaprocesswhereaheavynucleus(suchasuranium235)splitsintotwoormorelighternuclei,releasingalargeamountofenergy.Afterfission,thefissionproductsareoftenradioactiveandwillundergofurtherradioactivedecay.

19.Radioactiveequilibrium

Inadecayseries,ifthehalflifeoftheparentnucleusismuchlongerthanthatofthedaughternucleus,astateofradioactiveequilibriumcanbereached.Insecularequilibrium,theactivityofthedaughternucleusisequaltotheactivityoftheparentnucleus.

20.Biologicaleffectsofradiation

Radiationcancausedamagetolivingcells.Lowlevelradiationexposuremayincreasetheriskofcancer,whilehighlevelexposurecancauseradiationsickness,includingsymptomssuchasnausea,vomiting,andhairloss.

21.Radioactivetracers

Radioactiveisotopescanbeusedastracersinmedicalandindustrialapplications.Forexample,inmedicine,aradioactiveisotopecanbeinjectedintothebody,anditsmovementcanbetrackedusingaradiationdetectortodiagnosediseases.

22.Isotopeseparation

Isotopesofanelementhaveslightlydifferentphysicalandchemicalpropertiesduetotheirdifferentmasses.Methodssuchascentrifugationandgaseousdiffusioncanbeusedtoseparateisotopes,whichisimportantinnuclearpowerandnuclearweaponsproduction.

23.Energyreleasedinbetadecay

Inbetadecay,theenergyreleasedissharedbetweenthebetaparticle,theneutrino(orantineutrino),andtherecoilenergyofthedaughternucleus.Theenergyspectrumofbetaparticlesiscontinuousbecausetheenergycanbedistributedindifferentwaysamongthedecayproducts.

24.Radioactivedatingofrocks

Similartocarbon14dating,otherradioactiveisotopeswithlongerhalflivescanbeusedtodaterocks.Forexample,potassium40decaystoargon40withahalflifeofabout1.25billionyears.Bymeasuringtheratioofpotassium40toargon40inarocksample,theageoftherockcanbeestimated.

25.Comparisonofdecayrates

Differentradioactiveisotopeshavedifferentdecayrates.Isotopeswithshorthalflivesdecaymorerapidlythanthosewithlonghalflives.Forexample,polonium212hasahalflifeofabout0.3microseconds,whileuranium238hasahalflifeofabout4.5billionyears.

26.Quantumtunnelinginalphadecay

Theemissionofalphaparticlesfromanucleuscanbeexplainedbyquantumtunneling.Thealphaparticleisboundinsidethenucleusbythestrongnuclearforce,butthereisasmallprobabilitythatitcantunnelthroughthepotentialbarrierandescapefromthenucleus.

27.Radioactivewastemanagement

Radioactivewastefromnuclearpowerplantsandothernuclearfacilitiesmustbemanagedcarefully.Highlevelwasteisusuallystoredindeepgeologicalrepositoriestoisolateitfromtheenvironmentforalongtime.

28.Detectionofneutrinos

Neutrinosareverydifficulttodetectbecausetheyinteractveryweaklywithmatter.Specialdetectors,suchaslargeundergroundtanksfilledwithliquidscintillators,areusedtodetectneutrinos.Whenaneutrinointeractswithanatominthedetector,itcanproduceaflashoflightthatcanbedetected.

29.Betadecayenergyconservation

Inbetadecay,theconservationofenergyandmomentummustbesatisfied.Thetotalenergybeforedecay(therestenergyoftheparentnucleus)isequaltothetotalenergyafterdecay(therestenergyofthedaughternucleus,thekineticenergyofthebetaparticle,theenergyoftheneutrinoorantineutrino,andtherecoilenergyofthedaughternucleus).

30.Radioactivedecayandtheageoftheuniverse

Thestudyofradioactivedecaycanprovideinformationabouttheageoftheuniverse.Bymeasuringtheabundancesofdifferentradioactiveisotopesintheuniverseandtheirdecayproducts,scientistscanestimatethetimesincetheformationoftheseisotopes.

31.Roleofneutrinosinbetadecay

Neutrinoswereproposedtoexplainthecontinuousenergyspectrumofbetaparticles.Theycarryawayenergyandmomentuminbetadecay,ensuringthattheconservationlawsaresatisfied.

32.EffectsofradiationonDNA

RadiationcandamageDNAincells,leadingtomutations.Thesemutationscancausecellstomalfunctionorbecomecancerous.

33.Radioactivedecayinstars

Instars,radioactivedecayplaysaroleintheenergyproductionandevolutionofthestar.Forexample,thefusionoflightelementsinthestar'scoreproducesradioactiveisotopesthatcandecayandreleaseenergy.

34.Comparisonofalpha,beta,andgammaradiationintermsofionizingpower

Alphaparticleshavethehighestionizingpowerbecausetheyarerelativelylargeandcarrya+2charge.Betaparticleshavelowerionizingpowerthanalphaparticles,andgammarayshavethelowestionizingpoweramongthethreetypesofradiation.

35.Useofradioactiveisotopesinagriculture

Radioactiveisotopescanbeusedinagriculturetostudytheuptakeofnutrientsbyplants.Forexample,aradioactiveisotopeofphosphoruscanbeaddedtothesoil,anditsmovementintheplantcanbetracked.

36.Shieldingdesignfornuclearreactors

Nuclearreactorsproducelargeamountsofradiation,soshieldingiscrucial.Theshieldingdesignmusttakeintoaccountthedifferenttypesofradiation(alpha,beta,gamma,andneutrons)andtheirpenetrationabilities.

37.Decayofshortlivedisotopes

Shortlivedisotopesdecayveryrapidly,andtheirdetectionandstudyrequirespecialtechniques.Forexample,fasttimingdetectorsareusedtomeasuretheshorthalflivesoftheseisotopes.

38.Radioactivedecayandnuclearstability

Thestabilityofanucleusisrelatedtoitsneutrontoprotonratio.Nucleiwithanunstableneutrontoprotonratioaremorelikelytoundergoradioactivedecaytobecomemorestable.

39.Measurementofactivityindifferentenvironments

Theactivityofaradioactivesamplecanbeaffectedbytheenvironment.Forexample,ifthesampleisinahighpressureorhightemperatureenvironment,thedecayratemaybeslightlydifferentduetochangesintheatomicandnuclearstructure.

40.Interactionofradiationwithmatter

Whenradiationinteractswithmatter,itcancauseionization,excitationofatoms,andothereffects.Thetypeandextentoftheinteractiondependonthetypeofradiationandthepropertiesofthematter.

41.Safetystandardsforradioactivematerialsindifferentindustries

Differentindustrieshavedifferentsafetystandardsforhandlingradioactivematerials.Forexample,thenuclearpowerindustryhasverystrictsafetyregulations,whilethemedicalindustryhasregulationsregardingtheuseofradioactiveisotopesindiagnosisandtreatment.

42.Radioactivedecayandtheformationofelements

Radioactivedecayisinvolvedintheformationofelementsintheuniverse.Elementsheavierthanironareformedmainlythroughneutroncaptureandsubsequentradioactivedecayprocessesinsupernovae.

43.Effectofmagneticfieldsonbetaparticles

Betaparticlesarechargedparticles,sotheyaredeflectedbymagneticfields.Thedirectionandamountofdeflectiondependonthechargeofthebetaparticle(positiveornegative)andthestrengthanddirectionofthemagneticfield.

44.Radioactivedecayandthestudyofnuclearstructure

Thestudyofradioactivedecayprovidesinformationabouttheinternalstructureofnuclei.Forexample,theenergylevelsandtransitionsinthenucleuscanb