{"text_format":"1","workbook":"xlsx","n_sheets":8,"sheets":["Basic Analysis","Basic Graphs","AlphaSpec","Gross αβ","Gross αβ Graph","Gamma","Gamma Graphs","Lookup Tables"],"not_rendered":{"charts":5,"images":0,"macros":1,"external_links":0,"defined_names":199,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Basic Analysis","index":0,"n_rows":31,"n_cols":10,"rows_kept":31,"cut":false,"hidden":false,"merged":[[0,1,0,5],[28,0,28,7],[8,1,8,2],[9,1,9,2],[10,1,10,2],[3,1,3,2],[4,1,4,2],[5,1,5,2],[6,1,6,2],[7,1,7,2],[24,0,24,8],[25,0,25,8],[26,0,26,8],[23,0,23,8]]}
[null,"Basic Analysis"]
[]
[]
[null,"Activity unit =",null,"pCi",null,null,null,"Sample count time, tS =",100.0951093328682,"min"]
[null,"Analytical action level, AAL =",null,5,null,null,null,null,{"$f":"IF(RAND()>=0,\"\",\"Force a calculation after every edit\")","v":""}]
[null,"Required relative method uncertainty, ϕMR =",null,0.1,null,null,null,"ϕM =",{"$f":" IFERROR(SQRT((R.S / t.S + R.B / t.B) / R.N^2 + urel_D^2 + urel_DF^2), \"\")","v":0.1},{"$f":"IF(RAND()>0,\"\",\"\")","v":""}]
[null,"Required detection limit, MDCR =",null,1,null,null,null,"MDC =",{"$f":"IFERROR(getGSmdc(t.S, R.B, 1/t.S+1/t.B, (F.A*D*DF)), \"\")","v":1.0455523373262736}]
[null,"Background, RB =",null,1,"cpm"]
[null,"Bkgd count time, tB =",null,3000,"min",null,null,"Half-life, T1/2 =",{"$f":"VLOOKUP(Nuclide, Nuclide_Table[], 2, FALSE)","v":6.15},{"$f":"VLOOKUP(Nuclide,Nuclide_Table[],4,FALSE)","v":"h"}]
[null,"Sample decay time, tD =",null,5,"h",null,null,"urel(T1/2) =",{"$f":" IFERROR(VLOOKUP(Nuclide, Nuclide_Table[], 3, FALSE) / T.12, \"\")","v":4.878048780487804E-3}]
[null,"Nuclide =",null,"Ac-228",null,null,null,"Ft.D =",{"$f":"VLOOKUP(Unit_t.D, Time_Unit_Table[], 2, FALSE) / 60","v":60},{"$f":"IF(Unit_t.D=\"min\",\"\",\"min/\"&Unit_t.D)","v":"min/h"}]
[null,null,null,null,null,null,null,"FA =",{"$f":"VLOOKUP(Unit_Activity, ActUnit_Table[], 2, FALSE) * 60","v":2.2199999999999998},{"$f":"IF(Unit_Activity=\"dpm\",\"\",\"dpm/\"&Unit_Activity)","v":"dpm/pCi"}]
[null,null,"Divisor","Value","urel",null,null,"Decay constant, λ =",{"$f":" IFERROR( VLOOKUP(Nuclide, Nuclide_Table[], 5, FALSE), \"\")","v":1.8784476437938896E-3},"min−1"]
[null,null,"V",1,5.0000000000000001E-3,null,null,"Product of divisors, D =",{"$f":" IFERROR(PRODUCT(Main_Factor_Table[Value]), \"\")","v":0.30000000000000004}]
[null,null,"ε",0.4,0.01,null,null,"urel(D) =",{"$f":" IFERROR(SQRT(SUMSQ(Main_Factor_Table[urel])), \"\")","v":2.7386127875258306E-2}]
[null,null,"Y",0.75,2.5000000000000001E-2,null,null,"Decay before counting, DBC =",{"$f":"EXP(-λ * t.D * F.t.D)","v":0.56919380692610444}]
[null,null,"I",1,0,null,null,"Decay during counting, DDC =",{"$f":"IFERROR(DDCf(λ * t.S),\"\")","v":0.91161355594479931}]
[null,null,null,null,null,null,null,"Total decay factor, DF =",{"$f":"IFERROR(DBC * DDC, \"\")","v":0.51888479035366364}]
[null,null,null,null,null,null,null,"urel(DF) =",{"$f":"IFERROR(urelDF(λ, urel_T.12, t.D*F.t.D, t.S), \"\")","v":3.193178884899537E-3}]
[null,null,null,null,null,null,null,"Net count rate, RN =",{"$f":"IFERROR(D * DF * AAL * F.A, \"\")","v":1.7278863518777001},"cpm"]
[null,null,null,null,null,null,null,"Gross count rate, RS =",{"$f":"IFERROR(R.N + R.B, \"\")","v":2.7278863518777001},"cpm"]
[]
[]
["Options:"]
["1. Calculate the count time for a required relative method uncertainty at the AAL."]
["2. Calculate the count time for a required MDC."]
["3. Enter the count time manually."]
[]
["Model: AC = (RS − RB) / ((product of divisors) × DF)"]
[null,null,null,null,null,null,null,5,"iterations"]
[null,null,"pw=Keith"]

{"sheet":"Basic Graphs","index":1,"n_rows":65,"n_cols":11,"rows_kept":65,"cut":false,"hidden":false,"merged":[[64,10,64,22]]}
["Paired =",false]
["tS","tB","DDC","DF","RN","RS","ϕM","ϕMR","MDC","MDCR"]
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[]
[]
[]
[]
[]
[null,"Testing…"]
["n =",2]
[null,"x","ddcn(x)","test","DDC1","DDC","0","1","2"]
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[null,3,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":4.2726660657270855E-2},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":4.2726660657270855E-2},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-8.8983525169838248E-2},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":0.31673764387737868},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":0.31673764387737868},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-8.8983525169838248E-2},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":4.2726660657270855E-2}]
[null,4,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":2.380927170145174E-2},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":2.380927170145174E-2},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-5.677636284727057E-2},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":0.24542109027781644},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":0.24542109027781644},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-5.677636284727057E-2},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":2.380927170145174E-2}]
[null,5,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":1.4005567688270703E-2},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":1.4005567688270703E-2},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-3.8382892720219483E-2},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":0.1986524106001829},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":0.1986524106001829},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-3.8382892720219483E-2},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":1.4005567688270703E-2}]
[null,6,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":8.6854740331790831E-3},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":8.6854740331790831E-3},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-2.7295798187870431E-2},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":0.16625354130388895},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":0.16625354130388895},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-2.7295798187870431E-2},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":8.6854740331790831E-3}]
[null,7,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":5.6580981697928754E-3},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":5.6580981697928754E-3},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-2.0259284577052325E-2},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":0.14272687400492079},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":0.14272687400492079},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-2.0259284577052325E-2},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":5.6580981697928754E-3}]
[null,8,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":3.852523563499988E-3},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":3.852523563499988E-3},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-1.557782556795121E-2},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":0.12495806717151219},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":0.12495806717151219},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-1.557782556795121E-2},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":3.852523563499988E-3}]
[null,9,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":2.7263862960044518E-3},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":2.7263862960044518E-3},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-1.2330443234063375E-2},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":0.11109739891065704},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":0.11109739891065704},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-1.2330443234063375E-2},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":2.7263862960044518E-3}]
[null,10,{"$f":"IFERROR((-1)^n*logamma(n+1,Testing_Table[[#This Row],[x]])/(Testing_Table[[#This Row],[x]]^(n+1)),\"\")","v":1.9944612085689766E-3},{"$f":"ddcnf(n,Testing_Table[[#This Row],[x]])","v":1.9944612085689766E-3},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-9.995006007726126E-3},{"$f":"DDCf(Testing_Table[[#This Row],[x]])","v":9.9995460007023751E-2},{"$f":"IFERROR(logamma(1,Testing_Table[[#This Row],[x]])/Testing_Table[[#This Row],[x]],\"\")","v":9.9995460007023751E-2},{"$f":"DDC1f(Testing_Table[[#This Row],[x]])","v":-9.995006007726126E-3},{"$f":"ddc2f(Testing_Table[[#This Row],[x]])","v":1.9944612085689766E-3}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Note: A semi-log plot is better than a linear plot. A log-log plot straightens the curve even more but may be less intuitive."]

{"sheet":"AlphaSpec","index":2,"n_rows":35,"n_cols":9,"rows_kept":35,"cut":false,"hidden":false,"merged":[[33,3,33,4],[34,3,34,4],[0,1,0,4],[29,3,29,4],[30,3,30,4],[31,3,31,4],[32,3,32,4]]}
[null,"Alpha-Particle Spectrometry with Tracer"]
[]
[]
[null,"Result unit =","pCi","by",{"$f":" VLOOKUP(Unit_Result, ConcUnit_Table[],4,FALSE)","v":"Total"},null,"Sample count time, tS =",99.962206531279364,"min"]
[null,"Analytical action level, AAL =",1.2]
[null,"Required relative method uncertainty, ϕMR =",0.2,null,null,null,"ϕM =",{"$f":"IFERROR(SQRT( (R.SA/t.S+R.BA/t.B) / R.NA^2 + (R.ST/t.S+R.BT/t.B) / R.NT^2 + urel_V.A^2 + urel_I.A^2 + urel_DF.A^2 + urel_c.T^2 + urel_V.T^2 + urel_I.T^2 + urel_DF.T^2), \"\")","v":0.2},{"$f":"IF(RAND()>0,\"\",\"\")","v":""}]
[null,"Required detection limit, MDCR =",1,null,null,null,"MDC =",{"$f":"IFERROR(getGSmdc(t.S, R.BA, 1/t.S+1/t.B, (F.Res*ε*Y*V.A*F.V.A*I.A*DF.A)), \"\")","v":0.18639077397448761},{"$f":"Unit_Result","v":"pCi"}]
[null,"Sample aliquot, VA =",1,null,{"$f":" IF( IF(Unit_V.A=\"\", Type1, VLOOKUP(Unit_V.A, Aliquot_Unit_Table[], 2, FALSE)) = Type_Res, Type_Res, \"Mismatch\")","v":"Total"}]
[null,"urel(VA) =",1E-3,null,null,null,"Half-life, T1/2(Analyte) =",{"$f":"VLOOKUP(Analyte, Nuclide_Table[], 2, FALSE)","v":138.37629999999999},{"$f":"VLOOKUP(Analyte,Nuclide_Table[],4,FALSE)","v":"d"}]
[null,"Analyte alpha intensity, IA =",1,null,null,null,"urel(T1/2) =",{"$f":"VLOOKUP(Analyte, Nuclide_Table[], 3, FALSE) / T.12A","v":1.2285340770059613E-5}]
[null,"urel(IA) =",0,null,null,null,"Half-life, T1/2(Tracer) =",{"$f":"VLOOKUP(Tracer, Nuclide_Table[], 2, FALSE)","v":102},{"$f":"VLOOKUP(Tracer,Nuclide_Table[],4,FALSE)","v":"a"}]
[null,"Efficiency, ε =",0.15,null,null,null,"urel(T1/2) =",{"$f":"VLOOKUP(Tracer, Nuclide_Table[], 3, FALSE) / T.12T","v":4.9019607843137254E-2}]
[null,"Yield, Y =",0.75,null,null,null,"Analyte decay constant, λA =",{"$f":" IFERROR(VLOOKUP(Analyte, Nuclide_Table[], 5, FALSE), \"\")","v":3.4785740673958207E-6},"min−1"]
[null,"Analyte background, RBA =",3.0000000000000001E-3,"cpm",null,null,"Tracer decay constant, λT =",{"$f":" IFERROR(VLOOKUP(Tracer, Nuclide_Table[], 5, FALSE), \"\")","v":1.2920575205059492E-8},"min−1"]
[null,"Background count time, tB =",3000,"min",null,null,"Decay before counting, DBCA =",{"$f":"EXP(-λ.A * t.DA * F.t.DA)","v":0.97526530892184993}]
[null,"Analyte decay time, tDA =",5,"d",null,null,"Decay during counting, DDCA =",{"$f":" IFERROR(DDCf(λ.A * t.S), \"\")","v":0.99982615718079004}]
[null,"Analyte =","Po-210",null,null,null,"Analyte decay factor, DFA =",{"$f":" IFERROR(DBC.A * DDC.A, \"\")","v":0.97509576605106929}]
[null,"Tracer =","Po-209",null,null,null,"urel(DFA) =",{"$f":" IFERROR(urelDF(λ.A, urel_T.12A, t.DA * F.t.DA, t.S), \"\")","v":3.098312102866754E-7}]
[null,"Tracer age, AgeT =",1,"a",null,null,"Decay before counting, DBCT =",{"$f":"EXP(-λ.T * (Age.T * F.Age.T + t.DA * F.t.DA))","v":0.99313508320557009}]
[null,"Tracer concentration, cT =",20,"dpm/g",{"$f":" VLOOKUP(Unit_c.T, ConcUnit_Table[],4,FALSE)","v":"Mass"},null,"Decay during counting, DDCT =",{"$f":" IFERROR(DDCf(λ.T * t.S), \"\")","v":0.99999935421567454}]
[null,"urel(cT) =",0.03,null,null,null,"Tracer decay factor, DFT =",{"$f":" IFERROR(DBC.T * DDC.T, \"\")","v":0.99313444185450028}]
[null,"Tracer amount, VT =",1,"g",{"$f":" IF( IF(Unit_V.T=\"\", Type1, VLOOKUP(Unit_V.T, Aliquot_Unit_Table[], 2, FALSE)) = Type_c.T, Type_c.T, \"Mismatch\")","v":"Mass"},null,"urel(DFT) =",{"$f":" IFERROR(urelDF(λ.T, urel_T.12T, (Age.T * F.Age.T + t.DA * F.t.DA), t.S), \"\")","v":3.3770757449342871E-4}]
[null,"urel(VT) =",5.0000000000000001E-3,null,null,null,"Tracer activity, AT =",{"$f":" IF(Type_c.T=Type_V.T, (c.T*F.c.T) * (V.T*F.V.T), \"\")","v":20.000000000000004},"dpm"]
[null,"Tracer alpha intensity, IT =",1,null,null,null,"urel(AT) =",{"$f":" IF(Type_c.T=Type_V.T, SQRT(urel_c.T^2 + urel_V.T^2), \"\")","v":3.0413812651491099E-2}]
[null,"urel(IT) =",0,null,null,null,"Analyte net count rate, RNA =",{"$f":" IFERROR( (AAL*F.Res) * (V.A*F.V.A) * ε * Y * I.A * DF.A, \"\")","v":0.29223620108550541},"cpm"]
[null,"Tracer background, RBT =",1E-3,"cpm",null,null,"Tracer net count rate, RNT =",{"$f":" IFERROR(A.T * ε * Y * I.T * DF.T, \"\")","v":2.2345524941726262},"cpm"]
[null,null,null,null,null,null,"Analyte gross count rate, RSA =",{"$f":" IFERROR(R.NA + R.BA, \"\")","v":0.29523620108550541},"cpm"]
[null,null,null,null,null,null,"Tracer gross count rate, RST =",{"$f":" IFERROR(R.NT + R.BT, \"\")","v":2.2355524941726261},"cpm"]
[null,null,null,null,null,null,"Tracer gross counts, CST =",{"$f":" IFERROR(R.ST * t.S, \"\")","v":223.47076013400076},"cpm"]
[null,"Result unit factor, FRes =",{"$f":"VLOOKUP(Unit_Result, ConcUnit_Table[], 5, FALSE) * 60","v":2.2199999999999998},{"$f":"IF(F.Res=1,\"\",\"(dpm/\"&VLOOKUP(Unit_Result,ConcUnit_Table[],6,FALSE)&\") / (\"&Unit_Result&\")\")","v":"(dpm/1) / (pCi)"}]
[null,"Tracer concentration factor, Fc.T =",{"$f":" IF(Type_c.T=Type_V.T, VLOOKUP(Unit_c.T, ConcUnit_Table[], 5, FALSE) * 60, \"\")","v":1000.0000000000001},{"$f":"IF(F.c.T=1,\"\",\"(dpm/\"&VLOOKUP(Unit_c.T,ConcUnit_Table[],6,FALSE)&\") / (\"&Unit_c.T&\")\")","v":"(dpm/kg) / (dpm/g)"}]
[null,"Aliquot size factor, FV.A =",{"$f":"IF(Type_Res<>Type_V.A, \"\", IF(Unit_V.A=\"\",1,VLOOKUP(Unit_V.A, Aliquot_Unit_Table[], 3, FALSE)))","v":1},{"$f":" IFERROR(IF(F.V.A=1,\"\",VLOOKUP(Type_V.A,SI_Unit_Table[],2,FALSE) &\"/\"& Unit_V.A), \"Error\")","v":""},null,null,null,6,"iterations"]
[null,"Tracer amount factor, FV.T =",{"$f":" IF(Type_c.T<>Type_V.T, \"\", IF(Unit_V.T=\"\", 1, VLOOKUP(Unit_V.T, Aliquot_Unit_Table[], 3, FALSE)))","v":1E-3},{"$f":" IFERROR(IF(F.V.T=1,\"\",VLOOKUP(Type_V.T,SI_Unit_Table[],2,FALSE) &\"/\"& Unit_V.T), \"Error\")","v":"kg/g"}]
[null,"Decay time factor, Ft.DA =",{"$f":"VLOOKUP(Unit_t.DA, Time_Unit_Table[], 2, FALSE) / 60","v":1440},{"$f":"IF(Unit_t.DA=\"min\",\"\",\"min/\"&Unit_t.DA)","v":"min/d"}]
[null,"Tracer age factor, FAge.T =",{"$f":"VLOOKUP(Unit_Age.T, Time_Unit_Table[], 2, FALSE) / 60","v":525948.76666666672},{"$f":"IF(Unit_Age.T=\"min\",\"\",\"min/\"&Unit_Age.T)","v":"min/a"}]

{"sheet":"Gross αβ","index":3,"n_rows":17,"n_cols":11,"rows_kept":17,"cut":false,"hidden":false,"merged":[[13,5,16,5],[6,9,6,10],[7,9,7,10]]}
[null,"Gross α+β Analysis"]
[]
[]
[null,"Result unit =","pCi/L","by",{"$f":" VLOOKUP(Unit_Result,ConcUnit_Table[],4,FALSE)","v":"Volume"},null,null,"Sample count time, tS =",{"$f":" IF(OR(D<=0,Type_Res<>Type_V), \"None\", _xlfn.SWITCH(Option,1,t.Sα,2,t.Sβ,3,IF(OR(t.Sα=\"None\",t.Sβ=\"None\"),\"None\",MAX(t.Sα,t.Sβ)),t.S_std))","v":100},"min"]
[null,"α activity concentration, ACα =",20,null,null,null,null,"Alpha-to-beta cross-efficiency, εα→β =",{"$f":" ε.αα*X.αβ","v":1.0000000000000002E-2},"ⓘ"]
[null,"ϕMRα =",0.15,"ⓘ",null,null,null,"Beta-to-alpha cross-efficiency, εβ→α =",{"$f":" ε.ββ*X.βα","v":3.4999999999999996E-3},"ⓘ"]
[null,"β activity concentration, ACβ =",100,null,null,null,null,"Result unit factor, FRes =",{"$f":" IF(Type_Res<>Type_V, \"\", VLOOKUP(Unit_Result,ConcUnit_Table[],5,FALSE)*60)","v":2220},{"$f":"IF(F.Res=1,\"\",\"(dpm/\"&VLOOKUP(Unit_Result,ConcUnit_Table[],6,FALSE)&\") / (\"&Unit_Result&\")\")","v":"(dpm/m3) / (pCi/L)"}]
[null,"ϕMRβ =",0.1,"ⓘ",null,4,null,"Aliquot size factor, FV =",{"$f":" IF(Type_Res<>Type_V, \"\", IF(Type_V=Type1, 1, VLOOKUP(Unit_V, Aliquot_Unit_Table[], 3, FALSE)))","v":1E-3},{"$f":" IFERROR(IF(F.V=1,\"\",VLOOKUP(Type_V,SI_Unit_Table[],2,FALSE) &\"/\"& Unit_V), \"Error\")","v":"m3/L"}]
[null,"Aliquot size, V =",1,"L",{"$f":" IF(IF(Unit_V=\"\", Type1, VLOOKUP(Unit_V,Aliquot_Unit_Table[],2,FALSE)) = Type_Res, Type_Res, \"Mismatch\")","v":"Volume"},null,null,"Alpha net count rate, RNα =",{"$f":" IF(Type_Res=Type_V, IFERROR((AC.α*ε.αα + AC.β*ε.βα) * V * F.V * F.Res, \"\"), \"\")","v":5.2170000000000005},"cpm",{"$f":" IFERROR(IF(AND(Type_Res=Type_V, R.Nα > 100000), \"High\", \"\"), \"\")","v":""}]
[null,"Alpha efficiency, εα =",0.1,"ⓘ",null,null,null,"Beta net count rate, RNβ =",{"$f":" IF(Type_Res=Type_V, IFERROR((AC.β*ε.ββ + AC.α*ε.αβ) * V * F.V * F.Res, \"\"), \"\")","v":78.144000000000005},"cpm",{"$f":" IFERROR(IF(AND(Type_Res=Type_V, R.Nβ > 100000), \"High\", \"\"), \"\")","v":""}]
[null,"Beta efficiency, εβ =",0.35,"ⓘ",null,null,null,"tSα =",{"$f":" IFERROR(IF(Test_α > 0, (F.ββ^2*R.Sα + F.βα^2*R.Sβ) / Test_α, \"None\"), \"None\")","v":12.031822414040139},"min"]
[null,"Alpha-to-beta crosstalk, Xα→β =",0.1,"ⓘ",null,null,null,"tSβ =",{"$f":" IFERROR(IF(Test_β > 0, (F.αα^2*R.Sβ + F.αβ^2*R.Sα) / Test_β, \"None\"), \"None\")","v":1.3144493746034955},"min"]
[null,"Beta-to-alpha crosstalk, Xβ→α =",0.01,"ⓘ",null,null,null,"ϕMα =",{"$f":" IFERROR(SQRT((F.ββ^2)*(R.Sα/t.S+R.Bα/t.B) + (F.βα^2)*(R.Sβ/t.S+R.Bβ/t.B)) / (V*F.V*AC.α*F.Res), \"\")","v":5.2073369024632582E-2}]
[null,"Alpha background, RBα =",0.1,"cpm ⓘ",null,"The MQOs are based on counting uncertainty only.",null,"ϕMβ =",{"$f":" IFERROR(SQRT((F.αα^2)*(R.Sβ/t.S+R.Bβ/t.B) + (F.αβ^2)*(R.Sα/t.S+R.Bα/t.B)) / (V*F.V*AC.β*F.Res), \"\")","v":1.1472091730480548E-2}]
[null,"Beta background, RBβ =",1,"cpm ⓘ"]
[null,"Background count time, tB =",1000,"min"]
[null,"Standard count time =",100,"min ⓘ"]

{"sheet":"Gross αβ Graph","index":4,"n_rows":53,"n_cols":15,"rows_kept":53,"cut":false,"hidden":false,"merged":[[52,1,52,13]]}
[]
["ACα =",{"$f":" 'Gross αβ'!AC.α","v":20},{"$f":"'Gross αβ'!Unit_Result","v":"pCi/L"},"ACβ =",{"$f":" 'Gross αβ'!AC.β","v":100},{"$f":"'Gross αβ'!Unit_Result","v":"pCi/L"},"tS","u2(RNα)","u2(RNβ)","ϕMα","ϕMβ","ϕMRα","ϕMRβ","αMin","βMin"]
["V =",{"$f":" 'Gross αβ'!V","v":1},{"$f":"'Gross αβ'!Unit_V","v":"L"},null,null,null,1,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":5.3170999999999999},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":79.14500000000001},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":0.52024982045971735},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":0.11464921066015592},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},{"$f":" IFERROR(SQRT(F.ββ^2*(R.Bα/t.B) + F.βα^2*(R.Bβ/t.B)) / (V*F.V*AC.α*F.Res), \"None\")","v":2.2556337307182428E-3},{"$f":" IFERROR(SQRT(F.αα^2*(R.Bβ/t.B) + F.αβ^2*(R.Bα/t.B)) / (V*F.V*AC.β*F.Res), \"None\")","v":4.0759658035271768E-4}]
["FRes =",{"$f":"'Gross αβ'!F.Res","v":2220},null,"FV =",{"$f":"'Gross αβ'!F.V","v":1E-3},null,2,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":2.6586000000000003},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":39.573},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":0.36787563358551989},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":8.1069746638216172E-2},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
["tB =",{"$f":" 'Gross αβ'!t.B","v":1000},"min",null,null,null,5,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":1.0635000000000001},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":15.829800000000001},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":0.23267153982491148},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":5.1273981793666212E-2},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
["Fαα =",{"$f":" 'Gross αβ'!F.αα","v":2.8600028600028606},null,"Fαβ =",{"$f":" 'Gross αβ'!F.αβ","v":0.2860002860002861},null,10,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":0.53180000000000005},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":7.9154000000000009},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":0.1645313546531823},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":3.6257325769763621E-2},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
["Fββ =",{"$f":" 'Gross αβ'!F.ββ","v":10.01001001001001},null,"Fβα =",{"$f":" 'Gross αβ'!F.βα","v":0.10010010010010011},null,20,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":0.26595000000000002},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":3.9582000000000002},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":0.11635216918377245},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":2.5639420888029823E-2},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
["RBα =",{"$f":" 'Gross αβ'!R.Bα","v":0.1},"cpm","RBβ =",{"$f":"'Gross αβ'!R.Bβ","v":1},"cpm",50,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":0.10644000000000001},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":1.58388},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":7.3608312299793796E-2},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":1.6218866864636541E-2},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
["RSα =",{"$f":"'Gross αβ'!R.Sα","v":5.3170000000000002},"cpm","RSβ =",{"$f":"'Gross αβ'!R.Sβ","v":79.144000000000005},"cpm",100,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":5.3270000000000005E-2},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":0.79244000000000003},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":5.2073369024632582E-2},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":1.1472091730480548E-2},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
[null,null,null,null,null,null,200,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":2.6685E-2},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":0.39672000000000002},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":3.6855960475225165E-2},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":8.117112283468654E-3},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
[null,null,null,null,null,null,500,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":1.0734E-2},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":0.15928800000000001},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":2.3375146184288046E-2},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":5.1434118746571545E-3},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
[null,null,null,null,null,null,1000,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":5.4170000000000008E-3},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":8.0144000000000007E-2},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":1.6605501236999592E-2},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":3.6483435066259487E-3},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
[null,null,null,null,null,null,2000,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":2.7585000000000001E-3},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":4.0572000000000004E-2},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":1.1849695246274243E-2},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":2.5958183020634317E-3},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
[null,null,null,null,null,null,5000,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":1.1634E-3},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":1.6828800000000001E-2},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":7.695377904178723E-3},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":1.6718223728375357E-3},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
[null,null,null,null,null,null,10000,{"$f":" R.Sα/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bα/t.B","v":6.3170000000000001E-4},{"$f":" R.Sβ/Table_Gross_αβ_Graphs[[#This Row],[tS]] + R.Bβ/t.B","v":8.9143999999999994E-3},{"$f":" IFERROR(SQRT(F.ββ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]] + F.βα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]]) / (V*F.V*AC.α*F.Res), \"None\")","v":5.6703934879017001E-3},{"$f":" IFERROR(SQRT(F.αα^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNβ)]] + F.αβ^2*Table_Gross_αβ_Graphs[[#This Row],[u2(RNα)]]) / (V*F.V* AC.β*F.Res), \"None\")","v":1.2167836740019481E-3},{"$f":"'Gross αβ'!φMRα","v":0.15},{"$f":"'Gross αβ'!φMRβ","v":0.1},2.2556337307182428E-3,4.0759658035271768E-4]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
[]
[]
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[]
[]
[]
[]
[]
[null,"The curves asymptotically approach the minimum values as the sample count time increases."]

{"sheet":"Gamma","index":5,"n_rows":26,"n_cols":9,"rows_kept":26,"cut":false,"hidden":false,"merged":[[0,1,0,4],[20,1,20,4]]}
[null,"Gamma-Ray Spectrometry"]
[]
[]
[null,"Result unit =","pCi/g","by",{"$f":" VLOOKUP(Unit_Result, ConcUnit_Table[],4,FALSE)","v":"Mass"},null,"Sample count time, tS =",34.224546925436663,"min"]
[null,"Analytical action level, AAL =",0.5]
[null,"Required relative method uncertainty, ϕMR =",0.05,null,null,null,"ϕM =",{"$f":"IFERROR(SQRT( (R.N+(1+F)*R.B) / (t.S * R.N^2)  + urel_V^2 + urel_ε^2 + urel_I^2 + urel_DF^2), \"\")","v":5.000000000000001E-2},{"$f":"IF(RAND()>0,\"\",\"\")","v":""}]
[null,"Required detection limit, MDCR =",0.1,null,null,null,"MDC =",{"$f":"IFERROR(getGSmdc(t.S, R.B, (1 + n.P/n.BL) / t.S, (F.Res * ε * (V * F.V) * I * DF)), \"\")","v":3.3451264796512663E-2},{"$f":"Unit_Result","v":"pCi/g"}]
[null,"Sample aliquot, V =",400,"g",{"$f":" IF( IF(Unit_V=\"\", Type1, VLOOKUP(Unit_V, Aliquot_Unit_Table[], 2, FALSE)) = Type_Res, Type_Res, \"Mismatch\")","v":"Mass"}]
[null,"urel(V) =",1E-3,null,null,null,"Half-life, T1/2 =",{"$f":" VLOOKUP(Analyte, Nuclide_Table[], 2, FALSE)","v":8.0233000000000008},{"$f":"VLOOKUP(Analyte,Nuclide_Table[],4,FALSE)","v":"d"}]
[null,"Gamma intensity, Iγ =",0.6," ⓘ",null,null,"urel(T1/2) =",{"$f":" VLOOKUP(Analyte, Nuclide_Table[], 3, FALSE) / T.12","v":2.3681029003028677E-4}]
[null,"urel(Iγ) =",7.0000000000000001E-3,null,null,null,"Decay constant, λ =",{"$f":" IFERROR(VLOOKUP(Analyte, Nuclide_Table[], 5, FALSE), \"\")","v":5.9994292712747143E-5},"min−1"]
[null,"Efficiency, ε =",0.1,null,null,null,"Decay before counting, DBC =",{"$f":" EXP(-λ * t.D * F.t.D)","v":0.64923605484895941}]
[null,"urel(ε) =",0.02,null,null,null,"Decay during counting, DDC =",{"$f":" IFERROR(DDCf(λ * t.S), \"\")","v":0.99897406355442964}]
[null,"Baseline, RB =",1,"cpm ⓘ",null,null,"Decay factor, DF =",{"$f":" IFERROR(DBC * DDC, \"\")","v":0.64856997991851151}]
[null,"Peak width, nP =",16,"channels ⓘ",null,null,"urel(DF) =",{"$f":" IFERROR(urelDF(λ, urel_T.12, t.D * F.t.D, t.S), \"\")","v":1.0253534959395191E-4}]
[null,"Baseline, nBL =",6,"channels ⓘ"]
[null,"Decay time, tD =",5,"d",null,null,"Net count rate, RN =",{"$f":" IFERROR( (AAL*F.Res) * (V*F.V) * ε * I * DF, \"\")","v":17.27790426502915},"cpm"]
[null,"Analyte =","I-131",null,null,null,"Peak count rate, RP =",{"$f":" IFERROR(R.N + n.P*R.B, \"\")","v":33.27790426502915},"cpm"]
[]
[]
[null,"Based on a single photopeak with no background peak."]
[]
[null,null,null,null,null,null,null,7,"iterations"]
[null,null,null,null,null,null,"Result unit factor, FRes =",{"$f":" VLOOKUP(Unit_Result, ConcUnit_Table[], 5, FALSE) * 60","v":2220},{"$f":"IF(F.Res=1,\"\",\"(dpm/\"&VLOOKUP(Unit_Result,ConcUnit_Table[],6,FALSE)&\") / (\"&Unit_Result&\")\")","v":"(dpm/kg) / (pCi/g)"}]
[null,null,null,null,null,null,"Aliquot size factor, FV =",{"$f":" IF(Type_Res<>Type_V, \"\", IF(Unit_V=\"\",1,VLOOKUP(Unit_V, Aliquot_Unit_Table[], 3, FALSE)))","v":1E-3},{"$f":" IFERROR(IF(F.V=1,\"\",VLOOKUP(Type_V,SI_Unit_Table[],2,FALSE) &\"/\"& Unit_V), \"Error\")","v":"kg/g"}]
[null,null,null,null,null,null,"Decay time factor, Ft.D =",{"$f":" VLOOKUP(Unit_t.D, Time_Unit_Table[], 2, FALSE) / 60","v":1440},{"$f":"IF(Unit_t.D=\"min\",\"\",\"min/\"&Unit_t.D)","v":"min/d"}]

{"sheet":"Gamma Graphs","index":6,"n_rows":47,"n_cols":9,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
[]
["Analyte =",{"$f":"Gamma!Analyte","v":"I-131"}]
["AAL =",{"$f":"Gamma!AAL","v":0.5},{"$f":"Gamma!Unit_Result","v":"pCi/g"}]
["ε =",{"$f":"Gamma!ε","v":0.1}]
["V =",{"$f":"Gamma!V","v":400},{"$f":"Gamma!Unit_V","v":"g"}]
["I =",{"$f":"Gamma!I","v":0.6}]
["DBC =",{"$f":"Gamma!DBC","v":0.64923605484895941}]
["FRes =",{"$f":"Gamma!F.Res","v":2220}]
["FV =",{"$f":"Gamma!F.V","v":1E-3}]
["nP =",{"$f":"Gamma!n.P","v":16}]
["nBL =",{"$f":"Gamma!n.BL","v":6}]
["RB =",{"$f":"Gamma!R.B","v":1}]
["λ =",{"$f":"Gamma!λ","v":5.9994292712747143E-5},"min−1"]
["urel(ε × V × I) =",{"$f":"SQRT(Gamma!urel_ε^2 + Gamma!urel_V^2 + Gamma!urel_I^2)","v":2.1213203435596427E-2}]
[]
[null,"tS","DDC","DF","RN","ϕM","ϕMR","MDC","MDCR"]
[null,1,{"$f":"DDCf(λ * Table11[[#This Row],[tS]])","v":0.99997000345352061},{"$f":" DBC * Table11[[#This Row],[DDC]]","v":0.64921658000946403},{"$f":" (AAL * F.Res) * ε * (V * F.V) * I * Table11[[#This Row],[DF]]","v":17.295129691452125},{"$f":" SQRT((Table11[[#This Row],[RN]] + (1+(n.P/n.BL))*R.B) / (Table11[[#This Row],[tS]] * Table11[[#This Row],[RN]]^2) + urel_D^2 + urelDF(λ, Gamma!urel_T.12, (Gamma!t.D*Gamma!F.t.D), Table11[[#This Row],[tS]])^2)","v":0.26557084507791995},{"$f":"Gamma!φ.MR","v":0.05},{"$f":" getGSmdc(Table11[[#This Row],[tS]], R.B, (1+n.P/n.BL)/Table11[[#This Row],[tS]], F.Res * ε * (V * F.V) * I * Table11[[#This Row],[DF]])","v":0.26035928986088325},{"$f":"Gamma!MDC.R","v":0.1}]
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[null,"Activity Units",null,null,"Time Units",null,null,"SI Units"]
[null,"Unit","SI Factor",null,"Unit","SI Factor",null,"Type","SI Unit"]
[null,"Bq",1,null,"a",31556926,null,"Activity","Bq"]
[null,"dpm",{"$f":"1/60","v":1.6666666666666666E-2},null,"d",86400,null,"Mass","kg"]
[null,"kBq",1000,null,"h",3600,null,{"$f":"Type1","v":"Total"},"1"]
[null,"mBq",1E-3,null,"min",60,null,"Volume","m3"]
[null,"mCi",37000000,null,"s",1]
[null,"nCi",37]
[null,"pCi",3.6999999999999998E-2,null,"All unit conversion factors are based on SI units, although count times are more conveniently expressed in minutes, not seconds."]
[null,"μBq",9.9999999999999995E-7]
[null,"μCi",37000]
[]
[]
[null,"Radionuclides and Half-lives",null,null,null,null,null,"Activity Concentration Units"]
[null,"Nuclide","Half-life","u","Unit","λ / min−1",null,"Unit","Over","Under","Type","SI Factor","SI Unit (Under)"]
[null,"Ac-228",6.15,0.03,"h",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":1.8784476437938896E-3},null,"Bq",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"Bq"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":""},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Total"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"1"}]
[null,"Am-241",432.6,0.6,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":3.046460173176302E-9},null,"Bq/g",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"Bq"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"g"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Mass"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1000},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"kg"}]
[null,"Am-243",7367,23,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":1.7889217740139381E-10},null,"Bq/kg",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"Bq"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"kg"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Mass"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"kg"}]
[null,"Ba-133",3848.9,0.7,"d",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":1.2506227979999071E-7},null,"Bq/L",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"Bq"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"L"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Volume"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1000},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"m3"}]
[null,"Cm-244",18.11,0.03,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":7.2771875809832578E-8},null,"Bq/m3",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"Bq"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"m3"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Volume"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"m3"}]
[null,"Co-60",5.2710999999999997,8.0000000000000004E-4,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":2.5002346206978966E-7},null,"Bq/mg",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"Bq"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"mg"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Mass"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1000000},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"kg"}]
[null,"Cs-134",2.0644,1.4E-3,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":6.3839307833562694E-7},null,"Bq/mL",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"Bq"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"mL"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Volume"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1000000},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"m3"}]
[null,"Cs-137",30.05,0.08,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":4.3856860928987291E-8},null,"dpm",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"dpm"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":""},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Total"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1.6666666666666666E-2},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"1"}]
[null,"H-3",12.311999999999999,2.5000000000000001E-2,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":1.0704180238109715E-7},null,"dpm/g",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"dpm"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"g"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Mass"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":16.666666666666668},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"kg"}]
[null,"Hg-203",46.594000000000001,1.2E-2,"d",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":1.0330776682023098E-5},null,"dpm/kg",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"dpm"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"kg"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Mass"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1.6666666666666666E-2},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"kg"}]
[null,"I-131",8.0233000000000008,1.9E-3,"d",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":5.9994292712747143E-5},null,"dpm/L",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"dpm"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"L"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Volume"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":16.666666666666668},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"m3"}]
[null,"Mn-54",312.13,0.03,"d",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":1.5421529770357999E-6},null,"dpm/m3",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"dpm"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"m3"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Volume"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":1.6666666666666666E-2},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"m3"}]
[null,"Po-209",102,5,"a",{"$f":"LN(2) / (Nuclide_Table[[#This Row],[Half-life]] * VLOOKUP(Nuclide_Table[[#This Row],[Unit]],Time_Unit_Table[],2,FALSE) / 60)","v":1.2920575205059492E-8},null,"dpm/mg",{"$f":"UnitOver(ConcUnit_Table[[#This Row],[Unit]])","v":"dpm"},{"$f":"UnitUnder(ConcUnit_Table[[#This Row],[Unit]])","v":"mg"},{"$f":" IF(ConcUnit_Table[[#This Row],[Under]]=\"\", Type1, VLOOKUP(ConcUnit_Table[[#This Row],[Under]],Aliquot_Unit_Table[],2,FALSE))","v":"Mass"},{"$f":"GetFactor(ConcUnit_Table[[#This Row],[Unit]])","v":16666.666666666668},{"$f":"IF(ConcUnit_Table[[#This Row],[Under]]=\"\",\"1\",VLOOKUP(ConcUnit_Table[[#This Row],[Type]],SI_Unit_Table[],2,FALSE))","v":"kg"}]
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