Physics 30 Lesson 36 Radioactivity

Transcription

1 I. Radioaciviy Physics 30 Lesso 36 Radioaciviy Recall from Lesso 5 ha oe of Dalo s posulaes was ha aoms are permae ad uchageable. I 896, Heri Becquerel was doig experimes o fid x-ray emissios from phosphoresce crysals by placig hem o op of phoographic plaes wrapped i black paper. The crysals were he placed i suligh which would cause hem o fluoresce i.e. high frequecy ligh is absorbed by he crysal ad he reemied as lower frequecy ligh. If hey emied x-rays, he plaes would deec hem. Oe day he placed a uraium compoud o a phoographic plae. Sice here was o eough suligh o ha day he placed he apparaus i a drawer for a few days. Whe he developed he plaes he discovered ha hey had bee srogly exposed o somehig emied by he uraium compoud. Becquerel had accideally discovered radioaciviy (iiially called Becquerel rays). Marie ad Pierre Curie, uder Marie s direcio, sudied he radioacive elemes foud i a uraium ore called pichblede. They discovered ha he radioaciviy of a eleme is deermied by somehig iside he aoms which is uchaged by ay exeral facors such as hea, pressure ad eve by he elemes wih which i is combied i a compoud. Some elemes are usable ad decay spoaeously, releasig oe or more paricles. This is referred o as radioacive decay. I 903, Heri Becquerel ad Pierre & Marie Curie received he Nobel prize for Physics because of heir work i radioaciviy. I 9, Marie Curie received he Nobel prize for Chemisry for isolaig poloium ad radium from pichblede, boh of which were may imes more radioacive ha uraium. I 898, Eres Ruherford, a physicis from New Zealad workig a McGill Uiversiy i Moreal, sudied radioacive decay. He discovered ad amed wo paricles emied i radioacive emissio: alpha () ad bea () paricles. A year laer, Paul Villard, a Frech physicis, discovered a hird ype of emissio, gamma () rays. Alpha () paricles They are posiively charged paricles ejeced from a ucleus. (Alpha paricles are acually he uclei of helium aoms 4 He.) They are ejeced a high speed, bu have a rage of oly a few ceimeres i air. They are sopped by a ordiary shee of alumiium foil. Bea () paricles These are high eergy elecros ( 0 e ) ejeced from a ucleus. They are ejeced a varyig speeds, someimes close o he speed of ligh. High eergy paricles are able o peerae several ceimeres of alumiium. Gamma ( ) rays Gamma rays are phoos ( 0 0 ) wih very shor waveleghs. Their waveleghs ad eergies ca vary. High eergy rays ca peerae a leas 30 cm of lead ad km of air. Dr. Ro Lich 36

2 A simple mehod used o classify paricles is o sed hem hrough a mageic field (remember hose had rules). Depedig o which way he paricle urs i a mageic field, oe ca deermie wha kid of paricle i is. paricle (helium ucleus, + charge) X X X X X X X X X X X X X X X ray (high eergy phoo, o charge) X X X X X X X X X X paricle (elecro, - charge) Whe a radioacive isoope udergoes decay he resulig isoope is ofe radioacive as well. The series of uclear reacios required o reach a sable o-radioacive isoope is referred o as a uclear decay series. The series of reacios ca be displayed o a uclide char like he oe show. Example Wrie complee uclear equaios for he followig: A. The bea decay of horium-34. Thus Th e? 34 0? 90? Th e Pa B. The alpha decay of radium-6. Ra He? 6 4? 88? * Aomic mass: 34 =0 + A A = 34 Aomic umber: 90 = Z + (-) Z = 9 (eleme 9 is Pa - proaciium) Aomic mass: 6 = 4 + A A = Aomic umber: 88 = Z + Z = 86 (eleme 86 is R - rado) Thus Ra He 86 R * ivolves more ha jus he emissio of a elecro. See below. Dr. Ro Lich 36

3 II. Coservaio laws applied o alpha decay As we saw i Lesso 35, he old law of coservaio of mass was icorporaed io a broader ad more effecive law of coservaio of eergy whe Eisei's mass-eergy relaioship (E = mc ) was icluded. We will ow apply he mass-eergy coservaio law o he kieic eergies of he paricles emied by radioacive subsaces. The eergy of a alpha paricle ca be deermied from he mass of he pare radioacive ucleus, he mass of he alpha paricle, ad he mass of he daugher ucleus. The alpha paricle ad he daugher ucleus ogeher have a mass slighly smaller ha ha of he pare ucleus. The eergy equivalece of he mass defec is, or should be, equal o he kieic eergy of he emied alpha paricle. I he decay of horium-3, for example, a alpha paricle is emied ad he fial ucleus is radium- 8. Wihou measurig he masses of he uclei direcly, oe ca predic, usig coservaio of eergy, ha whe horium-3 emis a alpha paricle, he mass defici should equal he kieic eergy of he alpha paricle. mc Ek I heory, all he alpha paricles emied by horium-3 should have he same kieic eergy ad his predicio was verified i he 90s. I was foud ha he alpha paricles from horium-3 could all peerae.8 cm of air. I he case of poloium-, he paricles all peeraed 8.6 cm of air, while hose from radium- peeraed 3.3 cm. Thus, sice he peeraio is direcly relaed o he eergy of he paricle, he alpha paricles from a specific radioacive source all have he same eergy. (Acually, here were some irregulariies i he alpha paricle peeraio. Laer i was foud ha he origial radioacive ucleus, like orbiig elecros, could exis i a umber of excied saes. Whe a alpha paricle is emied from a excied ucleus, he alpha paricle carries away mos of his eergy. However, sice he ormal codiio of he ucleus is o be i is groud sae, he vas majoriy of emied alpha paricles have he same eergy.) III. Coservaio laws applied o bea decay For alpha paricles, he coservaio of mass-eergy worked very well, bu his was o so for bea paricles. If he same reasoig is applied o bea decay, he paricles emied from ideical radioacive uclei should each have he same eergy ad i was clear, as early as 900, ha his was o he case. I each bea decay here was a cerai loss of mass, which should have bee equivale o he kieic eergy of he emied bea paricle, bu i was foud ha he kieic eergy of he bea paricle had a rage of values. Accordig o he coservaio of mass-eergy, o bea paricle should have a kieic eergy less ha he eergy equivale of he mass decrease. Ad ye, bea paricles were regularly give off wih less kieic eergy ha prediced. I fac, very few bea paricles have he prediced maximum kieic eergy o average, he mos commo value is 40% of he maximum. O he surface, i appeared ha coservaio of masseergy failed for bea paricle producio. This was a alarmig coclusio o he physiciss of he 90s. I 93, Wolfgag Pauli suggesed a explaaio. He proposed ha if he bea paricle did o carry off all he available eergy he remaider migh be give o a secod Dr. Ro Lich

4 paricle. Bu wha would he properies of his myserious secod paricle be? To begi wih, i was udersood ha bea paricles are produced whe a euro i he ucleus is covered io a proo. p e 0 0 To saisfy he coservaio of elecrical charge, Pauli's paricle had o be eural. Furher, a charged paricle would be easily deecable, ad he ew paricle had o bee observed. Neural paricles are very difficul o deec direcly. From a coservaio of mass-eergy perspecive, whe a euro breaks dow io a proo ad a elecro, he loss i mass is equivale o approximaely oe-half he mass of a elecro. I fac, Pauli's paricle mus have bee cosiderably ligher, sice he emied elecro usually ges some of he eergy ad someimes all of i. As physiciss recalculaed heir esimaes of he mass of Pauli's paricle, i became clear ha i, like he phoo, was a massless paricle i had a res mass of zero. Pauli's paricle hus emerged as a eural, massless paricle. Erico Fermi, he grea Ialia physicis, suggesed ha his paricle be called he eurio, which i Ialia meas "lile eural oe". The eurio is usually give he symbol, which is he Greek leer "u". Now he equaio for euro decay ca be wrie: p e 0 0 The eurio, proposed by Pauli ad suppored by he subseque work of Fermi, received a mixed recepio i he world of physics. To some i appeared o be a myhical paricle creaed o save he law of coservaio of eergy, bu his was o he oly coservaio law saved by he eurio. Whe a euro is a res, is momeum is zero. Whe i decays, he emied elecro will have momeum as will he recoilig proo. Accordig o he coservaio of momeum, he elecro should shoo off i oe direcio ad he proo i exacly he opposie direcio, bu his is o wha is observed. The elecro ad proo are boh emied a a agle, which, as we leared i Lesso 3, is o possible. The iclusio of a eurio makes he e momeum of he sysem zero. Liear momeum is coserved. p + e Aoher coservaio law o be cosidered is he coservaio of agular momeum. Paricles have eergy ad agular momeum because of heir spi. Usig he quaum scale of measureme, he proo ad elecro boh have a spi of ½. Agular momeum ca, however, exis i wo variaios, clockwise +½ ad couer clockwise ½. The coservaio of agular momeum requires ha i a sysem coaiig a umber of paricles, he sum of he spis of he idividual paricles before he ieracio mus be equal o he sum of he spis of he idividual paricles afer he ieracio. Like he coservaio of mass-eergy ad liear momeum, agular momeum cao be coserved uless a eurio is produced. I summary, i appears ha he eurio is required i order o save o less ha hree coservaio laws: mass-eergy, liear momeum, ad agular momeum. The Dr. Ro Lich

5 sregh of hese argumes slowly coviced physiciss ha his myserious, ghoslike paricle mus be here, eve hough i could o be deeced. (Ulike charged paricles like proos ad elecros, eural paricles like euros ad eurios are very difficul o observe direcly. I fac, a eurio could pass hrough lead ha is oe ligh year hick wihou ieracig wih he lead. I addiio, if you look a your humb ail, 60 billio eurios pass hrough i from he Su every secod.) Twey five years afer Pauli heorised heir exisece, he eurio was experimeally verified. I 956 a paricle wih zero res mass, ravellig a he speed of ligh (like a phoo), wih liear momeum, ad a spi of ½ was observed. More recely (986), i has bee deermied ha he eurio s mass (if i has mass) is less ha a mere 7 ev/c (abou 9000 imes less ha a elecro). The issue of a ozero eurio mass is crucial i asrophysics. Eve if he eurio correspoded o jus a few ev/c, hey are so umerous ha much of he mass of he Uiverse would be ivisible eurios. Tha hidde mass migh well deermie he fae of he eire Uiverse. Bu our sory of he eurio does o ed here, here was oe more wis. I 98 Paul Dirac developed a relaivisic equaio for he elecro, ow kow as he Dirac equaio. I was immediaely clear o Dirac ha his equaio had wo kids of soluios. Oe se of soluios offered a correc ad cosise descripio of how a elecro should behave i a elecromageic field, icludig he ewly discovered pheomeo of elecro spi. Curiously, he equaio was foud o have egaive-eergy soluios i addiio o he ormal posiive oes. Dirac iiially ried o igore he egaive soluio as a mahemaical irregulariy, bu afer a ime he realised ha i could o be igored. By 93 Dirac proposed he exisece of a aielecro, a paricle wih he same mass as a elecro bu wih opposie charge. A year laer Carl Aderso, workig wih Millika, was sudyig cosmic-rays which sream i o Earh from space. The cosmic-rays were observed usig a cloud chamber iside a uiform mageic field so ha posiive ad egaive charges would follow opposie curved pahs. Amog he housads of phoographs ake, Aderso oiced oe wih wo opposiely curved, mirror image racks. Oe was ceraily a elecro, while he oher suggesed a aielecro. By he ed of he summer of 93, Aderso had clear evidece of he exisece of he aielecro which he amed he posiro. I ook Dirac a few years o comprehed ha he mahemaics of his equaio demaded he exisece of aimaer. This led him o remark ha he equaio was more iellige ha is auhor. Today's Sadard Model (see Lesso 37) shows ha every paricle (elecro, proo, euro, ec.) has a aiparicle (posiro, aiproo, aieuro, ec.). The same is rue for eurios. There are eurios ( ) ad aieurios ( ). (The bar above a symbol sigifies a aiparicle.) Dr. Ro Lich

6 The resul is ha we have wo ypes of bea decay: decay ivolves he rasformaio of a euro io a proo ad a elecro which also produces a aieurio p e 0 0 decays ivolvig he ucleus of a aom have he geeral form X Y A A 0 Z Z + decay ivolves he rasformaio of a proo io a euro ad a posiro which also produces a eurio p e decays ivolvig he ucleus of a aom have he geeral form X Y A A 0 Z Z Example Wrie complee uclear equaios for he followig: A. The decay of aciium-30. Thus Ac e? 30 0? 89? Ac e Th Aomic mass: 30 =0 + A A = 30 Aomic umber: 89 = Z + (-) Z = 90 (eleme 90 is Th - horium) B. The + decay of epuium-34. Thus Np e? 34 0? 93? Np e U Aomic mass: 34 =0 + A A = 34 Aomic umber: 93 = Z + (+) Z = 9 (eleme 9 is U - uraium) Noe: Much of his secio o Coservaio laws applied o bea decay goes beyod he Physics 30 curriculum. While I believe i is impora for you o udersad why he idea of a eurio was proposed ad subsequely observed, his will o be esed i he Physics 30 course. You are required o udersad decay ad + decay i erms of predicig pare ad daugher isoopes ad wriig proper decay equaios. Dr. Ro Lich

7 IV. Gamma radiaio Like he exciaio of aoms discussed i Lessos 30 ad 3, uclei also have a series of exciaio eergy levels. I he excied saes he ucleos are farher apar. As a resul, heir bidig eergy is greaer ha whe i he groud sae, ad he oal eergy of he ucleus is greaer. Whe makig a rasiio o a lower-eergy sae, a ucleus emis a gamma-ray phoo, similar o he phoo emied whe a elecro i a aom moves o a lower eergy level. However, he differece i eergy is much greaer for a ucleus oe ha he eergy scale is i MeV. Gamma decay does o chage eiher he aomic umber or he aomic mass. Ofe, a alpha or bea decay leaves he daugher ucleus i a highly excied sae. The excied ucleus he makes a rasiio o is groud sae ad emis a gamma ray. For example, whe he decay of boro- produces carbo-, he carbo ucleus is highly excied (represeed by a *) ad quickly emis a gamma ray: 0 B C 5 6 C 6 6 C The eergy of a gamma ray depeds o he eergy levels ad he degree of exciaio of he paricular ucleus. Gamma rays ca have eergies ragig from housads o millios of elecro vols. V. Biological effecs of ioizig radiaio I is required ha i addiio you read Pearso pages 808 ad 809. Ioizig radiaio cosiss of phoos ad/or movig paricles ha have sufficie eergy o kock a elecro ou of a aom or molecule, hus formig a io. The phoos usually lie i he ulraviole, x-ray, or -ray regios of he elecromageic specrum, while he movig paricles ca be he ad paricles emied durig radioacive decay. A eergy of roughly 0 o 35 ev is eeded o ioize a aom or molecule, ad he paricles ad -rays emied durig uclear disiegraio ofe have eergies of several millio ev. Therefore, a sigle paricle, paricle, or -ray ca ioize housads of molecules. The effec of radiaio o livig orgaisms depeds o he eergy i carries, is abiliy o ioize aoms ad molecules, ad he deph o which i ca peerae livig issue. The charge ad eergy of he radiaio deermie how ioizig i is. The eergy also affecs how far he radiaio ca peerae. Nuclear radiaio is poeially harmful o humas because he ioizaio i produces ca sigificaly aler he srucure of molecules wihi a livig cell. The aleraios ca lead o he deah of he cell ad eve he orgaism iself. Despie he poeial hazards, ioizig radiaio is used i medicie for diagosic ad herapeuic purposes, such as locaig boe fracures ad reaig cacer. The hazards ca be miimized oly if he fudameals of radiaio exposure, icludig dose uis ad he biological effecs of radiaio, are udersood. Dr. Ro Lich

8 Radiaio Hazards from Naural Sources Ouside he Body Radiaio Typical Peeraio Ioizaio Hazard Travels abou 5 cm i air. alpha high low Cao peerae ski. Travels abou cm i air. bea Peeraes abou cm io he body. moderae low Travels grea disaces i air. gamma low high Peeraes righ hrough he body. Alhough ad paricles are much less peeraig ha gamma radiaio, hey ca sill be exremely harmful if emied by maerial absorbed io he body, because he earby issue has a coiuig exposure o he radiaio. For example, healh scieiss have calculaed ha breahig i a speck of dus coaiig jus µg of pluoium is virually cerai o cause lug cacer wihi 30 years. Everyoe is coiually exposed o backgroud radiaio from aural sources, such as cosmic rays (high-eergy paricles ha come from ouside he solar sysem), radioacive maerials i he evirome, radioacive uclei (primarily carbo 4 6 C ad poassium 40 9K ) wihi our ow bodies, ad rado. The able o he righ liss he average biologically equivale doses received from hese sources by a perso i he Uied Saes. Accordig o his able, rado is a major coribuor o he aural backgroud radiaio. Rado is a odourless radioacive gas ad poses a healh hazard because, whe ihaled, i ca damage he lugs ad cause cacer. Rado is foud i soil ad rocks ad eers houses hrough cracks ad crevices i he foudaio. The amou of rado i he soil varies grealy hroughou he coury, wih some localiies havig sigifica amous ad ohers havig virually oe. Accordigly, he dose ha ay idividual receives ca vary widely from he average value of 00 mrem/yr. I may houses, he ery of rado ca be reduced sigificaly by sealig he foudaio agais ery of he gas ad providig good veilaio so i does o accumulae. To he aural backgroud of radiaio, a sigifica amou of ma-made radiaio has bee added, mosly from medical/deal diagosic x-rays. The effecs of radiaio o humas ca be grouped io wo caegories, accordig o he ime spa bewee iiial exposure ad he appearace of physiological sympoms: () shor-erm or acue effecs ha appear wihi a maer of miues, days, or weeks, ad () log-erm or lae effecs ha appear years, decades, or eve geeraios laer. Radiaio sickess is he geeral erm applied o he acue effecs of radiaio. Depedig o he severiy of he dose, a perso wih radiaio sickess ca exhibi ausea, vomiig, fever, diarrhea, ad loss of hair. Ulimaely, deah ca occur. The severiy of radiaio sickess is relaed o he dose received. Dr. Ro Lich

9 VI. Decay rae ad half-life Radioacive elemes do o decay all a oce. Their decay rae is govered by a logarihmic or expoeial equaio: N N o where N umber of radioacive uclei remaiig or mass remaiig or aciviy of he maerial N o origial umber of radioacive uclei or origial mass or origial aciviy of he maerial umber of half lives* *A half-life ( / ) is he ime i akes for ½ of he pare isoope o decay io he daugher isoope or he ime i akes for he radioaciviy level o decrease by ½. Half-lives ca rage from a few rilliohs of a secod o rillios of years depedig o he sabiliy of he isoope. pare daugher 3 pare 00% daugher 0% pare 50% daugher 50% pare 5% daugher 75% pare.5% daugher 87.5% Example 3 The half-life of a radioacive isoope is.5 years. If he aciviy of he origial sample of his isoope was 3. x 0 3 Bq, wha is is aciviy afer 5 years. N No 3 N 3.0 Bq 5.0y.5y N Bq Dr. Ro Lich

10 Number of pare uclei remaiig Example 4 A.0 gram sample of a radioacive isoope udergoes radioacive decay. If he half life of he isoope is 45 miues, how much of his isoope remais afer 5.0 hours? N No 6.67 N.0g 5.0h 0.75h N 0.00g 6.67 Example 5 If he aciviy of a radioacive sample of Q is 8 Bq ad 8.0 hours laer is aciviy is 7 Bq, wha is he half life of Q? N N 4 o 7Bq 8Bq 7Bq 8Bq 8.0h 4.0h We ca also use decay curves o deermie he half-life of a eleme. Whe a se of daa is give, oe ca graph he resuls ad he deermie he half-life. To deermie he half-life off a decay curve, fid a ierval o he verical axis where he mass or decay rae is decreased by ½. The half-life is he ime (horizoal axis) for ha ierval. N o N o 4 N o 8 N o 3 Time Dr. Ro Lich

11 VII. Pracice problems. Wrie he equaio for he alpha decay of pluoium-44.. Wrie he equaio for he bea-egaive decay of oxyge Wrie he equaio for he bea-posiive decay of fluorie The followig daa was colleced for he decay rae of echeium-04. Wha is he half-life of echeium-04? ime (mi) decay rae (cous/s) decay rae Time (mi) Dr. Ro Lich 36

12 VIII. Had-i assigme. How may proos ad euros are here i he ucleus of(a) oxyge-6 ad (b) i-0. Wrie he isoope symbol for each of he above elemes.. Wrie a equaio o show he bea-egaive decay of phosphorous I each of he followig equaios, deermie he emied paricle(s) i each case a. R Po? e. La Ce? U 90Th b.? f. c Nd Pr? Cl S? g. Pb Bi? Po 8Pb 6 d. Ra R? h.? Radium-6 decays o poloium-4 as follows: (a) (b) (c) (d) (e) Ra R Po Pb Bi Wha kid of paricle is emied i each of he rasmuaios labeled (a) o (e). 5. The half-life of a cerai radioacive isoope is 0 h. How much of a origial 30 g sample will remai he same radioacive isoope afer (a) 40 h? (b) 80 h? (c) 5 days? (80 g, 0 g, 5 g) 6. A experime was performed o deermie he half-life of echeium-99. The aciviy was measured ad he resuls are recorded below. Time (h) Po Aciviy (kbq) A. Plo a graph of aciviy versus ime. B. Usig he graph, deermie he half-life of echeium-99. C. Predic he aciviies for he followig imes: (i) 7 h (ii) 9 h (iii) 6 h 7. A radioacive sample was moiored for radiaio wih he followig resuls: Time (s) Aciviy (cous/s) A. Plo a aciviy - ime graph o graph paper. B. Esimae he half-life for his sample. Explai your mehod. Dr. Ro Lich 36

13 8. Sroium-8 has a half-life of 5.0 d. If you begi wih a sample havig a mass of 40 g, i how may days will you have oly 7.5 g of sroium-8 lef? (75.0 days) 9. The average aural radioaciviy of m 3 of rado gas is 0 emissios per secod, or 0 Bq. If he half-life of rado gas is 4 d, how log will i ake for m 3 of rado gas o reach a average radioaciviy of.5 Bq? (8.0 days) 0. I 9.0 days he umber of radioacive uclei decreases o oe-eighh he umber iiially prese. Wha is he half-life (i days) of he maerial? (3.0 days). Whe uraium-35 is bombarded by a euro, he fissio producs iclude zircoium-96, hree free euros, ad aoher daugher isoope. Wrie a equaio o show his uclear reacio ad he ideiy of he oher daugher isoope.. Fid he eergy i MeV released whe alpha decay covers horium-8 ( u) io radium-4 ( u). The mass of a alpha paricle is u. ( 4.86 MeV) Dr. Ro Lich