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Radioactivedecay
FromWikipedia,thefreeencyclopedia

Radioactivedecay(alsoknownasnucleardecayorradioactivity)is
theprocessbywhichanunstableatomicnucleuslosesenergy(interms
ofmassinitsrestframe)byemittingradiation,suchasanalpha
particle,betaparticlewithneutrinooronlyaneutrinointhecaseof
electroncapture,gammaray,orelectroninthecaseofInternal
conversion.Amaterialcontainingsuchunstablenucleiisconsidered
radioactive.Certainhighlyexcitedshortlivednuclearstatescandecay
throughneutronemission,ormorerarely,protonemission.

Radioactivedecayisastochastic(i.e.random)processatthelevelof Alphadecayisonetypeof
singleatoms,inthat,accordingtoquantumtheory,itisimpossibleto radioactivedecay,inwhichanatomic
predictwhenaparticularatomwilldecay,[1][2][3]regardlessofhowlong nucleusemitsanalphaparticle,and
theatomhasexisted.However,foracollectionofatoms,the therebytransforms(or"decays")into
collection'sexpecteddecayrateischaracterizedintermsoftheir anatomwithamassnumber
measureddecayconstantsorhalflives.Thisisthebasisofradiometric decreasedby4andatomicnumber
dating.Thehalflivesofradioactiveatomshavenoknownupperlimit, decreasedby2.
spanningatimerangeofover55ordersofmagnitude,fromnearly
instantaneoustofarlongerthantheageoftheuniverse.

Aradioactivenucleuswithzerospincanhavenodefinedorientation,andhenceemitsthetotalmomentumof
itsdecayproductsisotropically(alldirectionsandwithoutbias).Iftherearemultipleparticlesproducedduring
asingledecay,asinbetadecay,theirrelativeangulardistribution,orspindirectionsmaynotbeisotropic.
Decayproductsfromanucleuswithspinmaybedistributednonisotropicallywithrespecttothatspin
direction,eitherbecauseofanexternalinfluencesuchasanelectromagneticfield,orbecausethenucleuswas
producedinadynamicprocessthatconstrainedthedirectionofitsspin.Suchaparentprocesscouldbea
previousdecay,oranuclearreaction.[4][5][6][note1]

Thedecayingnucleusiscalledtheparentradionuclide(orparentradioisotope[note2]),andtheprocessproduces
atleastonedaughternuclide.Exceptforgammadecayorinternalconversionfromanuclearexcitedstate,the
decayisanucleartransmutationresultinginadaughtercontainingadifferentnumberofprotonsorneutrons(or
both).Whenthenumberofprotonschanges,anatomofadifferentchemicalelementiscreated.

Thefirstdecayprocessestobediscoveredwerealphadecay,betadecay,andgammadecay.Alphadecayoccurs
whenthenucleusejectsanalphaparticle(heliumnucleus).Thisisthemostcommonprocessofemitting
nucleons,buthighlyexcitednucleicanejectsinglenucleons,orinthecaseofclusterdecay,specificlight
nucleiofotherelements.Betadecayoccurswhenthenucleusemitsanelectronorpositronandaneutrino,ina
processthatchangesaprotontoaneutronortheconverse.Highlyexcitedneutronrichnuclei,formedasthe
productofothertypesofdecay,occasionallyloseenergybywayofneutronemission,resultinginachange
fromoneisotopetoanotherofthesameelement.Thenucleusmaycaptureanorbitingelectron,causinga
protontoconvertintoaneutroninaprocesscalledelectroncapture.Alloftheseprocessesresultinawell
definednucleartransmutation.

Bycontrast,thereareradioactivedecayprocessesthatdonotresultinanucleartransmutation.Theenergyof
anexcitednucleusmaybeemittedasagammarayinaprocesscalledgammadecay,orthatenergymaybelost
whenthenucleusinteractswithanorbitalelectroncausingitsejectionfromtheatom,inaprocesscalled
internalconversion.

Anothertypeofradioactivedecayresultsinproductsthatvary,appearingastwoormore"fragments"ofthe
originalnucleuswitharangeofpossiblemasses.Thisdecay,calledspontaneousfission,happenswhenalarge
unstablenucleusspontaneouslysplitsintotwo(oroccasionallythree)smallerdaughternuclei,andgenerally
leadstotheemissionofgammarays,neutrons,orotherparticlesfromthoseproducts.
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Forasummarytableshowingthenumberofstableandradioactivenuclidesineachcategory,seeradionuclide.
Thereare29naturallyoccurringchemicalelementsonEarththatareradioactive.Theyarethosethatcontain34
radionuclidesthatdatebeforethetimeofformationofthesolarsystem,andareknownasprimordialnuclides.
Wellknownexamplesareuraniumandthorium,butalsoincludedarenaturallyoccurringlonglived
radioisotopes,suchaspotassium40.Another50orsoshorterlivedradionuclides,suchasradiumandradon,
foundonEarth,aretheproductsofdecaychainsthatbeganwiththeprimordialnuclides,oraretheproductof
ongoingcosmogenicprocesses,suchastheproductionofcarbon14fromnitrogen14intheatmosphereby
cosmicrays.Radionuclidesmayalsobeproducedartificiallyinparticleacceleratorsornuclearreactors,
resultingin650ofthesewithhalflivesofoveranhour,andseveralthousandmorewithevenshorterhalflives.
[Seehereforalistofthesesortedbyhalflife.]

Contents
1 Historyofdiscovery
2 Earlyhealthdangers
2.1 Xrays
2.2 Radioactivesubstances
2.3 Radiationprotection
3 Unitsofradioactivity
4 Typesofdecay
5 Radioactivedecayrates
6 Mathematicsofradioactivedecay
6.1 Universallawofradioactivedecay
6.1.1 Onedecayprocess
6.1.2 Chaindecayprocesses
6.1.3 Alternativedecaymodes
6.2 Corollariesofthedecaylaws
6.3 Decaytiming:definitionsandrelations
6.3.1 Timeconstantandmeanlife
6.3.2 Halflife
6.4 Example
7 Changingdecayrates
7.1 GSIanomaly
8 Theoreticalbasisofdecayphenomena
9 Occurrenceandapplications
9.1 SzilardChalmerseffect
10 Originsofradioactivenuclides
11 Decaychainsandmultiplemodes
12 Associatedhazardwarningsigns
13 Seealso
14 Notes
15 References
15.1 Inline
15.2 General
16 Externallinks

Historyofdiscovery
Radioactivitywasdiscoveredin1896bytheFrenchscientistHenriBecquerel,whileworkingwith
phosphorescentmaterials.[7]Thesematerialsglowinthedarkafterexposuretolight,andhesuspectedthatthe
glowproducedincathoderaytubesbyXraysmightbeassociatedwithphosphorescence.Hewrappeda

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photographicplateinblackpaperandplacedvariousphosphorescentsalts
onit.Allresultswerenegativeuntilheuseduraniumsalts.Theuranium
saltscausedablackeningoftheplateinspiteoftheplatebeingwrappedin
blackpaper.Theseradiationsweregiventhename"BecquerelRays".

Itsoonbecameclearthattheblackeningoftheplatehadnothingtodowith
phosphorescence,astheblackeningwasalsoproducedbynon
phosphorescentsaltsofuraniumandmetallicuranium.Itbecameclear
fromtheseexperimentsthattherewasaformofinvisibleradiationthat
couldpassthroughpaperandwascausingtheplatetoreactasifexposedto
PierreandMarieCurieintheir
light.
Parislaboratory,before1907
Atfirst,itseemedasthoughthenewradiationwassimilartothethen
recentlydiscoveredXrays.FurtherresearchbyBecquerel,ErnestRutherford,PaulVillard,PierreCurie,Marie
Curie,andothersshowedthatthisformofradioactivitywassignificantlymorecomplicated.Rutherfordwas
thefirsttorealizethatallsuchelementsdecayinaccordancewiththesamemathematicalexponentialformula.
RutherfordandhisstudentFrederickSoddywerethefirsttorealizethatmanydecayprocessesresultedinthe
transmutationofoneelementtoanother.Subsequently,theradioactivedisplacementlawofFajansandSoddy
wasformulatedtodescribetheproductsofalphaandbetadecay.[8][9]

Theearlyresearchersalsodiscoveredthatmanyotherchemicalelements,besidesuranium,haveradioactive
isotopes.AsystematicsearchforthetotalradioactivityinuraniumoresalsoguidedPierreandMarieCurieto
isolatetwonewelements:poloniumandradium.Exceptfortheradioactivityofradium,thechemicalsimilarity
ofradiumtobariummadethesetwoelementsdifficulttodistinguish.

MarieandPierreCuriesstudyofradioactivityisanimportantfactorinscienceandmedicine.Aftertheir
researchonBecquerel'sraysledthemtothediscoveryofbothradiumandpolonium,theycoinedtheterm
"radioactivity".[10]Theirresearchonthepenetratingraysinuraniumandthediscoveryofradiumlaunchedan
eraofusingradiumforthetreatmentofcancer.Theirexplorationofradiumcouldbeseenasthefirstpeaceful
useofnuclearenergyandthestartofmodernnuclearmedicine.[10]

Earlyhealthdangers
Thedangersofionizingradiationdueto
radioactivityandXrayswerenot
immediatelyrecognized.

Xrays

ThediscoveryofxraysbyWilhelm
Rntgenin1895ledtowidespread
experimentationbyscientists,physicians,
andinventors.Manypeoplebegan
recountingstoriesofburns,hairlossand
worseintechnicaljournalsasearlyas1896.
InFebruaryofthatyear,ProfessorDaniel
andDr.DudleyofVanderbiltUniversity
performedanexperimentinvolvingX TakinganXrayimagewithearlyCrookestubeapparatusin1896.
rayingDudley'sheadthatresultedinhis TheCrookestubeisvisibleinthecentre.Thestandingmanis
hairloss.AreportbyDr.H.D.Hawks,of viewinghishandwithafluoroscopescreenthiswasacommonway
hissufferingseverehandandchestburnsin ofsettingupthetube.Noprecautionsagainstradiationexposureare
anXraydemonstration,wasthefirstof beingtakenitshazardswerenotknownatthetime.
manyotherreportsinElectricalReview.[11]

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Otherexperimenters,includingElihuThomsonandNikolaTesla,alsoreportedburns.Thomsondeliberately
exposedafingertoanXraytubeoveraperiodoftimeandsufferedpain,swelling,andblistering.[12]Other
effects,includingultravioletraysandozone,weresometimesblamedforthedamage,[13]andmanyphysicians
stillclaimedthattherewerenoeffectsfromXrayexposureatall.[12]

Despitethis,thereweresomeearlysystematichazardinvestigations,andasearlyas1902WilliamHerbert
RollinswrotealmostdespairinglythathiswarningsaboutthedangersinvolvedinthecarelessuseofXrays
wasnotbeingheeded,eitherbyindustryorbyhiscolleagues.Bythistime,RollinshadprovedthatXrays
couldkillexperimentalanimals,couldcauseapregnantguineapigtoabort,andthattheycouldkillafetus.[14]
Healsostressedthat"animalsvaryinsusceptibilitytotheexternalactionofXlight"andwarnedthatthese
differencesbeconsideredwhenpatientsweretreatedbymeansofXrays.

Radioactivesubstances

However,thebiologicaleffectsofradiation
duetoradioactivesubstanceswerelesseasy
togauge.Thisgavetheopportunityfor
manyphysiciansandcorporationstomarket
radioactivesubstancesaspatentmedicines.
Exampleswereradiumenematreatments,
andradiumcontainingwaterstobedrunk
astonics.MarieCurieprotestedagainstthis
sortoftreatment,warningthattheeffectsof Radioactivityischaracteristicofelementswithlargeatomicnumber.
radiationonthehumanbodywerenotwell Elementswithatleastonestableisotopeareshowninlightblue.
understood.Curielaterdiedfromaplastic Greenshowselementswhosemoststableisotopehasahalflife
anaemia,likelycausedbyexposureto measuredinmillionsofyears.Yellowandorangeareprogressively
ionizingradiation.Bythe1930s,aftera lessstable,withhalflivesinthousandsorhundredsofyears,down
numberofcasesofbonenecrosisanddeath towardoneday.Redandpurpleshowhighlyandextremely
ofradiumtreatmententhusiasts,radium radioactiveelementswherethemoststableisotopesexhibithalflives
containingmedicinalproductshadbeen measuredontheorderofonedayandmuchless.
largelyremovedfromthemarket
(radioactivequackery).

Radiationprotection

OnlyayearafterRntgen'sdiscoveryofXrays,theAmericanengineerWolframFuchs(1896)gavewhatis
probablythefirstprotectionadvice,butitwasnotuntil1925thatthefirstInternationalCongressofRadiology
(ICR)washeldandconsideredestablishinginternationalprotectionstandards.Theeffectsofradiationon
genes,includingtheeffectofcancerrisk,wererecognizedmuchlater.In1927,HermannJosephMuller
publishedresearchshowinggeneticeffectsand,in1946,wasawardedtheNobelPrizeinPhysiologyor
Medicineforhisfindings.

ThesecondICRwasheldinStockholmin1928andproposedtheadoptionoftherontgenunit,andthe
'InternationalXrayandRadiumProtectionCommittee'(IXRPC)wasformed.RolfSievertwasnamed
Chairman,butadrivingforcewasGeorgeKayeoftheBritishNationalPhysicalLaboratory.Thecommittee
metin1931,1934and1937.

AfterWorldWarII,theincreasedrangeandquantityofradioactivesubstancesbeinghandledasaresultof
militaryandcivilnuclearprogrammesledtolargegroupsofoccupationalworkersandthepublicbeing
potentiallyexposedtoharmfullevelsofionisingradiation.ThiswasconsideredatthefirstpostwarICR
convenedinLondonin1950,whenthepresentInternationalCommissiononRadiologicalProtection(ICRP)
wasborn.[15]SincethentheICRPhasdevelopedthepresentinternationalsystemofradiationprotection,
coveringallaspectsofradiationhazard.

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Unitsofradioactivity
TheInternationalSystemofUnits(SI)unitofradioactiveactivityisthe
becquerel(Bq),namedinhonourofthescientistHenriBecquerel.One
Bqisdefinedasonetransformation(ordecayordisintegration)per
second.

Anolderunitofradioactivityisthecurie,Ci,whichwasoriginally
definedas"thequantityormassofradiumemanationinequilibrium
withonegramofradium(element)".[16]Today,thecurieisdefinedas
3.7 1010disintegrationspersecond,sothat1curie(Ci)=
3.7 1010Bq.Forradiologicalprotectionpurposes,althoughtheUnited Graphicshowingrelationships
StatesNuclearRegulatoryCommissionpermitstheuseoftheunitcurie betweenradioactivityanddetected
alongsideSIunits,[17]theEuropeanUnionEuropeanunitsof ionizingradiation
measurementdirectivesrequiredthatitsusefor"publichealth...
purposes"bephasedoutby31December1985.[18]

Typesofdecay
Earlyresearchersfoundthatanelectricormagneticfieldcouldsplitradioactive
emissionsintothreetypesofbeams.Theraysweregiventhenamesalpha,beta,
andgamma,inorderoftheirabilitytopenetratematter.Whilealphadecaywas
observedonlyinheavierelementsofatomicnumber52(tellurium)andgreater,the
othertwotypesofdecaywereproducedbyalloftheelements.Lead,atomic
number82,istheheaviestelementtohaveanyisotopesstable(tothelimitof
measurement)toradioactivedecay.Radioactivedecayisseeninallisotopesofall
elementsofatomicnumber83(bismuth)orgreater.Bismuth,however,isonlyvery
slightlyradioactive,withahalflifegreaterthantheageoftheuniverse
radioisotopeswithextremelylonghalflivesareconsideredeffectivelystablefor
practicalpurposes.
Alphaparticlesmaybe
Inanalysingthenatureofthedecayproducts,itwasobviousfromthedirectionof
completelystoppedbya
theelectromagneticforcesappliedtotheradiationsbyexternalmagneticand
sheetofpaper,beta
electricfieldsthatalphaparticlescarriedapositivecharge,betaparticlescarrieda
particlesbyaluminium
negativecharge,andgammarayswereneutral.Fromthemagnitudeofdeflection,
shielding.Gammarays
itwasclearthatalphaparticlesweremuchmoremassivethanbetaparticles.
canonlybereducedby
Passingalphaparticlesthroughaverythinglasswindowandtrappingthemina
muchmoresubstantial
dischargetubeallowedresearcherstostudytheemissionspectrumofthecaptured
mass,suchasaverythick
particles,andultimatelyprovedthatalphaparticlesareheliumnuclei.Other
layeroflead.
experimentsshowedbetaradiation,resultingfromdecayandcathoderays,were
highspeedelectrons.Likewise,gammaradiationandXrayswerefoundtobe
highenergyelectromagneticradiation.

Therelationshipbetweenthetypesofdecaysalsobegantobeexamined:Forexample,gammadecaywas
almostalwaysfoundtobeassociatedwithothertypesofdecay,andoccurredataboutthesametime,or
afterwards.Gammadecayasaseparatephenomenon,withitsownhalflife(nowtermedisomerictransition),
wasfoundinnaturalradioactivitytobearesultofthegammadecayofexcitedmetastablenuclearisomers,
whichwereinturncreatedfromothertypesofdecay.

Althoughalpha,beta,andgammaradiationsweremostcommonlyfound,othertypesofemissionwere
eventuallydiscovered.Shortlyafterthediscoveryofthepositronincosmicrayproducts,itwasrealizedthatthe
sameprocessthatoperatesinclassicalbetadecaycanalsoproducepositrons(positronemission),alongwith
neutrinos(classicalbetadecayproducesantineutrinos).Inamorecommonanalogousprocess,calledelectron
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capture,someprotonrichnuclideswerefoundtocapturetheirownatomic
electronsinsteadofemittingpositrons,andsubsequentlythesenuclides
emitonlyaneutrinoandagammarayfromtheexcitednucleus(andoften
alsoAugerelectronsandcharacteristicXrays,asaresultofthere
orderingofelectronstofilltheplaceofthemissingcapturedelectron).
Thesetypesofdecayinvolvethenuclearcaptureofelectronsoremission
ofelectronsorpositrons,andthusactstomoveanucleustowardtheratio
ofneutronstoprotonsthathastheleastenergyforagiventotalnumberof
nucleons.Thisconsequentlyproducesamorestable(lowerenergy)
nucleus.

(Atheoreticalprocessofpositroncapture,analogoustoelectroncapture,is
possibleinantimatteratoms,buthasnotbeenobserved,ascomplex Transitiondiagramfordecay
modesofaradionuclide,with
antimatteratomsbeyondantiheliumarenotexperimentallyavailable.[19]
neutronnumberNandatomic
Suchadecaywouldrequireantimatteratomsatleastascomplexas
beryllium7,whichisthelightestknownisotopeofnormalmatterto numberZ(shownare,,p+,
undergodecaybyelectroncapture.) andn0emissions,ECdenotes
electroncapture).
Shortlyafterthediscoveryoftheneutronin1932,EnricoFermirealized
thatcertainrarebetadecayreactionsimmediatelyyieldneutronsasa
decayparticle(neutronemission).Isolatedprotonemissionwas
eventuallyobservedinsomeelements.Itwasalsofoundthatsome
heavyelementsmayundergospontaneousfissionintoproductsthat
varyincomposition.Inaphenomenoncalledclusterdecay,specific
combinationsofneutronsandprotonsotherthanalphaparticles(helium
nuclei)werefoundtobespontaneouslyemittedfromatoms.

Othertypesofradioactivedecaywerefoundtoemitpreviouslyseen
particles,butviadifferentmechanisms.Anexampleisinternal
conversion,whichresultsinaninitialelectronemission,andthenoften
furthercharacteristicXraysandAugerelectronsemissions,although
theinternalconversionprocessinvolvesneitherbetanorgammadecay.
Aneutrinoisnotemitted,andnoneoftheelectron(s)andphoton(s)
emittedoriginateinthenucleus,eventhoughtheenergytoemitallof
themdoesoriginatethere.Internalconversiondecay,likeisomeric
transitiongammadecayandneutronemission,involvesthereleaseof
energybyanexcitednuclide,withoutthetransmutationofoneelement
intoanother. Typesofradioactivedecayrelatedto
NandZnumbers
Rareeventsthatinvolveacombinationoftwobetadecaytypeevents
happeningsimultaneouslyareknown(seebelow).Anydecayprocess
thatdoesnotviolatetheconservationofenergyormomentumlaws(andperhapsotherparticleconservation
laws)ispermittedtohappen,althoughnotallhavebeendetected.Aninterestingexamplediscussedinafinal
section,isboundstatebetadecayofrhenium187.Inthisprocess,betaelectrondecayoftheparentnuclideis
notaccompaniedbybetaelectronemission,becausethebetaparticlehasbeencapturedintotheKshellofthe
emittingatom.Anantineutrinoisemitted,asinallnegativebetadecays.

Radionuclidescanundergoanumberofdifferentreactions.Thesearesummarizedinthefollowingtable.A
nucleuswithmassnumberAandatomicnumberZisrepresentedas(A,Z).Thecolumn"Daughternucleus"
indicatesthedifferencebetweenthenewnucleusandtheoriginalnucleus.Thus,(A1,Z)meansthatthemass
numberisonelessthanbefore,buttheatomicnumberisthesameasbefore.

Ifenergycircumstancesarefavorable,agivenradionuclidemayundergomanycompetingtypesofdecay,with
someatomsdecayingbyoneroute,andothersdecayingbyanother.Anexampleiscopper64,whichhas29
protons,and35neutrons,whichdecayswithahalflifeofabout12.7hours.Thisisotopehasoneunpaired

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protonandoneunpairedneutron,soeithertheprotonortheneutroncandecaytotheoppositeparticle.This
particularnuclide(thoughnotallnuclidesinthissituation)isalmostequallylikelytodecaythroughpositron
emission(18%),orthroughelectroncapture(43%),asitdoesthroughelectronemission(39%).Theexcited
energystatesresultingfromthesedecayswhichfailtoendinagroundenergystate,alsoproducelaterinternal
conversionandgammadecayinalmost0.5%ofthetime.

Morecommoninheavynuclidesiscompetitionbetweenalphaandbetadecay.Thedaughternuclideswillthen
normallydecaythroughbetaoralpha,respectively,toendupinthesameplace.

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Modeofdecay Participatingparticles Daughternucleus

Decayswithemissionofnucleons:
Alphadecay Analphaparticle(A=4,Z=2)emittedfromnucleus (A4,Z2)
Proton
Aprotonejectedfromnucleus (A1,Z1)
emission
Neutron
Aneutronejectedfromnucleus (A1,Z)
emission
Doubleproton
Twoprotonsejectedfromnucleussimultaneously (A2,Z2)
emission
Spontaneous
Nucleusdisintegratesintotwoormoresmallernucleiandotherparticles
fission
Nucleusemitsaspecifictypeofsmallernucleus(A1,Z1)whichislarger (AA1,ZZ1)+
Clusterdecay
thananalphaparticle (A1,Z1)
Differentmodesofbetadecay:
decay Anucleusemitsanelectronandanelectronantineutrino (A,Z+1)
Positron
emission(+ Anucleusemitsapositronandanelectronneutrino (A,Z1)
decay)
Electron Anucleuscapturesanorbitingelectronandemitsaneutrinothedaughter
(A,Z1)
capture nucleusisleftinanexcitedunstablestate
Afreeneutronornucleusbetadecaystoelectronandantineutrino,but
theelectronisnotemitted,asitiscapturedintoanemptyKshellthe
Boundstate daughternucleusisleftinanexcitedandunstablestate.Thisprocessisa
(A,Z+1)
betadecay minorityoffreeneutrondecays(0.0004%)duetothelowenergyof
hydrogenionization,andissuppressedexceptinionizedatomsthathave
Kshellvacancies.
Doublebeta
Anucleusemitstwoelectronsandtwoantineutrinos (A,Z+2)
decay
Double
Anucleusabsorbstwoorbitalelectronsandemitstwoneutrinosthe
electron (A,Z2)
daughternucleusisleftinanexcitedandunstablestate
capture
Electron
capturewith Anucleusabsorbsoneorbitalelectron,emitsonepositronandtwo
(A,Z2)
positron neutrinos
emission
Double
positron Anucleusemitstwopositronsandtwoneutrinos (A,Z2)
emission
Transitionsbetweenstatesofthesamenucleus:
Isomeric
Excitednucleusreleasesahighenergyphoton(gammaray) (A,Z)
transition
Internal Excitednucleustransfersenergytoanorbitalelectron,whichis
(A,Z)
conversion subsequentlyejectedfromtheatom

Radioactivedecayresultsinareductionofsummedrestmass,oncethereleasedenergy(thedisintegration
energy)hasescapedinsomeway.Althoughdecayenergyissometimesdefinedasassociatedwiththe
differencebetweenthemassoftheparentnuclideproductsandthemassofthedecayproducts,thisistrueonly
ofrestmassmeasurements,wheresomeenergyhasbeenremovedfromtheproductsystem.Thisistrue
becausethedecayenergymustalwayscarrymasswithit,whereveritappears(seemassinspecialrelativity)
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accordingtotheformulaE=mc2.Thedecayenergyisinitiallyreleasedastheenergyofemittedphotonsplus
thekineticenergyofmassiveemittedparticles(thatis,particlesthathaverestmass).Iftheseparticlescometo
thermalequilibriumwiththeirsurroundingsandphotonsareabsorbed,thenthedecayenergyistransformedto
thermalenergy,whichretainsitsmass.

Decayenergythereforeremainsassociatedwithacertainmeasureofmassofthedecaysystem,calledinvariant
mass,whichdoesnotchangeduringthedecay,eventhoughtheenergyofdecayisdistributedamongdecay
particles.Theenergyofphotons,thekineticenergyofemittedparticles,and,later,thethermalenergyofthe
surroundingmatter,allcontributetotheinvariantmassofthesystem.Thus,whilethesumoftherestmassesof
theparticlesisnotconservedinradioactivedecay,thesystemmassandsysteminvariantmass(andalsothe
systemtotalenergy)isconservedthroughoutanydecayprocess.Thisisarestatementoftheequivalentlawsof
conservationofenergyandconservationofmass.

Radioactivedecayrates
Thedecayrate,oractivity,ofaradioactivesubstanceischaracterizedby:

Constantquantities:

Thehalflifet1/2,isthetimetakenfortheactivityofagivenamountofaradioactivesubstanceto
decaytohalfofitsinitialvalueseeListofnuclides.

Thedecayconstant ,"lambda"theinverseofthemeanlifetime,sometimesreferredtoassimply
decayrate.

Themeanlifetime ,"tau"theaveragelifetime(1/elife)ofaradioactiveparticlebeforedecay.

Althoughtheseareconstants,theyareassociatedwiththestatisticalbehaviorofpopulationsofatoms.In
consequence,predictionsusingtheseconstantsarelessaccurateforminusculesamplesofatoms.

Inprincipleahalflife,athirdlife,orevena(1/2)life,canbeusedinexactlythesamewayashalflifebut
themeanlifeandhalflifet1/2havebeenadoptedasstandardtimesassociatedwithexponentialdecay.

Timevariablequantities:

Totalactivity A,isthenumberofdecaysperunittimeofaradioactivesample.
NumberofparticlesN,isthetotalnumberofparticlesinthesample.
SpecificactivitySA,numberofdecaysperunittimeperamountofsubstanceofthesampleattimeset
tozero(t=0)."Amountofsubstance"canbethemass,volumeormolesoftheinitialsample.

Thesearerelatedasfollows:

whereN0istheinitialamountofactivesubstancesubstancethathasthesamepercentageofunstable
particlesaswhenthesubstancewasformed.

Mathematicsofradioactivedecay
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Universallawofradioactivedecay

Radioactivityisoneveryfrequentlygivenexampleofexponentialdecay.Thelawdescribesthestatistical
behaviourofalargenumberofnuclides,ratherthanindividualatoms.Inthefollowingformalism,thenumber
ofnuclidesorthenuclidepopulationN,isofcourseadiscretevariable(anaturalnumber)butforany
physicalsampleNissolargethatitcanbetreatedasacontinuousvariable.Differentialcalculusisusedto
modelthebehaviourofnucleardecay.

Themathematicsofradioactivedecaydependonakeyassumptionthatanucleusofaradionuclidehasno
"memory"orwayoftranslatingitshistoryintoitspresentbehavior.Anucleusdoesnot"age"withthepassage
oftime.Thus,theprobabilityofitsbreakingdowndoesnotincreasewithtime,butstaysconstantnomatter
howlongthenucleushasexisted.Thisconstantprobabilitymayvarygreatlybetweendifferenttypesofnuclei,
leadingtothemanydifferentobserveddecayrates.However,whatevertheprobabilityis,itdoesnotchange.
Thisisinmarkedcontrasttocomplexobjectswhichdoshowaging,suchasautomobilesandhumans.These
systemsdohaveachanceofbreakdownperunitoftime,thatincreasesfromthemomenttheybegintheir
existence.

Onedecayprocess

ConsiderthecaseofanuclideAthatdecaysintoanotherBbysomeprocessAB(emissionofother

particles,likeelectronneutrinoseandelectronseasinbetadecay,areirrelevantinwhatfollows).Thedecay
ofanunstablenucleusisentirelyrandomanditisimpossibletopredictwhenaparticularatomwilldecay.
However,itisequallylikelytodecayatanyinstantintime.Therefore,givenasampleofaparticular
radioisotope,thenumberofdecayeventsdNexpectedtooccurinasmallintervaloftimedtisproportional
tothenumberofatomspresentN,thatis[20]

Particularradionuclidesdecayatdifferentrates,soeachhasitsowndecayconstant .Theexpecteddecay
dN/Nisproportionaltoanincrementoftime,dt:

ThenegativesignindicatesthatNdecreasesastimeincreases,asthedecayeventsfollowoneafteranother.
Thesolutiontothisfirstorderdifferentialequationisthefunction:

whereN0isthevalueofNattimet=0.[20]

Wehaveforalltimet:

whereNtotalistheconstantnumberofparticlesthroughoutthedecayprocess,whichisequaltotheinitial
numberofAnuclidessincethisistheinitialsubstance.

IfthenumberofnondecayedAnucleiis:

B
thenthenumberofnucleiof ,i.e.thenumberofdecayed
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thenthenumberofnucleiofB,i.e.thenumberofdecayedAnuclei,is

ThenumberofdecaysobservedoveragivenintervalobeysPoissonstatistics.Iftheaveragenumberofdecays
is<N>,theprobabilityofagivennumberofdecaysNis[20]

Chaindecayprocesses

Chainoftwodecays

Nowconsiderthecaseofachainoftwodecays:onenuclideAdecayingintoanotherBbyoneprocess,thenB
decayingintoanotherCbyasecondprocess,i.e.ABC.Thepreviousequationcannotbeappliedto
thedecaychain,butcanbegeneralizedasfollows.SinceAdecaysintoB,thenBdecaysintoC,theactivityof
AaddstothetotalnumberofBnuclidesinthepresentsample,beforethoseBnuclidesdecayandreducethe
numberofnuclidesleadingtothelatersample.Inotherwords,thenumberofsecondgenerationnucleiB
increasesasaresultofthefirstgenerationnucleidecayofA,anddecreasesasaresultofitsowndecayintothe
thirdgenerationnucleiC.[21]Thesumofthesetwotermsgivesthelawforadecaychainfortwonuclides:

TherateofchangeofNB,thatisdNB/dt,isrelatedtothechangesintheamountsofAandB,NBcanincrease
asBisproducedfromAanddecreaseasBproducesC.

Rewritingusingthepreviousresults:

Thesubscriptssimplyrefertotherespectivenuclides,i.e.NAisthenumberofnuclidesoftypeA,NA0isthe
initialnumberofnuclidesoftypeA,AisthedecayconstantforAandsimilarlyfornuclideB.Solvingthis
equationforNBgives:

InthecasewhereBisastablenuclide(B=0),thisequationreducestotheprevioussolution:

asshownaboveforonedecay.Thesolutioncanbefoundbytheintegrationfactormethod,wherethe
integratingfactoriseBt.Thiscaseisperhapsthemostuseful,sinceitcanderiveboththeonedecayequation
(above)andtheequationformultidecaychains(below)moredirectly.

Chainofanynumberofdecays

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Forthegeneralcaseofanynumberofconsecutivedecaysinadecaychain,i.e.
A1A2AiAD,whereDisthenumberofdecaysandiisadummyindex(i=1,2,3,...D),
eachnuclidepopulationcanbefoundintermsofthepreviouspopulation.InthiscaseN2=0,N3=0,...,
ND=0.Usingtheaboveresultinarecursiveform:

ThegeneralsolutiontotherecursiveproblemisgivenbyBateman'sequations:[22]

Bateman'sequations

Alternativedecaymodes

Inalloftheaboveexamples,theinitialnuclidedecaysintojustoneproduct.[23]Considerthecaseofoneinitial
nuclidethatcandecayintoeitheroftwoproducts,thatisABandACinparallel.Forexample,ina
sampleofpotassium40,89.3%ofthenucleidecaytocalcium40and10.7%toargon40.Wehaveforalltime
t:

whichisconstant,sincethetotalnumberofnuclidesremainsconstant.Differentiatingwithrespecttotime:

definingthetotaldecayconstantintermsofthesumofpartialdecayconstantsBandC:

Noticethat

SolvingthisequationforNA:

whereNA0istheinitialnumberofnuclideA.Whenmeasuringtheproductionofonenuclide,onecanonly
observethetotaldecayconstant.ThedecayconstantsBandCdeterminetheprobabilityforthedecayto
resultinproductsBorCasfollows:

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becausethefractionB/ofnucleidecayintoBwhilethefractionC/ofnucleidecayintoC.

Corollariesofthedecaylaws

TheaboveequationscanalsobewrittenusingquantitiesrelatedtothenumberofnuclideparticlesNina
sample

Theactivity:A=N.
Theamountofsubstance:n=N/L.
Themass:M=Arn=ArN/L.

whereL=6.022 1023isAvogadro'sconstant,Aristherelativeatomicmassnumber,andtheamountofthe
substanceisinmoles.

Decaytiming:definitionsandrelations

Timeconstantandmeanlife

FortheonedecaysolutionAB:

theequationindicatesthatthedecayconstanthasunitsoft1,andcanthusalsoberepresentedas1/ ,where
isacharacteristictimeoftheprocesscalledthetimeconstant.
Inaradioactivedecayprocess,thistimeconstantisalsothemeanlifetimefordecayingatoms.Eachatom
"lives"forafiniteamountoftimebeforeitdecays,anditmaybeshownthatthismeanlifetimeisthearithmetic
meanofalltheatoms'lifetimes,andthatitis,whichagainisrelatedtothedecayconstantasfollows:

ThisformisalsotruefortwodecayprocessessimultaneouslyAB+C,insertingtheequivalentvaluesof
decayconstants(asgivenabove)

intothedecaysolutionleadsto:

Halflife

Amorecommonlyusedparameteristhehalflife.Givenasampleofaparticularradionuclide,thehalflifeis
thetimetakenforhalftheradionuclide'satomstodecay.Forthecaseofonedecaynuclearreactions:

thehalflifeisrelatedtothedecayconstantasfollows:set
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thehalflifeisrelatedtothedecayconstantasfollows:setN=N0/2andt=T1/2to
obtain

Thisrelationshipbetweenthehalflifeandthedecayconstantshowsthathighly
radioactivesubstancesarequicklyspent,whilethosethatradiateweaklyendurelonger.
Halflivesofknownradionuclidesvarywidely,frommorethan1019years,suchasforthe
verynearlystablenuclide209Bi,to1023secondsforhighlyunstableones.

Thefactorofln(2)intheaboverelationsresultsfromthefactthattheconceptof"half Simulationof
life"ismerelyawayofselectingadifferentbaseotherthanthenaturalbaseeforthe manyidentical
atoms

lifetimeexpression.Thetimeconstant isthee1life,thetimeuntilonly1/eremains, undergoing
about36.8%,ratherthanthe50%inthehalflifeofaradionuclide.Thus, islongerthan radioactive
t1/2.Thefollowingequationcanbeshowntobevalid: decay,starting
witheither4
atoms(left)or
400(right).The
Sinceradioactivedecayisexponentialwithaconstantprobability,eachprocesscouldas numberatthe
easilybedescribedwithadifferentconstanttimeperiodthat(forexample)gaveits"(1/3) topindicates
life"(howlonguntilonly1/3isleft)or"(1/10)life"(atimeperioduntilonly10%isleft), howmanyhalf
liveshave

andsoon.Thus,thechoiceof andt1/2formarkertimes,areonlyforconvenience,and elapsed.
fromconvention.Theyreflectafundamentalprincipleonlyinsomuchastheyshowthat
thesameproportionofagivenradioactivesubstancewilldecay,duringanytimeperiod
thatonechooses.

Mathematically,thenthlifefortheabovesituationwouldbefoundinthesamewayasabovebysetting
N=N0/n,t=T1/nandsubstitutingintothedecaysolutiontoobtain

Example

Asampleof14Chasahalflifeof5,730yearsandadecayrateof14disintegrationperminute(dpm)pergram
ofnaturalcarbon.

Ifanartifactisfoundtohaveradioactivityof4dpmpergramofitspresentC,wecanfindtheapproximateage
oftheobjectusingtheaboveequation:

where:

years,

years.

Changingdecayrates
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Theradioactivedecaymodesofelectroncaptureandinternalconversionareknowntobeslightlysensitiveto
chemicalandenvironmentaleffectsthatchangetheelectronicstructureoftheatom,whichinturnaffectsthe
presenceof1sand2selectronsthatparticipateinthedecayprocess.Asmallnumberofmostlylightnuclides
areaffected.Forexample,chemicalbondscanaffecttherateofelectroncapturetoasmalldegree(ingeneral,
lessthan1%)dependingontheproximityofelectronstothenucleus.In7Be,adifferenceof0.9%hasbeen
observedbetweenhalflivesinmetallicandinsulatingenvironments.[24]Thisrelativelylargeeffectisbecause
berylliumisasmallatomwhosevalenceelectronsarein2satomicorbitals,whicharesubjecttoelectron
capturein7Bebecause(likeallsatomicorbitalsinallatoms)theynaturallypenetrateintothenucleus.

In1992,Jungetal.oftheDarmstadtHeavyIonResearchgroupobservedanaccelerateddecayof163Dy66+.
Althoughneutral163Dyisastableisotope,thefullyionized163Dy66+undergoesdecayintotheKandL
shellsto163Ho66+withahalflifeof47days.[25]

Rhenium187isanotherspectacularexample.187Renormallybetadecaysto187Oswithahalflifeof41.6
109years,[26]butstudiesusingfullyionised187Reatoms(barenuclei)havefoundthatthiscandecreasetoonly
33years.Thisisattributedto"boundstatedecay"ofthefullyionisedatomtheelectronisemittedintothe
"Kshell"(1satomicorbital),whichcannotoccurforneutralatomsinwhichalllowlyingboundstatesare
occupied.[27]

Anumberofexperimentshavefoundthatdecayratesofothermodesofartificial
andnaturallyoccurringradioisotopesare,toahighdegreeofprecision,
unaffectedbyexternalconditionssuchastemperature,pressure,thechemical
environment,andelectric,magnetic,orgravitationalfields.[28]Comparisonof
laboratoryexperimentsoverthelastcentury,studiesoftheOklonaturalnuclear
reactor(whichexemplifiedtheeffectsofthermalneutronsonnucleardecay),and
astrophysicalobservationsoftheluminositydecaysofdistantsupernovae(which
occurredfarawaysothelighthastakenagreatdealoftimetoreachus),for Decayrateofradon222as
example,stronglyindicatethatunperturbeddecayrateshavebeenconstant(at afunctionofdateandtime
leasttowithinthelimitationsofsmallexperimentalerrors)asafunctionoftime ofday.Thecolorbargives
aswell. thepoweroftheobserved
signalandrepresents~4%
Recentresultssuggestthepossibilitythatdecayratesmighthaveaweak seasonaldecayrate
dependenceonenvironmentalfactors.Ithasbeensuggestedthatmeasurements variation.
ofdecayratesofsilicon32,manganese54,andradium226exhibitsmall
seasonalvariations(oftheorderof0.1%),[29][30][31]whilethedecayofradon222
isreportedtoexhibitlarge4%peaktopeakseasonalvariations,[32]proposedtoberelatedtoeithersolarflare
activityorthedistancefromtheSun.However,suchmeasurementsarehighlysusceptibletosystematicerrors,
andasubsequentpaper[33]hasfoundnoevidenceforsuchcorrelationsinsevenotherisotopes(22Na,44Ti,
108Ag,121Sn,133Ba,241Am,238Pu),andsetsupperlimitsonthesizeofanysucheffects.

GSIanomaly

Anunexpectedseriesofexperimentalresultsfortherateofdecayofheavyhighlychargedradioactiveions
circulatinginastorageringhasprovokedtheoreticalactivityinanefforttofindaconvincingexplanation.The
ratesofweakdecayoftworadioactivespecieswithhalflivesofabout40sand200sarefoundtohavea
significantoscillatorymodulation,withaperiodofabout7s.[34]Theobservedphenomenonisknownasthe
GSIanomaly,asthestorageringisafacilityattheGSIHelmholtzCentreforHeavyIonResearchinDarmstadt
Germany.Asthedecayprocessproducesanelectronneutrino,someoftheproposedexplanationsforthe
observedrateoscillationinvokeneutrinoproperties.Initialideasrelatedtoflavouroscillationmetwith
skepticism.[35]Amorerecentproposalinvolvesmassdifferencesbetweenneutrinomasseigenstates.[36]

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Theoreticalbasisofdecayphenomena
Theneutronsandprotonsthatconstitutenuclei,aswellasotherparticlesthatapproachcloseenoughtothem,
aregovernedbyseveralinteractions.Thestrongnuclearforce,notobservedatthefamiliarmacroscopicscale,
isthemostpowerfulforceoversubatomicdistances.Theelectrostaticforceisalmostalwayssignificant,and,in
thecaseofbetadecay,theweaknuclearforceisalsoinvolved.

Theinterplayoftheseforcesproducesanumberofdifferentphenomenainwhichenergymaybereleasedby
rearrangementofparticlesinthenucleus,orelsethechangeofonetypeofparticleintoothers.These
rearrangementsandtransformationsmaybehinderedenergetically,sothattheydonotoccurimmediately.In
certaincases,randomquantumvacuumfluctuationsaretheorizedtopromoterelaxationtoalowerenergystate
(the"decay")inaphenomenonknownasquantumtunneling.Radioactivedecayhalflifeofnuclideshasbeen
measuredovertimescalesof55ordersofmagnitude,from2.3x1023seconds(forhydrogen7)to6.9x1031
seconds(fortellurium128).[37]Thelimitsofthesetimescalesaresetbythesensitivityofinstrumentationonly,
andtherearenoknownnaturallimitstohowbrieforlongadecayhalflifeforradioactivedecayofa
radionuclidemaybe.

Thedecayprocess,likeallhinderedenergytransformations,maybeanalogizedbyasnowfieldonamountain.
Whilefrictionbetweentheicecrystalsmaybesupportingthesnow'sweight,thesystemisinherentlyunstable
withregardtoastateoflowerpotentialenergy.Adisturbancewouldthusfacilitatethepathtoastateofgreater
entropy:Thesystemwillmovetowardsthegroundstate,producingheat,andthetotalenergywillbe
distributableoveralargernumberofquantumstatesthusresultinginanavalanche.Thetotalenergydoesnot
changeinthisprocess,but,becauseofthesecondlawofthermodynamics,avalancheshaveonlybeenobserved
inonedirectionandthatistowardthe"groundstate"thestatewiththelargestnumberofwaysinwhichthe
availableenergycouldbedistributed.

Suchacollapse(adecayevent)requiresaspecificactivationenergy.Forasnowavalanche,thisenergycomes
asadisturbancefromoutsidethesystem,althoughsuchdisturbancescanbearbitrarilysmall.Inthecaseofan
excitedatomicnucleus,thearbitrarilysmalldisturbancecomesfromquantumvacuumfluctuations.A
radioactivenucleus(oranyexcitedsysteminquantummechanics)isunstable,andcan,thus,spontaneously
stabilizetoalessexcitedsystem.Theresultingtransformationaltersthestructureofthenucleusandresultsin
theemissionofeitheraphotonorahighvelocityparticlethathasmass(suchasanelectron,alphaparticle,or
othertype).

Occurrenceandapplications
AccordingtotheBigBangtheory,stableisotopesofthelightestfiveelements(H,He,andtracesofLi,Be,and
B)wereproducedveryshortlyaftertheemergenceoftheuniverse,inaprocesscalledBigBang
nucleosynthesis.Theselighteststablenuclides(includingdeuterium)survivetotoday,butanyradioactive
isotopesofthelightelementsproducedintheBigBang(suchastritium)havelongsincedecayed.Isotopesof
elementsheavierthanboronwerenotproducedatallintheBigBang,andthesefirstfiveelementsdonothave
anylonglivedradioisotopes.Thus,allradioactivenucleiare,therefore,relativelyyoungwithrespecttothe
birthoftheuniverse,havingformedlaterinvariousothertypesofnucleosynthesisinstars(inparticular,
supernovae),andalsoduringongoinginteractionsbetweenstableisotopesandenergeticparticles.Forexample,
carbon14,aradioactivenuclidewithahalflifeofonly5,730years,isconstantlyproducedinEarth'supper
atmosphereduetointeractionsbetweencosmicraysandnitrogen.

Nuclidesthatareproducedbyradioactivedecayarecalledradiogenicnuclides,whethertheythemselvesare
stableornot.Thereexiststableradiogenicnuclidesthatwereformedfromshortlivedextinctradionuclidesin
theearlysolarsystem.[38][39]Theextrapresenceofthesestableradiogenicnuclides(suchasXe129from
primordialI129)againstthebackgroundofprimordialstablenuclidescanbeinferredbyvariousmeans.

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Radioactivedecayhasbeenputtouseinthetechniqueofradioisotopiclabeling,whichisusedtotrackthe
passageofachemicalsubstancethroughacomplexsystem(suchasalivingorganism).Asampleofthe
substanceissynthesizedwithahighconcentrationofunstableatoms.Thepresenceofthesubstanceinoneor
anotherpartofthesystemisdeterminedbydetectingthelocationsofdecayevents.

Onthepremisethatradioactivedecayistrulyrandom(ratherthanmerelychaotic),ithasbeenusedinhardware
randomnumbergenerators.Becausetheprocessisnotthoughttovarysignificantlyinmechanismovertime,it
isalsoavaluabletoolinestimatingtheabsoluteagesofcertainmaterials.Forgeologicalmaterials,the
radioisotopesandsomeoftheirdecayproductsbecometrappedwhenarocksolidifies,andcanthenlaterbe
used(subjecttomanywellknownqualifications)toestimatethedateofthesolidification.Theseinclude
checkingtheresultsofseveralsimultaneousprocessesandtheirproductsagainsteachother,withinthesame
sample.Inasimilarfashion,andalsosubjecttoqualification,therateofformationofcarbon14invariouseras,
thedateofformationoforganicmatterwithinacertainperiodrelatedtotheisotope'shalflifemaybe
estimated,becausethecarbon14becomestrappedwhentheorganicmattergrowsandincorporatesthenew
carbon14fromtheair.Thereafter,theamountofcarbon14inorganicmatterdecreasesaccordingtodecay
processesthatmayalsobeindependentlycrosscheckedbyothermeans(suchascheckingthecarbon14in
individualtreerings,forexample).

SzilardChalmerseffect

TheSzilardChalmerseffectisdefinedasthebreakingofachemicalbondbetweenanatomandthemolecule
thattheatomispartof,asaresultofanuclearreactionoftheatom.Theeffectcanbeusedtoseparateisotopes
bychemicalmeans.ThediscoveryofthiseffectisduetoL.SzilrdandT.A.Chalmers.[40]

Originsofradioactivenuclides
RadioactiveprimordialnuclidesfoundintheEarthareresiduesfromancientsupernovaexplosionsthat
occurredbeforetheformationofthesolarsystem.Theyarethefractionofradionuclidesthatsurvivedfromthat
time,throughtheformationoftheprimordialsolarnebula,throughplanetaccretion,anduptothepresenttime.
Thenaturallyoccurringshortlivedradiogenicradionuclidesfoundintoday'srocks,arethedaughtersofthose
radioactiveprimordialnuclides.Anotherminorsourceofnaturallyoccurringradioactivenuclidesare
cosmogenicnuclides,thatareformedbycosmicraybombardmentofmaterialintheEarth'satmosphereor
crust.ThedecayoftheradionuclidesinrocksoftheEarth'smantleandcrustcontributesignificantlytoEarth's
internalheatbudget.

Decaychainsandmultiplemodes
Thedaughternuclideofadecayeventmayalsobeunstable(radioactive).Inthiscase,ittoowilldecay,
producingradiation.Theresultingseconddaughternuclidemayalsoberadioactive.Thiscanleadtoa
sequenceofseveraldecayeventscalledadecaychain(seethisarticleforspecificdetailsofimportantnatural
decaychains).Eventually,astablenuclideisproduced.

Anexampleisthenaturaldecaychainof238U:

Uranium238decays,throughalphaemission,withahalflifeof4.5billionyearstothorium234
whichdecays,throughbetaemission,withahalflifeof24daystoprotactinium234
whichdecays,throughbetaemission,withahalflifeof1.2minutestouranium234
whichdecays,throughalphaemission,withahalflifeof240thousandyearstothorium230
whichdecays,throughalphaemission,withahalflifeof77thousandyearstoradium226
whichdecays,throughalphaemission,withahalflifeof1.6thousandyearstoradon222
whichdecays,throughalphaemission,withahalflifeof3.8daystopolonium218
whichdecays,throughalphaemission,withahalflifeof3.1minutestolead214
whichdecays,throughbetaemission,withahalflifeof27minutestobismuth214
whichdecays,throughbetaemission,withahalflifeof20minutestopolonium214
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whichdecays,throughalphaemission,withahalflifeof160
microsecondstolead210
whichdecays,throughbetaemission,withahalflifeof22
yearstobismuth210
whichdecays,throughbetaemission,withahalflifeof5
daystopolonium210
whichdecays,throughalphaemission,withahalflifeof140
daystolead206,whichisastablenuclide.

Someradionuclidesmayhaveseveraldifferentpathsofdecay.For
example,approximately36%ofbismuth212decays,through
alphaemission,tothallium208whileapproximately64%of Gammarayenergyspectrumofuranium
bismuth212decays,throughbetaemission,topolonium212.Both ore(inset).Gammaraysareemittedby
thallium208andpolonium212areradioactivedaughterproducts decayingnuclides,andthegammaray
ofbismuth212,andbothdecaydirectlytostablelead208. energycanbeusedtocharacterizethe
decay(whichnuclideisdecayingto
Associatedhazardwarningsigns which).Here,usingthegammaray
spectrum,severalnuclidesthataretypical
ofthedecaychainof 238Uhavebeen
identified: 226Ra, 214Pb, 214Bi.

Thetrefoilsymbol 2007ISOradioactivity
usedtoindicate dangersymbol
ionisingradiation. intendedforIAEA
Category1,2and3
sourcesdefinedas
dangeroussources
capableofdeathor
seriousinjury.[41]

Thedangerousgoods
transportclassification
signforradioactive
materials

Seealso
Actinidesinthe environment
WikimediaCommonshas
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Backgroundradiation Nuclearpharmacy mediarelatedtoRadioactive

Chernobyldisaster Nuclearphysics decaybymode.
Crimesinvolving Nuclearpower
radioactivesubstances Particledecay
Decaychain Poissonprocess
Decaycorrect Radiation
Falloutshelter Radiationtherapy
Halflife Radioactivecontamination
Inducedradioactivity Radioactivityinbiology
Listsofnucleardisasters Radiometricdating
andradioactiveincidents Radionuclidea.k.a."radio
NationalCouncilon isotope"
RadiationProtectionand Secularequilibrium
Measurements Transientequilibrium
Nuclearengineering
Nuclearmedicine

Notes
1.SeeWuexperimentamongothercounterexampleswhenthedecayingatomisinfluencedbyexternalfactors.
2.Radionuclideisthemorecorrectterm,butradioisotopeisalsoused.Thedifferencebetweenisotopeandnuclideis
explainedatIsotope#Isotopevs.nuclide.

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