Geiger Counter Measurement of the Half-Life of 137 Ba

Transcription

1 Purpse: This labratry will use a shrt-lived 137Ba istpe and a Geiger cunter t accmplish the fllwing bjectives: Measurement f the activity f the 137 Ba surce as a functin f time. Determinatin f the half-life f the 137 Ba frm the activity versus time data. Equipment: Radiatin Mnitr (Geiger Cunter) 137 Ba Surce Dispsable Planchet Lgger-Pr, ULI, etc. Thery: tms are cmpsed f a nucleus cntaining neutrns and prtns surrunded by a clud f electrns. given chemical element cntains a fixed number f prtns in the nucleus but pssibly differing numbers f neutrns. The frms f a given element having different numbers f neutrns are called istpes f this element. The cmplete descriptin f all aspects f a given istpe is given by the symbls X N where X stands fr the chemical symbl f the element, is the number f prtns which is called the atmic number, N is the number f neutrns, and is called the mass number where = 6 + N. s an example the symbl Ra stands fr the istpe f radium with 88 prtns and 138 neutrns, and thus 6 neutrns plus prtns. Other istpes f radium must als have 88 prtns but can have a different number f neutrns. Usually the 6 number f neutrns is nt displayed explicitly and the symbl is given as 88 Ra. It is inferred frm this symbl that the number f neutrns is 6 88 = 138. Sme nuclei are unstable and decay spntaneusly int ther nuclei. There are three different types f prcesses that ccur naturally and prduce natural radiactivity. In additin, there are a large number f radiactive istpes that are prduced by nuclear reactins fr istpes that n lnger appear naturally. Many such istpes are available cmmercially fr many practical uses. Presumably all the man-made radiactive istpes were naturally ccurring at ne time, but they decayed away because their half-lives were much shrter than the age f the earth. Fr all types f radiactivity the prcess is identified by the type f particle prduced in the decay. lpha decay is a prcess by which an unstable nucleus ejects a particle called an 4 alpha particle. In fact an alpha particle is really just a twice inized He atm. Thus an 4 alpha particle is just the nucleus f an He atm cnsisting f the tw prtns and tw neutrns left when the tw electrns have been remved frm a neutral atm. The prcess in which a radiactive nucleus X decays by alpha decay is described by X He + Y r X α Y Eq f 7

2 where the symbl α stands fr the alpha particle r nucleus prduced. s an 6 example f alpha decay cnsider the case when the radiactive nucleus is 88 Ra. ccrding t Eq. 1, the decay prduces an alpha particle and a daughter nucleus f 86 Rn. Beta decay is a prcess taking place inside the nucleus which essentially amunts t either a neutrn being turned int a prtn r a prtn being turned int a neutrn. When this prcess happens either an electrn r anti-electrn (called a psitrn) is prduced. When the particle prduced is an rdinary electrn, it is called a β - and when the particle prduced is a psitrn, it is called a β +. The prcess in which a radiactive nucleus X decays by ne f the beta decay events is described by ne f the equatins shwn belw: 4 He 1 + X β + Y r X β + Y Eq ctually, Eqs. are nt cmplete. In each case there is in fact anther particle created called a neutrin r an antineutrin. These particles interact very weakly with matter and are extremely difficult t detect. They culd nt be detected by the detectin prcess that 40 will be used in tday s labratry. s an example f Eqs. the radiactive nuclide K decays bth by β + and β -. In the case f β - 40 decay the daughter nucleus is Ca and in the case f β + 40 decay the daughter nucleus is 18 r. Many nuclides that underg beta decay nly d s by ne f the prcesses. Gamma decay is a prcess in which a nucleus that has an excess f energy lwers its energy state by the emissin f a high energy phtn called a gamma ray. The prcess is very much analgus t the prcess whereby excited atms lse energy when they emit visible light phtns. The decay is described by X * X + γ 0 Eq. 3 where the * indicates the excess energy, and γ is the symbl fr a gamma ray r phtn. Nte that when gamma emissin ccurs there is n change in the nucleus as far as the number f prtns r neutrns. Only the energy f the nucleus is altered. basic cncept f radiactive decay is that the prbability f decay fr each type f radiactive nuclide is cnstant. In ther wrds, there are a predictable number f decays per secnd even thugh it is nt pssible t predict which nuclei amng the sample will decay. quantity called the decay cnstant λ characterizes this cncept. It is the prbability f decay per unit time fr ne radiactive nucleus. The fundamental cncept is that because λ is cnstant, it is pssible t predict the rate f decay fr a radiactive sample. The value f the cnstant λ is, f curse, different fr each radiactive nuclide. Cnsider a sample f N radiactive nuclei with a decay cnstant f λ. The rate f decay f the nuclei is related t λ and N by the equatin = λn Eq f 7

3 The symbl stands fr the rate f change f N with time t. The minus sign in the equatin means that must be negative because the number f radiactive nuclei is decreasing. The number f radiactive nuclei at t = 0 is designated as N. The questin f interest is hw many radiactive nuclei N are left at sme later time t. The answer t that questin is fund by rearranging Eq. 4 and integrating it, subject t the cnditin that N = N at t = 0. The result f that prcedure is: N λt = N e Eq. 5 Eq. 5 states that the number f nuclei N at sme later time t decreases expnentially frm the riginal number N that are present. secnd questin f interest if the value f f the radiactive sample. That can be fund by substituting the expressin fr N frm Eq. 5 back int Eq. 4. The result is λt = λn e Eq. 6 Furthermre, the expressin fr in Eq. 4 can then be substituted int Eq. 6 leading t λn = λn e λt Eq. 7 The quantity λn is called the activity f the radiactive sample. Since λ is the prbability f decay fr ne nucleus, the quantity λn is the number f decays per unit time fr N nuclei. Typically λ is expressed as the prbability f decay per secnd and s in that case, λn is the number f decays per secnd frm a sample f N nuclei. The symbl is used fr activity ( = λn) and thus Eq. 7 becmes e λt = Eq. 8 Eqs. 5 and 8 state that bth N, the number f nuclei, and, the activity, decay expnentially accrding t the same expnential factr. Fr measurements made n real radiactive nuclei the activity is usually measured. nther useful frm f Eq. 8 can be derived by inverting the equatin and taking the natural lgarithm f bth sides f the equatin leading t ln( ) = λt Eq. 9 n imprtant cncept assciated with radiactive decay prcesses is the cncept f half-life. The time fr the sample t g frm the initial number f nuclei N t nehalf that value N is defined as the half-life t ½. If Eq. 5 is slved fr the time t when N = N the result is ln() = λ 1 = λ t Eq f 7

4 This same result culd als be btained by cnsidering the time fr the activity t g frm t. In rder t study these radiactive prcesses, it is necessary t be able t detect the presence f these particles that are the prduct f the decay. lthugh there are many frms in which devices can be cnstructed t accmplish the detectin, they all have ne feature in cmmn. Every practical device that detects radiatin des s by allwing the particles t interact with matter, and then uses that interactin as the basis fr detectin. The particular device that will be used in this labratry is called a Geiger cunter. It cnsists f a tube in which the incident particle interacts and a scaling circuit t cunt the pulses. diagram f a Geiger tube is shwn in Fig. 1. The Geiger tube is a small metal cylinder with a thin self-supprting wire alng the axis f the cylinder. The wire is insulated frm the cylinder. The cylindrical wall f the tube serves as the negative electrde (cathde), and the wire alng the axis is the psitive electrde (ande). t the entrance end f the tube there is a thin windw frmed by a very thin piece f fragile mica. Inside the cunter is a special gas mixture that is inized by any radiatin that penetrates the windw. In peratin a vltage is applied acrss the electrdes. The applied vltage creates a large electric field in the tube and the field is especially large in the regin near the central wire. When radiatin passes thrugh the windw and inizes the gas, the large electric field causes an acceleratin f the free electrns. These accelerated electrns cause additinal inizatins creating what is referred t as an avalanche effect. The ttal number f in-electrn pairs created by a single incident particle is f the rder f ne millin. Cathde Incident Radiatin Vltage applied between the ande and the cathde Windw nde Figure 1 Diagram f the essential elements f a Geiger tube. The electrns are mre mbile and drift tward the psitive central wire. When they arrive at the wire their negative charge causes the vltage f the wire t be lwered, and this sudden drp in vltage creates a pulse which is cunted by the electrnic circuitry. Each pulse cunted signifies the passage f a particle thrugh the cunter. The ins recmbine with electrns, leaving the gas neutral again and ready fr the passage f anther particle. The whle prcess takes a time f the rder f 300 micrsecnds, and during that time if anther particle ges thrugh the cunter, it may nt be cunted. Thus ne disadvantage f Geiger cunters is the dead time during which cunts may be missed. This is a negligible effect unless the cunt rate is very high. 4 f 7

5 Experiment: Part : Halflife f Ba Plug a Radiatin Mnitr int DG1 f a ULI. Make sure yu d nt have the radiatin mnitr with a nte n the back saying it des nt wrk with Lgger Pr.. Open file named halflife.mbl frm the Experiments flder n the desktp f yur cmputer. If the file halflife.mbl des nt exist, click n the Lgger Pr icn t start it running. Once it is up, g t File > Open > Lgger Pr > Experiments > Prbes and Sensrs > Radiatin Mnitr > Cunts vs. time.mbl. This will pen the crrect experiment file. 3. We nw need t determine the amunt f backgrund radiatin. With n radiactive surce near the windw f the radiatin mnitr, click the Cllect buttn and cllect data fr 300 secnds (5 minutes). The file shuld be set up t autmatically cllect data in 5-secnd intervals. When yu have reached the end f the cllectin time, use the nalyze > Examine functin t determine the average number f radiatin cunts per interval. 4. G t Setup > Data Cllectin > Sampling and change the length f the experiment t 600 secnds (10 minutes). 5. The 137 Ba istpe must be prepared at the time f its use because it has such a shrt half-life. Yu must be cmpletely ready t take data befre getting yur sample. Yu shuld set the radiatin mnitr n its end s that the Geiger windw pints upward (tward the ceiling). Yu will be placing the planchet directly n the screen prtecting Geiger windw, being VERY CREFUL nt t spill the istpe. ny radiactive substance spilling int the windw will ruin the Geiger cunter. 6. Obtain the istpe sample frm yur instructr. Gently place the planchet n the radiatin mnitr. Immediately click Cllect. Nw sit back and let the cmputer take data. 7. When yu are dne, carefully remve the planchet frm the radiatin mnitr. Pur the remaining liquid dwn the sink and thrughly rinse and dry the planchet. 8. Repeat the entire prcedure, if required by yur instructr. nalysis: Part : Half life f Ba Cpy the time and radiatin data int Graphical nalysis s that yu can manipulate the data. Duble-click n each clumn heading t re-name the clumn. The unit f time is secnds, and radiatin has n units. 5 f 7

6 . T subtract the average backgrund radiatin cunts per time interval frm each radiatin data pint, g t Data > New Calculated Clumn. In the dialg bx that pps up, title the new clumn cunts, and in the Equatin area chse Variables > radiatin, then subtract yur number f backgrund cunts. 3. Plt a graph f cunts vs. time. Yu will wrk with this set f data t determine the half-life f 137 Ba. 4. Remember that the half-life is defined as the time it takes fr half f the riginal sample t decay. The number f nuclei, N, is directly related t the activity,, which is essentially what yu have graphed. Yu can make a direct estimate f the half life, and its uncertainty, by finding the time, t ½, at which (t) = ½. 5. Determine, frm yur data, hw t find λ, the decay prbability. Determine als, the uncertainty in λ. 6. Once yu have the decay prbability, yu can calculate the half-life frm Eq Calculate the percent difference between the half-life determined in Step 4, and that determined in Step D yur values fr t ½ agree within uncertainties? Results: Write at least ne paragraph describing the fllwing: what yu expected t learn abut the lab (i.e. what was the reasn fr cnducting the experiment?) yur results, and what yu learned frm them Think f at least ne ther experiment might yu perfrm t verify these results Think f at least ne new questin r prblem that culd be answered with the physics yu have learned in this labratry, r be extraplated frm the ideas in this labratry. 6 f 7

7 Clean-Up: Befre yu can leave the classrm, yu must clean up yur equipment, and have yur instructr sign belw. If yu d nt turn in this page with yur instructr s signature with yur lab reprt, yu will receive a 5% pint reductin n yur lab grade. Hw yu divide clean-up duties between lab members is up t yu. Clean-up invlves: Cmpletely dismantling the experimental setup Remving tape frm anything yu put tape n Drying-ff any wet equipment Putting away equipment in prper bxes (if applicable) Returning equipment t prper cabinets, r t the cart at the frnt f the rm Thrwing away pieces f string, paper, and ther detritus (i.e. yur water bttles) Shutting dwn the cmputer nything else that needs t be dne t return the rm t its pristine, pre lab frm. I certify that the equipment used by has been cleaned up. (student s name),. (instructr s name) (date) 7 f 7