A2Physics物理出國英語RadioactivityPart1Evidenceforthenucleus

1.RadioactivitywasfirstdiscoveredbyHenriBecquerelin1896.Henoticedthaturaniumsaltscouldexposeaphotographicplateevenwhenitwaswrappedinblackpaper.Thisindicatedthatsomeformofinvisibleradiationwasbeingemittedbytheuranium.

2.MarieandPierreCuriefurtherinvestigatedradioactivity.Theydiscoveredtwonewradioactiveelements,poloniumandradium.Theirworkshowedthatradioactivitywasanatomicscalephenomenon,notachemicalreaction.

3.TheearlyunderstandingoftheatomwasbasedontheplumpuddingmodelproposedbyJ.J.Thomson.Inthismodel,theatomwasthoughttobeasphereofpositivechargewithnegativelychargedelectronsembeddedinit,likeplumsinapudding.

4.ErnestRutherfordconductedthefamousgoldfoilexperimentin1909.Heusedathinsheetofgoldfoilandbombardeditwithalphaparticles.Alphaparticlesarepositivelychargedheliumnuclei.

5.Accordingtotheplumpuddingmodel,thealphaparticlesshouldhavepassedthroughthegoldfoilwithonlyminordeflections.Thepositivechargeintheatomwasassumedtobespreadoutevenly,sothealphaparticleswouldnotencounteralargeenoughforcetocausesignificantdeflection.

6.However,Rutherford'sresultswereastonishing.Mostofthealphaparticlespassedstraightthroughthegoldfoil,butasmallfractionweredeflectedatlargeangles,andsomeevenbouncedstraightback.

7.ThisledRutherfordtoconcludethattheatomhasaverysmall,dense,positivelychargednucleusatitscenter.Thefactthatmostalphaparticlespassedthroughindicatedthatmostoftheatomisemptyspace.Thelargeangledeflectionsandbackscatteringwereduetothealphaparticlescomingclosetothepositivelychargednucleusandbeingrepelledbythestrongelectrostaticforce.

8.ThesizeofthenucleuscanbeestimatedfromtheRutherfordscatteringexperiment.Theclosestapproachofanalphaparticletothenucleusoccurswhenallofitsinitialkineticenergyisconvertedintoelectrostaticpotentialenergy.

9.Theelectrostaticpotentialenergybetweenanalphaparticle(charge(q_1=2e))andanucleusofcharge(q_2=Ze)atadistance(r)isgivenby(U=frac{kq_1q_2}{r}),where(k=frac{1}{4piepsilon_0}).

10.Byequatingtheinitialkineticenergyofthealphaparticle(K)tothemaximumpotentialenergy(U),wecanfindtheclosestapproach(r_{min}).Thisgivesanupperboundestimateofthesizeofthenucleus.

11.Thechargeofthenucleusisrelatedtotheatomicnumber(Z)oftheelement.Thenumberofprotonsinthenucleusisequalto(Z),andthepositivechargeofthenucleusis(Ze),where(e)istheelementarycharge((e=1.6times10^{19}C)).

12.Themassofthenucleusisconcentratedintheprotonsandneutrons.Protonsandneutronshaveapproximatelythesamemass((m_papproxm_napprox1.67times10^{27}kg)).

13.Theatomicmassnumber(A)isthesumofthenumberofprotons((Z))andneutrons((N))inthenucleus,i.e.,(A=Z+N).

14.Isotopesareatomsofthesameelement(same(Z))butwithdifferentnumbersofneutrons(different(N)andthusdifferent(A)).Forexample,carbon12((^{12}C))has6protonsand6neutrons,whilecarbon14((^{14}C))has6protonsand8neutrons.

15.Thestabilityofanucleusdependsonthebalancebetweentheattractivestrongnuclearforceandtherepulsiveelectrostaticforce.Thestrongnuclearforceactsbetweenprotonsandneutronsandisresponsibleforholdingthenucleustogether.

16.Forlightnuclei,theratioofneutronstoprotons((N/Z))iscloseto1.Astheatomicnumber(Z)increases,the(N/Z)ratioalsoincreasestomaintainnuclearstability.

17.Radioactivedecayoccurswhenanucleusisunstable.Therearethreemaintypesofradioactivedecay:alphadecay,betadecay,andgammadecay.

18.Inalphadecay,anucleusemitsanalphaparticle((^{4}He)nucleus).Thegeneralequationforalphadecayis(_{Z}^{A}Xrightarrow_{Z2}^{A4}Y+_{2}^{4}He),where(X)istheparentnucleusand(Y)isthedaughternucleus.

19.Alphadecayisaresultofthestrongnuclearforcenotbeingabletoholdthelargenucleustogether.Thealphaparticleisabletotunnelthroughthepotentialenergybarriersurroundingthenucleus.

20.Betadecaycanbeoftwotypes:betaminus((beta^))decayandbetaplus((beta^+))decay.In(beta^)decay,aneutroninthenucleusisconvertedintoaproton,anelectron,andanantineutrino.Theequationis(_{Z}^{A}Xrightarrow_{Z+1}^{A}Y+_{1}^{0}e+bar{nu}_e).

21.In(beta^+)decay,aprotonisconvertedintoaneutron,apositron,andaneutrino.Theequationis(_{Z}^{A}Xrightarrow_{Z1}^{A}Y+_{+1}^{0}e+nu_e).

22.Betadecayisgovernedbytheweaknuclearforce.Theweakforceisresponsibleforthetransformationofquarkswithinprotonsandneutrons.

23.Gammadecayoccurswhenanucleusisinanexcitedstate.Thenucleusemitsagammarayphotontotransitiontoalowerenergystate.Theequationforgammadecayis(_{Z}^{A}X^rightarrow_{Z}^{A}X+gamma),where(X^)istheexcitedstatenucleus.

24.Theactivity(A)ofaradioactivesampleisdefinedasthenumberofdecaysperunittime.Itismeasuredinbecquerels(Bq),where(1Bq=1decay/s).

25.Theactivityofasampleisproportionaltothenumberofradioactivenuclei(N)presentinthesample.Mathematically,(A=lambdaN),where(lambda)isthedecayconstant.

26.Thedecayconstant(lambda)isacharacteristicofaparticularradioactiveisotope.Itrepresentstheprobabilityperunittimethatasinglenucleuswilldecay.

27.Thehalflife(T_{1/2})ofaradioactiveisotopeisthetimetakenforhalfoftheradioactivenucleiinasampletodecay.Itisrelatedtothedecayconstantbytheformula(T_{1/2}=frac{ln2}{lambda}).

28.Thenumberofradioactivenuclei(N)inasampleasafunctionoftime(t)followstheexponentialdecaylaw(N=N_0e^{lambdat}),where(N_0)istheinitialnumberofradioactivenuclei.

29.Theactivity(A)ofasamplealsofollowsanexponentialdecaylaw(A=A_0e^{lambdat}),where(A_0)istheinitialactivity.

30.Themeanlifetime(tau)ofaradioactivenucleusistheaveragetimeanucleusexistsbeforeitdecays.Itisrelatedtothedecayconstantby(tau=frac{1}{lambda}).

31.Theenergyreleasedinradioactivedecayiscalledthedecayenergyorthedisintegrationenergy(Q).ItiscalculatedfromthemassdifferencebetweentheparentnucleusandthedaughterproductsusingEinstein'smassenergyequivalence(E=mc^2).

32.Foralphadecay,the(Q)valueis(Q=(m_Xm_Ym_{He})c^2),where(m_X)isthemassoftheparentnucleus,(m_Y)isthemassofthedaughternucleus,and(m_{He})isthemassofthealphaparticle.

33.Inbetadecay,the(Q)valuetakesintoaccountthemassesoftheparentanddaughternuclei,aswellasthemassoftheelectronorpositronandtheenergycarriedawaybytheneutrinoorantineutrino.

34.Gammarayphotonshaveveryhighenergy.Theenergyofagammarayphotonisgivenby(E=hf),where(h)isPlanck'sconstant((h=6.63times10^{34}Js))and(f)isthefrequencyofthephoton.

35.Thepenetrationpowerofdifferenttypesofradiationvaries.Alphaparticleshavethelowestpenetrationpowerandcanbestoppedbyasheetofpaper.Betaparticlescanpenetrateafewmillimetersofaluminum,whilegammarayshavethehighestpenetrationpowerandcanpassthroughseveralcentimetersoflead.

36.Theionizingpowerofradiationistheabilitytoionizeatoms.Alphaparticleshavethehighestionizingpowerbecauseoftheirlargemassandcharge.Gammarayshavethelowestionizingpoweramongthethreemaintypesofradiation.

37.Radioactivedatingisatechniqueusedtodeterminetheageofancientobjects.Carbon14datingisbasedonthedecayofcarbon14inlivingorganisms.

38.Whenanorganismisalive,ittakesincarbonfromtheenvironment,andtheratioofcarbon14tocarbon12initsbodyisthesameastheratiointheatmosphere.Aftertheorganismdies,thecarbon14decays,andbymeasuringtheremainingamountofcarbon14,theageoftheorganismcanbeestimated.

39.Uraniumleaddatingisusedtodaterocks.Uranium238decaysthroughaseriesofstepstolead206withaverylonghalflife((T_{1/2}=4.5times10^{9}years)).

40.TheRutherfordscatteringformulagivesthedifferentialcrosssectionforthescatteringofalphaparticlesbyanucleus.Itisbasedontheclassicaltheoryofelectrostaticscattering.

41.Theformulaforthedifferentialcrosssection(frac{dsigma}{dOmega})inRutherfordscatteringis(frac{dsigma}{dOmega}=left(frac{Ze^2}{4piepsilon_02K}right)^2frac{1}{sin^{4}(theta/2)}),where(theta)isthescatteringangleand(K)istheinitialkineticenergyofthealphaparticle.

42.Thetotalcrosssection(sigma)isobtainedbyintegratingthedifferentialcrosssectionoverallsolidangles.

43.Theconceptofcrosssectionisimportantinunderstandingtheprobabilityofanuclearreactionorscatteringevent.Itrepresentstheeffectiveareathatatargetnucleuspresentstoanincomingparticle.

44.TheGeigerMarsdenexperiment,whichwaspartofRutherford'swork,providedtheexperimentaldatafortheRutherfordscatteringformula.Theymeasuredthenumberofalphaparticlesscatteredatdifferentangles.

45.TheBohrmodeloftheatom,whichwasdevelopedafterRutherford'sdiscoveryofthenucleus,incorporatedtheideaofacentralnucleuswithelectronsorbitingarounditindiscreteenergylevels.

46.TheBohrmodelwassuccessfulinexplainingthespectrallinesofthehydrogenatom.Itintroducedtheconceptofquantizationofangularmomentum(L=nhbar),where(n=1,2,3,c