Investigation of Uncertainty Sources in the Determination of Beta Emitting Tritium in the UAL

Transcription

1 Investgaton of Uncertanty Sorces n the Determnaton of Beta Emttng Trtm n the UL. Specfcaton lqd scntllaton conter LSC s sed to determne the actvty concentraton n Bq/dm 3 of the beta emttng trtm n rne samples. Measrement procedre For the LSC measrement a qench crve s needed. To measre the qench crve the absorpton of 99 rne samples and water had been measred wth a spectral photometer. From these reslts 13 had been selected to represent the whole absorpton spectrm from 0.05 for water p to 1.44 for a very dark colored rne sample. From each sample ml had been taken nto a low dffson plastc val and spked wth H-3 wth 10000DPM actvty. 14mL scntllaton cocktal had been added to the val. The measre conssts of the followng stages: Ppette ml Sample 14 ml Scntllaton Coctal IP Backgrond Cont LSC Cont Calbraton Qench Crve Effcency ESULT Fgre 1: H-3 Measrement 1

2 Calclaton The measrand s the H-3 actvty concentraton n Bq/L, based on the energy regon of kev, s gven by: C 60ε V 0.01 a av [Bq/L] Where: the crrent remanng actvty, [Bq/L] C the Conts ate n the regon for trtm, [cpm] ε the Interpolated Contng Effcency V a the lqot Volme, [L] av the Mean ecovery Factor, [%] the Decay Correcton Factor: ln t e T1/ e t e the Elapsed tme from the samplng date to the measrng date, [years] T 1/ the Half Lfe of Trtm, [years] The factor of 60 s sed to convert cpm to cps to obtan actvty n Bq. Effcency s the rato of measred conts to the nmber of decay events, whch occr drng a measrement nterval. The contng effcences are determned by sng effcency crves qench crve Identfyng and nalysng Uncertanty Sorces The estmaton of ncertantes contans the followng steps: Exploraton of all factors nflencng the measrement, Qantfcaton of the ncertantes connected to each factors by measrement reslts or by expert jdgment f applcable, Estmaton of the overall ncertanty of the measrement. Uncertanty Sorces Conts n the contng regon for H-3 Qench Crve Contng Effcency Sample Volme ecovery factor Measrng tme <0.1%

3 Decay correcton Temperatre The dfferent effects and ther nflences are shown as a case and effect dagram n Fgre. Qantfyng the ncertanty components For collecton and analyss of the conts comng from trtm the QantaSmart software s sed. Net Conts Determned by the evalaton software Backgrond correcton C Net C gross C backgrond where: C net the Net Conts ate for the contng regon of H-3, [cpm] C gross the Gross sm of the Sample Conts rate wthn the contng regon of H-3, [cpm] C backgrond the Backgrond Conts ate for the contng regon of H-3, [cpm] The evalaton software reports Sgma % %s parameter. Ths vale represents the percent of ncertanty n a gross cont vale wth 95% confdence lmts. It s calclated as: % s C 00 gross t Where: t Measrng tme n mntes lqot Volme ml alqot s taken wth a ppette for the Trtm analyss. The volme s sbject to three major sorces of ncertanty: The ncertanty n the certfed adjstable ppette. epeatablty of the adjsted ppette The actal temperatre dffers from the temperatre at whch the volme of the ppette was calbrated Calbraton: The manfactrer qotes an naccracy for.5ml of 1.%. rectanglar dstrbton s assmed. 3

4 1.% 0.70% 3 epeatablty: The ncertanty de to the varatons of fllng was estmated from a seres of ten fll and weght experment and gave a standard ncertanty of 0.%, whch s very smlar to the vale gven by the manfactrer. Temperatre: ccordng to the manfactrer the volmetrc ppette had been calbrated at temperatre range of 0-5 o C. s the temperatre of the laboratory s wthn ths range, the ncertanty from ths effect can be omtted. The contrbtons are combned to the standard ncertanty V as: V % Qench Crve - Effcency Qench de to color of the sample For the Qench calbraton 13 rne samples were sed and spked wth a known actvty of Trtm. ccordng to the certfcate of the reference solton the overall ncertanty for the actvty concentraton s.5% at the 99.7% confdence level. It means that the standard ncertanty s.5%/30.83%. The actvty n the Qench set s obtaned as: spke C, reference m Where: spke the Crrent ctvty n the Qench set, [dpm] C,reference the ctvty-concentraton of the reference solton, [dpm/g] T1/ the Decay Correcton Factor: e t e the Elapsed tme from the reference date to the measrng date, [years] T 1/ the Half Lfe of Trtm, [years] ln m the Mass taken from the reference solton n g The ncertanty for the actvty n the Qench set s: t e, reference m C spke spke C, reference m The manfactrer dentfes three ncertanty sorces for the tare weghng: The repeatablty The readablty dgtal resolton of the balance scale The contrbton de to the ncertanty n the calbraton fncton of the scale lnearty and senstvty. 4

5 Model eqaton: m m m m [g] rep ln read The ncertanty assocated wth the mass of the soltons s estmated sng data from the manfactrer s recommendatons for the analytcal balance model BP1S. epeatablty : the standard devaton s qoted as ± g. Normal dstrbton. eadablty : the dgtal resolton of the balance s g. rectanglar dstrbton s assmed: Lnearty g 5.77E 05g 3 : the dfference from the actal wegh on the scale pan and the readng of the scale s wthn the lmts of ±0.000 g. rectanglar dstrbton s assmed g 1.15E 04g 3 These components have to be taken nto accont twce becase of the weght by dfference. The three components are combned to gve the standard ncertanty m. m E E 04.08E 04g ln t T 1/ e T 1/.44E 05.08E 04 spke 8749dpm.15E dpm.93E E 0 Therefore the relatve standard ncertanty for the actvty n the qench set s 0.95% The cont effcency for the Qench set s calclated as: C ε 100 spke Where: ε the Cont Effcency for the th val, [%] spke the ctvty n the Qench set, [dpm] C the Conts ate n the regon for trtm for the th val, [cpm] ε ε C C spke spke 5

6 QIP Crrent ctvty, Conts ate, [cpm] Contng Effcency % tsie/ec Vale Unc. Vale Unc. Vale Unc ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± ± E ± ± For the Effcency Crve fttng there s not too mch nformaton from the software. For that reason, the OIGIN software was sed for the non-lnear crve ft of the emprcal data. In Excel the least sqare ft analyss was performed to determne the standard devaton. Excel Least Sqares ft to 0 1 *x* x^3 * x^3... TheoryCoef0 Coef1*x Coef*x^ DeltaY experment-theory SmSm of Delta Sqared Standard Error SQT Sm/n*n-1 Coeffcents Expermental Data For Least Sqares X Y Theory Delta Delta Sqared E Sm Ch Standard Sqared Unc. Sε, [%]

7 The relatve standard ncertanty for the nterpolated effcency s calclated from the combnaton of the ncertanty assocated wth the least sqare ft analyss and the combned ncertanty of the contng effcency. ε ε ε Sε ε ε Therefore the relatve standard ncertanty for the nterpolated contng effcency s 5.7% ecovery Factor For the determnaton of the recovery factor for control samples are sed wth dfferent actvtes.the records n every H-3 work lst can be fond and t s the followng: H-3 ct. Conc. on the λ 1.55E-04 1/day Std. I 9.79E05 ± 8.16E03 Bq/L Std. II 1.98E05 ± 1.64E03 Bq/L Std. III 1.01E04 ± 8.7E01 Bq/L Std. IV 1.96E03 ± 1.6E01 Bq/L The control samples were prepared sng blank rne samples and trtm reference solton. ccracy of the scntllator addton was observed to be 0.03% checkng the repeatablty of fve measrements. Ths ncertanty can be neglected. The recovery factor s calclated as: 100 ; spke,, t C ; ε 0.01V 60 a spke,, t ln te λte T1/ spke, spke, e spke, e Where: ecovery Factor n % of the th Spke Control Sample Measred ctvty Concentraton n Bq/L of the th Spke Control Sample spke,,t ctvty Concentraton n Bq/L at t elapsed tme of the th Spke Control Sample spke, ctvty Concentraton n Bq/L at reference tme of the th Spke Control Sample Decay Correcton Factor C Conts ate n CPM of the th Spke Control Sample ε Cont Effcency for the th Spke Control Sample V a lqot Volme n L taken from the th Spke Control Sample 7

8 8 λ Decay ate n 1/years for Trtm Isotope t e Elapsed Tme n years between the eference and Measrng Date T 1/ Half Lfe n years for Trtm Isotope The ncertanty for the ecovery Factors s:,, % V V s a a spke spke ε ε ln h h T T t From the for control samples the average recovery factor s calclated as: av The ncertanty of the average recovery factor s calclated as: av Wth ths formla n GUM Workbench we can take nto accont the proportonal relevance of each component, rather than treatng each component eqally. To redce the effect of photolmnescence and statc electrcty the samples are placed n the conter, whch s refrgerated for two days. t ths tme the temperatre of the samples and the conter shold be the same. Combned Standard Uncertanty The relatve standard ncertanty for the decay corrected actvty concentraton s calclated as: % V V s av av ε ε Envronmental effects

9 For the determnaton of the combned standard ncertanty the GUM Workbench wll be sed. Fle Evalaton Software eport Combnng elatve Standard Uncertanty GUM Workbench _ % 6.06% 6.0% Practcal Example Intercomparson 004 Sample C Fle _133 eference Date Measrng date: Method Evalaton Software Investgated ttached Table below ttached Qantfed Uncertanty by dfferent methods Descrpton Uncertanty n 1s Conts n the regon of kev 0.79 statstcal Posson dstrbton * * Sqare of combned ncertanty of the above factors 0.6 Interpolated Contng Effcency ncldes * 5.7 Spked ctvty * lqot taken * Decay correcton * Conts Posson dstrbton * Crve Fttng * Sqare of combned ncertanty of the above factors 7.77 ecovery ncldes *.81 Control samples average * Interpolate Contng Effcency * Conts Posson dstrbton * Volme of Control alqot * Sqare of combned ncertanty of the above factors 7.90 Volme of Sample alqot 0.73 Decay Correcton <0.1 Sqare of combned ncertanty of the above factors 0.53 Expert Jdgment Lmnescence and statc electrcty < 0.1 The overall combned ncertanty for the actvty n ths example s: % at 1 sgma relablty 9

10 ef./samplng Date Measrng Date Spreadsheet calclaton of trtm measrement ncertanty Half Lfe / E01 ± 0.1 years E E01 ± 0.1 years E-05 Name: Sample C CPM Effcency Volme Decay Factor ecovery I ecovery II ecovery III ecovery IV ecovery V Vale 1.69E0 cpm 0.%.00E-03 L % 86.75% 89.5% 84.59% 87.1% elatve Standard Uncertanty 1.57 % 5.7 % 0.73 % 3.9E-03 % 0.0 % 0.45 %.08 % 5.80 % 5.40 % 5.40 % 5.50 % 6.13 %.81 % CPM Effcency 0.0% 0.0% 1.6% 0.0% 0.0% 0.% Volme.00E-03.00E-03.00E-03.01E-03.00E-03.00E-03 Decay Factor 9.96E E E E E E-01 ecovery V 87.1% 87.1% 87.1% 87.1% 87.1% 89.57% ctvty conc. 8.04E03 Bq/L 8.10E E E E03 7.8E E01-4.0E0-5.83E E E0.14E E03 1.6E E E-0 4.8E E0 Bq/L 5.76 % σ: 8.04E03 Bq/L / % 10

11 Uncertantes n Trtm Measrement ecovery V Decay Factor Volme Effcency CPM ctvty conc % 1.00 %.00 % 3.00 % 4.00 % 5.00 % 6.00 % 7.00 % elatve Standard Uncertanty Ths graph shows the dfferent contrbtons to the measrement ncertanty of the actvty concentraton of H-3. 11

12 CPM sample ecovery Backgrond Correcton T 1/ Certfcate eference V eference CPM Control Backgrond Correcton Control Calbraton Ppette epeatablty Calbraton Ppette ε Qench epeatablty V Control eference T 1/ C Trtm V standard epeatablty Certfcate Standard Calbraton Ppette Calbraton Ppette Standard epeatablty T 1/ ε Qench Expert Jdgmentt V Sample Fgre. Case and effect dagram: Uncertantes n Trtm measrement 1