Chapter 13: Radioactivity

Transcription

1 Chaptr 13: Radioactivity 13.1 Radioactivity Dcay L.O Explain and dcays Radioactivity / Radioactiv dcay is disintgration of unstabl nuclus to a mor stabl daughtr nuclid with th mission of alpha, bta particls and gamma ray. Radioactiv dcay is a spontanous and random procss. Random mans th tim of dcay of ach atom cannot b prdictd. Spontanous mans it happns by itslf without xtrnal stimuli (unplannd). Th dcay is unaffctd by normal physical or chmical procsss, such as hat, prssur and chmical ractions. 3 kinds of rays ar producd by naturally occurring radioactivity: alpha particl (α), bta particl (β) and gamma rays (γ). lpha Dcay (α) 4 n -particl is a H nuclus consists of two protons and two nutrons. It is positivly chargd particl and its valu is + with mass of 4.15 u. lpha particl has last pntrating ability, can b blockd by a sht of papr. Its motion can b dflctd by both magntic fild & lctric fild. Whn a nuclus undrgos alpha dcay it loss 4 nuclons ( protons and nutrons). Th raction can b rprsntd by gnral quation blow: Z X Z 4 4 Y H Parnt Daughtr α-particl Enrgy rlasd Q 1

2 Bta Dcay (β) Bta particl has sam mass as an lctron or.549 u.. Bta particl can b lctrically positiv ( β + or positron ) or ngativ ( β - or ngatron ) o Symbol for positron: o Symbol for ngatron: 1 or, 1 1 or, 1 Bta particl has modrat pntrating ability and blocks by a fw millimtrs aluminum. Its motion can b dflctd by both magntic fild & lctric fild. typ of bta dcay: o o ngatron, β - dcay positron, β + dcay ngatron, β - dcay β - dcay occurs whn an unstabl nuclus has too many nutrons compard with th numbr of protons. Through th β - dcay, a nutron is convrtd into a proton and crats a mor stabl daughtr nuclus. Gnral form for β dcay is Z X 1Y 1 v Z nothr lmntary particl calld antinutrino ( v ) mittd in this dcay. Existnc of antinutrino is a must in ordr to oby th law of consrvation of nrgy & angular momntum (to account th missing nrgy in ngatron dcay). Exampl: Parnt Daughtr β-particl ntinutrino Enrgy rlasd Q

3 positron, β + dcay β + dcay occurs whn an unstabl nuclus has too many protons compard with th numbr of nutrons. Through th β + dcay, a proton is convrtd into a nutron and crats a mor stabl daughtr nuclus. Gnral form for β + dcay is Z X 1Y 1 v Z nothr lmntary particl calld nutrino (v) mittd in this dcay. Existnc of nutrino is a must in ordr to oby th law of consrvation of nrgy & angular momntum (to account th missing nrgy in positron dcay). Exampl: Parnt Daughtr β-particl utrino Enrgy rlasd Q Gamma Dcay (γ) Gamma ray is a high nrgy photon. It is unchargd (nutral) and zro mass (mission of gamma ray dos not chang th parnt nuclus into a diffrnt nuclid). Gamma ray has th most pntrating ability a fw cntimtrs in lad. It cannot b dflctd by any magntic fild. Gamma rays ar mittd whn an xcitd nuclus jumps to lowr nrgy lvl. Vry oftn, a nuclus is lft in an xcitd nrgy stat aftr it has undrgon alpha or bta dcay. This nuclus can thn undrgo nd dcay to lowr nrgy lvl by mitting a high nrgy photon calld gamma (γ) ray. Th dcay can b writtn as: Z X * Excitd nrgy stat Z X Lowr nrgy 3 stat γ-ray

4 Comparison of th proprtis btwn alpha particl, bta particl and gamma ray. Dflction in lctric fild Dflction in magntic fild Exampl Qustion Solution Writ an quation to rprsnt th dcay. What is th wavlngth of th.186 MV γ-ray 6 photon mittd by radium Ra 88? 4

5 d L.O Stat dcay law and us Law of radioactiv dcay stats that for a radioactiv sourc, th rat of dcay ( d/ ) is proportional to th numbr of radioactiv nucli prsnt (or not yt dcayd),. Mathmatically, d gativ sign mans th numbr of nucli prsnt dcrass with tim Dcay constant L.O Dfin and dtrmin activity, and dcay constant, From d, w gt d Dcay constant, λ is th ratio of rat of dcay to th numbr of radioactiv atoms in sampl. SI unit for dcay constant, λ: s -1 Th dcay constant is a charactristic of th radioactiv nuclid. It has diffrnt valus for diffrnt nuclids. Th largr th dcay constant, th gratr is th rat of dcay. ctivity, of a radioactiv sampl is dfind as th numbr of dcays (or disintgrations) pr scond that occur. d SI unit for activity, : Bcqurl (Bq) o 1 Bq = 1 dcay pr scond nothr SI unit usually usd: Curi ( Ci ) o 1 Ci = Bq 5

6 L.O Driv and us t or t From th basic law of radioactiv dcay: d Rarranging th quation: d Suppos that at tim t = s, th numbr of undcayd nucli in th radioactiv sampl is o t tim t = t, lt th numbr of undcayd nucli lft is Intgrat th abov quation: d ln t t t ln t t t This quation is calld xponntial law of radioactiv dcay. It stats that th disintgration or radioactiv dcays of a radioactiv substanc rducs xponntially with tim. From th law of radioactiv dcay, d and dfinition of activity, d and t t t and t ctivity at tim t ctivity at tim t = 6

7 L.O Dfin and us half lif Graph of (numbr of rmaining nuclus) vrsus t (dcay tim) Th dcay rat of a nuclid is commonly xprssd in trms of its half-lif rathr than th dcay constant. Half-lif T ½ is dfind as tim rquird for th numbr of radioactiv nucli to dcras to half of th original numbr of nucli. From t, whn t = T ½ and : T1 1 T1 1 T T 1 ln ln T 1 Th half-lif of any givn radioactiv nuclid is constant; it dos not dpnd on th numbr of nucli prsnt. Th units of th half-lif ar scond (s), minut (min), hour (hr), day and yar (yr). 7

8 Exampl Qustion Th half lif of th radioactiv nuclus Radium, 6 88 Ra is yar. a) What is th dcay constant of this nuclus? b) If a sampl contains Ra nucli at t = s, dtrmin its activity at this tim. c) What is th activity aftr sampl is. 1 3 yar old? Solution Initially, a radioactiv sampl contains of nucli. Th half-lif of th sampl is T 1/. Calculat th numbr of nucli prsnt aftr.5t 1/. 8% of a radioactiv substanc dcays in 4 days. Dtrmin a) th dcay constant b) its half lif radioactiv sampl contains 3.5 µg of pur C, which has a half lif of.4 min. a) Dtrmin th numbr of nucli in th sampl at t = s. b) What is th activity in Bcqurl of th sampl initially and aftr 8. h? c) Calculat th numbr of radioactiv nucli rmaining aftr 8. h? 8

9 Exrcis Qustion radioactiv sourc contains g of Pu-39. If th sourc mits 3 alpha particls pr scond, calculat a. th dcay constant b. th half-lif (Givn vogadro constant, = mol -1 ) nswr: s -1 ; s Thorium-34 has a half-lif of 4 days. Th initial activity of this isotop is 1 Ci. Calculat a. th activity of th isotop aftr 7 days b. th tim takn for th activity to fall to.5 Ci nswr: 1.5 μci; 48 days uranium-38 isotop which has a half-lif of 4.47 x 1 9 yars dcays by mitting alpha 34 particl into thorium-34 nuclus 9 Th. Calculat a. th dcay constant b. th mass of uranium-38 rquird to dcay with activity of 6. Ci c. th numbr of alpha particls pr scond for th dcay of 3. g uranium-38 nswr: yars -1 ; g; particls/scond Th half-lif of Radon Rn is 4. s. 19 a. What do th numbrs 86 and 19 rprsnt in th symbol 86 Rn? 19 b. Calculat th dcay constant of 86 Rn. c. Givn that 19 g of Radon contains atoms, calculat th rat of disintgration 19 of 1. g of Rn 86. nswr:.173 s -1, Bq Radioactiv can b usd for radioactiv dating, i.. a mthod to dtrmin th ag of an artifact basd on dcay rat and half-lif of carbon-14. Th half-lif of carbon-14 is known to b 56 yars. If a 1 gram of carbon sampl from a liv tr givs th dcay rat of 5 pr hour and a 1 gram sampl from an artifact givs dcay rat of 1 pr hour, calculat th ag of th artifact. nswr: yars 9

10 13. Radioisotops as tracrs L.O Explain th application of radioisotops as tracrs. Radioisotop (unstabl isotop) is an isotop which is xhibits radioactivity (known as radioactiv isotop). Sinc th proprtis of radioactiv nuclids such as half-lif and th particl mission ar unaffctd by xtrnal factors such as prssur, tmpratur and chmical composition, radioisotops ar suitabl as tracrs. Th progrss of a small amount of a wak radioisotop injctd into a systm can b tracd by a dtctor. i) To invstigat mtabolic pathways or blood flow: 1. small quantity of iodin-131 is injctd into a patint s bloodstram and latr builds up in th kidnys. Th procss of th iodin is masurd by a dtctor outsid th body around th kidny rgion. If thr is a blockag, th count rat will ris.. It is usd to invstigat organs in human body such as kidny, thyroid gland, hart, brain, and tc 3. It also usd to monitor th blood flow and masur th blood volum. 4. Th volum of blood in th bloodstram, V can b dtrmind by using dilution mthod as givn blow. 1 V 1 V whr 1 = activity pr unit volum of th blood drawn from th patint V 1 = activity pr unit volum of th blood in th blood stram V Exampl Qustion small volum of a solution which contains a radioactiv isotop of sodium a-4 has an activity of Bq. Th solution is injctd into th bloodstram of a patint. Th half-lif of th sodium isotop is 15 hours. ftr 3 hours, th activity of 1. cm 3 of blood is masurd and found to b.5 Bq. Estimat th volum of blood in th patint. Solution 1

11 ii) Dtcting laks in undrground pips: 1. Th xact position of an undrground pip can b locatd if a small quantity of sodium-4 is addd to th liquid bing carrid by th pip.. Gigr countr can b usd to dtct th laks. 3. ny laks would b dtctd by an incras in radiation rading. 4. Th soil clos to th lak bcoms radioactiv. 5. Th short-livd radioisotop is usd to avoid from th prmannt contamination of th soil. iii) Dtcting brain tumors: 1. Tchnitium-99 is a gamma mittr (half-lif 6 hours) and is usd as a mdical tracr.. Whn injctd into th blood stram, 99 Tc will not b absorbd by th brain, bcaus of th blood-brain barrir. 3. Howvr, tumors do not hav this barrir. Thus, brain tumors radily absorb th 99 Tc. 4. Ths tumors thn show as gamma-ray mittrs on dtctors xtrnal to th body. 5. Th short-livd radioisotop is usd so that it can quickly liminat from th body. 6. Othr radioisotops usd in mdicin: dtrmin th nlargmnt of thyroid gland with iodin I-131 dtrmin th location of blood clogs with 4 a 11

12 iv) To masur th war and tar of machin part and th ffctivnss of lubricants: 1. Th rat at which th piston in an ngin xprinc war and tar whn using diffrnt typs of lubricating oil can b dtrmin using a suitabl radioactiv tracr such as iron-56.. small amount of tracr is addd to th mtal that is usd to mak th piston. 3. If th ngin is running, th mtal that wars off from th piston falls into th lubricating oil. 4. By masuring th activity of th lubricating oil using a G-M tub, th rat of war and tar can b calculatd. 5. Th tst can thn b rpatd using diffrnt lubricating oil to dtrmin which oil causs th last war and tar. v) Carbon-14 dating 1. Carbon-14 is a radioisotop with a long half-lif of 56 yars.. Th bombardmnt of nutrons in cosmic rays from outr spac with nitrogn in th atmosphr producs carbon Th rat of formation of carbon-14 is qual to that of th rat of dcay. Th ratio of carbon-14 to th stabl carbon-1 in atmosphr is constant. 4. Living things absorb carbon-14 in carbon dioxid through photosynthsis and rspiration. Thrfor th ratio of carbon-14 to th stabl carbon-1 in living things is qual to that in atmosphr. 5. Whn a living thing dis, th activity of carbon-14 in th dad animals or plants dcrass with tim bcaus rspiration and photosynthsis stop. 6. By masuring th activity of carbon-14 of a living carbon, th archaological ag of th spcimn can b stimatd. 7. Othr than carbon-14 dating, gologists us rlativs dating tchniqu (which com first) and absolut dating tchniqu (ratio) to dtrmin th ag of fossils and th ag of rocks. This is Su th largst & most complt tyrannosaurus rx vr found. It is currntly on display at th Fild Musum in Chicago. Palontologists us th disintgration of radioactiv nucli to dat th fossil rmains of xtinct spcis. 1