Radioactivity. By the end of this chapter you should be able to : describe the properties of alpha , beta and gamma radiations ; explain why some nuclei are unstable in terms of the relative number of neutrons to protons ; define half-life and find it from a graph ;
Bytheend of thischapteryoushouldbeableto:
describe theproperties of alpha, beta and gamma radiations;
explainwhysomenuclei are unstable in terms of therelativenumber of neutronstoprotons;
define half-life and finditfrom a graph;
solveproblems of radioactivedecay.
Earlyexperimentswithradioactivesourcesconfirmedthatthreeseparatekinds of emissionstook place. Calledalpha, beta and gamma radiationsorparticles, theseemissionscouldbedistinguishedonthebasis of theirdifferentionizing and penetratingpower.
Bylettingtheseionizingradiationspassthroughregions of magnetic (orelectric) fieldsitwasseenthattwo of theemissionswereoppositelycharged and thethirdwaselectrically neutral.
The positive emissionswerecalledalphaparticles and weresoonidentified as nuclei of helium. Thus, thealphaparticleshave a massthatisaboutfout times themass of thehydrogenatom and anelectricchargeequalto +2e.
Thenegativeemissions(beta particles) wereidentified as electrons (charge –e) byexperiments similar toThomson’se/mexperiment, whichmeasuredthecharge-to-mass-ratio.
Theelectrically neutral emissions are called gamma rays and are photonswithverysmallwavelengths. Typicallythesewavelengths are smallerthan 10-12 m.
Onewaytodetectradiationistotakeadvantage of theirionizingeffect. In theGeiger-Müllertube, radiationenters a chamberthrough a thinwindow. Thechamberisfilledwith a gas, whichisionizedbytheincomingradiation. The positive ionsacceleratetowardtheearthedcasing and theelectronstowardthe positive electrode and so more ions are created as a result of collisionswiththe gas molecules. Thisregisters as a current in thecounterconnectedtothe GM tube.
There are about 2500 nuclides, butonlyabout 300 of them are stable; therest are unstable. A Segre plotis a plot of neutronnumber versus protonnumberforthestablenuclei. Thestraight line correspondstonucleithathavethesamenumber of protons and neutrons. As thenumber of protons in thenucleusincreases, theelectrostaticrepulsionbetweenthemgrows as well, butthestrong nuclear forcedoesnotgrowproportionatelysinceitis a short-rangeforce. Thus, extra neutronsmustbeput in thenucleus in ordertoensurestabilitythroughanincreased nuclear forcewithoutparticipating in therepulsiveelectricforce.
Anexample of alphadecayisthat of uraniumdecayingintothorium:
Heliumnuclei, beingmuchlighterthanthorium, actuallymoveawayfromtheuraniumnucleuswith a certainamount of kineticenergy. Theenergy of thealphaparticleemitted can beeitheronespecificvalueor a series of specificvaloues.
Note that in thereactionrepresentingthisdecay, the total atomicnumberontheright-handside of thearrowmatchestheatomicnumbertotheleft of thearrow. Thesameholdsforthemassnumber.
Thesecondexample of a radioactivedecayisthat of beta decay, such as
Note theappearence of theelectron (the beta particle) in thisdecay. Theotherparticleistheelectron antineutrino. Unlikealphadecay, theenergy of theemitted beta particle has a continuousrange of energy, a continuousspectrum.
Thethirdexample of a decayinvolvestheemission of a photon:
Thestarontheuraniumnucleusontheleftside of thearrowmeansthatthenucleusis in anexcitedstate. Nuclei, likeatoms, can onlyexist in specificenergystates. Thereexists a lowestenergystate and excitedstateswithenergieslargerthanthat of thegroundstate. Whenever a nucleusmakes a transitionfrom a highto a lowerenergystate, itemits a photonwhoseenergyequalstheenergydifferencebetweentheinitial and final energystates of thenucleus.
Usingtheequation in theleft, we can calculatethewavelength of theemittedphotons (~10-12m).
Thechanges in theatomic and massnumbers of a nucleuswhenitundergoesradiactivedecay can berepresented in a diagram of massnumberagainstatomicnumber. A radioactivenucleussuch as thorium (Z = 90) decaysfirstbyalphadecayintothenucleus of radium (Z = 88). Radium, whichisalsoradioactive, decaysintoactinium (Z = 89) by beta decay. Furtherdecaystake place untiltheresultingnucleusisstable.
Thelaw of radioactivedecaystatesthatthenumber of nucleithatwilldecay per secondisproportionaltothenumber of atomspresentthathavenotyetdecayed.
Thisis a form of a physicallawimplying a statisticalorrandomnature. Thismeansthatwecannotpredictexactlywhen a particular nucleuswilldecay. But, given a largenumber of nuclei, theradioactivedecaylaw can beusedtopredictthenumber of atomsthatwillhavedecayedafter a giveninterval of time. Theradioactivedecaylaw leads toanexponentialdecrease of thenumber of decayingnuclei.
Thereexists a certaininterval of time, calledthehalf-life, suchthataftereachhalf-lifethenumber of nucleithathavenotyetdecayedisreducedby a factor of 2.
We can also define the concept of decayrateoractivity—thenumber of nucleidecaying per second. Theunit of activityisthe becquerel (Bq); 1 Bq isiqualtoonedecay per second.