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# EP ADOCKE TID : 102RQ-R N 41 ) 102RQ-RN-5- 3 43 ) 102RQ-RN-5- 5 45 ) 102RQ-RN-5- 7 47 ) 102RQ-RN-5- 9 49 ) 102RQ-RN-5-1 1 51 ) 102RQ-RN-5-1 3 53 ) 102RQ-RN-5-1 5 55 ) 102RQ-RN-3- 4 57 ) 59 ) 61 ) 63 ) 65 ) 67 ) 69 ) 71 ) 73 ) 75 ) 77) 79 ) Ste p 3 : FOR ASR C INTERNA LUS E ONL Y CD : OA : / 

# 42 ) 102RQ-RN-5- 4 44 ) 102RQ-RN-5- 6 46 ) 102RQ-RN-5- 8 48 ) 102RQ-RN-5-1 0 50 ) 102RQ-RN-5-1 2 52 ) 102RQ-RN-5-1 4 54 ) (102RQ-RN-5-3 1 ) 56 ) 102RQ-RN-2-5- 1 58 ) 60 ) 62 ) 64 ) 66 ) 68 ) 70 ) 72 ) 74 ) 76 ) 78 ) 80 )

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xNumbe r 3 5 O F 28 3 Initials/Date : LD S / 3-8-200 7P. 2 

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SUPPLEMENTAR

YTECHNICA

L BACKGROUN

DDOCUMEN

T TO SUPPOR T TH E ADJUSTMEN

T O F RADIONUCLID

E REPORTABLE QUANTITIES :

METHOD S AN

DRESULT S FO

RCALCULATIONS O

F RADIONUCLID

E REPORTABLE QUANTITIE S UNDE RVARYIN

GSET S O

F CONDITIONS

EMERGENC

YRESPONS E DIVISIO

N Offic e o f Emergenc

y an dRemedia l Respons e U.S . Environmenta l Protectio nAgenc y

Jun e 18 , 198 7P. 3

METHOD S AN D RESULT S FO R CALCULATION S O FRADIONUCLID E REPORTABL E QUANTITIE S UNDE R VARYIN G SET S O FCONDITION S



### 1 . BACKGROUN D Th e Comprehensiv e Environmenta l Response , Compensation , an d Liabilit yAc t (CERCLA ) require s immediat e notificatio n t o the Nationa l Respons e Cente r whe n a hazardou s substanc e designate d unde r CERCL Ai s release d int o th e environmen t i n an amoun t equa l t o o r greate r than the reportabl e quantit y(RQ ) fo r tha t substance
. Radionuclide s ar e designate d hazardou s substance s unde r CERCL Aan d the curren t RQ fo r radionuclides , establishe d b ySectio n 102(b ) o f CERCLA , i s on e pound
. CERCLA , however , authorize s th e Environmenta l Protectio n Agenc y (EPA ) t o adjus t statutor yRQ s b yregulatio n i f deeme d appropriate
. Recognizing tha t a one-poun d RQ i s no t appropriat e fo r al l radionuclides , EPArecentl yha s publishe d a Notic e o f Propose d Rulemaking (NPRM ) t o adjus t th e statutor

yR Q fo r radionuclide s (5 2 FR 8172 , Marc h16 , 1987)
. Th e Agency propose d specifi c RQ adjustment s for the 75 7 radionuclide s fo r whic hthe Internationa l Commissio n o n Radiatio n Protectio n (ICRP ) ha s provide d metaboli c dat a an d recommende d intak e limit s i n ICRP Publicatio n 30. l Al l radionuclide s no t listed b yth e ICRP wer e groupe d int o a generi c clas s o f "radionuclides, " wit hon e propose d RQ fo r the entir e class
. Al l o f th e propose d RQ s ar e i n unit s o f curies
. A s discusse d in the Technica l Backgroun d Documen t (TBD ) supporting the propose d RQ rulemaking, 2 the propose d radionuclid e RQ s wer e develope d b y determining the quantit yo f radionuclide s that , i f release d unde r a se t o f conservative exposur e conditions , coul d resul t i n an individua l receiving an effective whol e bod ydose-equivalen t o f 50 0 millirem
. Th e Agencyconsidere d hypothetica l release s int o variou s environmenta l medi a an d huma n exposure s vi a thre e pathways : inhalation ; ingestio n o f contaminate d groun d water ; an

d direc t exposure . Using a se t o f conservative assumption s t o analyz e eac h exposur e pathway , the pathwaytha t wa s foun d t o b e the mos t critica l for a radionuclid e (i.e. , th e on e tha t yielde d th e lowes t releas e value ) wa s use d a s the basi s fo r the RQ adjustmen t for tha t radionuclide
. Th e equation s o r model s use d t o examin e possibl e exposur e vi a th e above

mentione d pathway s rel yo n severa l parameter s an d define d exposur e conditions
. Fou r condition s o r parameter s tha t hav e a significan t bearing o n the RQ

1 Internationa l Commissio n o n Radiatio n Protection , Annal s o f the ICRP : Limit s fo r Intake s o f Radionuclide s b yWorkers , ICRP Publicatio n 30 , 1980
. 2 U.S . Environmenta l Protectio n Agency , Technica l Backgroun d Documen t t o Suppor t Propose d Rulemaking Pursuan t t o Sectio n 10 2 o f CERCLA : Radionuclides , EmergencyRespons e Division , Offic e o f Emergencyan d Remedia l Response , 1986
.P. 4

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result s are : (1 ) the distanc e betwee n the poin t o f releas e an d the poin t o f exposure ; (2 ) the dose-equivalen t limi t tha t the hypothetically-expose d individua l i s permitte d t o receive ; (3 ) the exten t o f radioactive deca yduring transpor t t o the poin t o f exposur e an d ove r the perio d o f exposure ; an d (4 ) th e time perio d ove r whic han individua l i s exposed
. Th e model s use d t o calculat e the propose d RQ s i n the NPR Massume that : th e distanc e fro mthe poin t o f releas e t o the poin t o f exposur e i s 3 0 meters ; the dose-equivalen t limi t i s 50 0 milliremeffective whol e bod ydose ; an

d ther e i s n o radioactive decay(fo r the sak e o f conservatis man d simplicity)
. Fo r the perio d o f exposure , the model s use d i n the NPR Massume tha t person s ar e expose d fo r on e dayfo r inhalation an d direc t exposure , bu t tha t person s ar e expose d fo r longe r period s throughthe ingestio n pathwa yi n orde r t o accoun t fo r the slow movemen t o f radionuclide s i n groun d water . Sinc e publishing the NPRM , EPAha s analyze d howthe propose d R Q adjustment s woul d var yi f differen t assumption s ar e use d wit hregard t o the distanc e t o the exposur e point , dose-equivalen t limit , exten t o f radioactive decay , an

d exposur e period
. Thi s pape r derive s th e model s use d t o calculat e radionuclid e RQ s unde r severa l alternat e set s o f assumption s an d summarize s th e result s o f thes e alternat e calculations
. Th e ra wresult s obtaine d fro m eac hcalculatio n can b e foun d i n the Superfun

d docke t supporting the radionuclid e rul e (Superfun d Docke t No . 102RQ-RN)
. Th e remainde r o f thi s pape r i s divide d int o four mai n sections
. I n Sectio n 2 , the set s o f alternat e condition s use d t o calculat e radionuclid e RQ s ar e defined
. Including th e se t o f mode l condition s use d t o deriv e the propose d RQ s i n the NPRM , a tota l o f 1 9 differen t set s o f condition s involving variation s i n the exposure-poin t distance , dose-equivalen t limit , exten t o f radioactiv e decay , an d exposur e perio d wer e evaluated
. I n Sectio n 3 , an overviewo f the approache s use d t o calculat e the RQ s unde r the variou s set s o f condition s i s provided
. Whil e Sectio n 3 present s the genera l rational e an d concept s use d t o tak e int o accoun t the variou s conditions , the particula r equation s an

d value s for parameter s use d i n the differen t calculation s ar e no t derive d unti l Sectio n 4
. Finally , Sectio n 5 present s the summar yan d ra w result s obtaine d fro mthe equation s derive d i n Sectio n 4
. 2

. CALCULATION S PERFORME D FO R THI S ANALYSI S Radionuclid e RQ s wer e calculate d using differen t assumption s regarding :

• distance s betwee n the poin t o f radionuclid e releas e an d th e poin t o f exposure ;

• duration s o f exposur e t o the radionuclid e releas e for a hypothetica l individual ;

• dose-equivalen t limit s tha t the expose d individua l i s permitte d t o receive ; an dP. 5

• assumption s wit hregard t o th e exten t o f radioactive deca yfro mth e time tha t the radionuclid e i s release d t o the en d o f the time tha t a perso n i s expose d t o the release
. Th e variou s combination s o f thes e assumption s tha t defin e the calculation s performe d for thi s analysi s ar e listed i n Exhibi t 1
. Th e firs t se t o f assumption s show n i n Exhibi t 1 i s the on e use d t o calculat e the radionuclid e RQ s propose d i n the NPRM . Th e method s use d t o calculat e RQ s unde r thi s se t o f conditions , a s wel l a s the result s fro mthes e calculations , ar e summarize d her e t o permi t compariso n wit hth e alternat e set s o f assumption s define d b yconditio n number s 1 through18
. Al l o f th e RQ adjustment s i n th e NPR Mwer e determine d b yon e o f the following exposur e pathways : inhalation ; ingestio n o f groun d water ; direc t exposur e t o a poin t source ; an d direc t exposur e b ysubmersio n i n an airborn e cloud
. Othe r ingestion pathway s (i.e. , ingestio n o f vegetable s contaminate d b yairborn e depositio n an d ingestion o f surfac e water ) als o wer e evaluate d but , unde r the se t o f assumption s evaluate d i n the NPRM , wer e foun d t o b e les s critica l for mos t radionuclide s a s compare d t o the ingestion o f groun d water . I t i s recognized , however , tha t change s i n the exposur e condition s (mos t notably , a differen t assumptio n wit hregard t o th e exten t o f radioactive decay ) coul d increas e significantl ythe relative importanc e o f the vegetabl e ingestio n pathway
. I n addition , EPArecognize s tha t exposur e pathway s othe r than th e one s considere d previousl yals o exis t an d coul d i n fac t b e mor e critica l (i.e. , lea d t o lowe r RQs ) for some radionuclides
. Fo r example , th e ingestion o f contaminate d mil k i s a possibl e exposur e pathwa ytha t coul d lea

d t o lowe r RQ s for some radionuclides
. Fo r thi s analysis , therefore , EP Aha s expande d the approac huse d i n the NPR Mt o conside r additiona l exposur e pathway s i n greate r detail
. Fo r eachse t o f assumption s show n i n Exhibi t 1 tha t involve s a distanc e o f 3 0 meters , a separat e calculatio n wa s performe d t o evaluat e exposure s throughthe following pathways : inhalation , ingestion o f groun d water , ingestion o f vegetable s contaminate d b

yairborn e deposition , ingestio n o f milk , an d direc t exposure . Direc t exposur e t o a poin t sourc e wa s evaluate d for al l radionuclide s excep t the isotope s o f the nobl e gase s argon , krypton , an d xenon ; fo r thes e radionuclides , direc t exposur e b ysubmersio n i n a clou d wa s evaluated
. Fo r thos e set s o f assumption s involving a distanc e o f 1 meter , the onl yexposur e pathwa ytha t wa s evaluate d wa s direc t exposur e t o a poin t source . A n analysi s assuming a distanc e o f 1 mete r for the othe r exposur e pathway s wa s no t performe d becaus e sucha clos e distanc e fo r the othe r pathway s generall ywoul d b e unrealisti c an

d woul d yiel d overl yconservative results
. Th e Agencyals o considere d i n thi s analysi s the potentia l exposur e resulting fro

mthe ingestio n o f vegetable s contaminate d b yradionuclide-bearing irrigatio n water . A n equatio n t o calculat e releas e value s for thi s exposur e pathwaywa s developed , bu t base d o n the rang e o f inpu t value s t o b e use d i n thi s equation , EP

Adetermine d tha t releas e value s for the irrigation pathway alway s woul d b e highe r than thos e fo r the ground-wate r ingestio n pathwayan dP. 6

EXHIBI T 1 COMBINATIONS O F ASSUMPTION S DEFININ GTH E RADIONUCLID E R Q CALCULATION S

Conditio n Numbe r

NPR Mc / 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 Distanc e fro m Re l t o eas e Poin t Exposur e Poin t (Meters ) a /

3 0 3 0 3 0 1 3 0 3 0 1 1 3 0 3 0 1 1 d / d / d /



## _ y 3 0 3 0 1 Perio d o f

Direc t Exposur e (Days ) b /

1 1 1 1 1 1 1 1 36 5 36 5 1 1 d / d / d / d / 1 36 5 1 Whol e Bod y Dos e Limi t (Rem )

0. 5 0.02 5 0. 1 0. 1 0.02 5 0. 1 0. 5 0.02 5 0. 5 0. 5 2 5 0. 5 5 500 0 2 5 50 0 0. 5 0. 1 0. 1 Radioactiv e

Decay Considered ?

N o N o N o N o Ye s Ye s N o Ye s N o Ye s Ye s Ye s N o N o N o N o Ye s N o Ye s

a / Fo r eachse t o f condition s involving a distanc e o f 3 0 meters , a separat e calculatio n wa s performe d t o evaluat e radionuclid e release s an d exposure s throughal l the pathway s considere d i n thi s analysis ; fo r eac hse t o f condition s involving a distanc e o f 1 meter , however , onl ydirec t exposure s t o a poin t sourc e wer e evaluated
. b / Th e period s o f exposur e listed her e wer e use d onl yi n the evaluatio n o f direc t exposure s t o a poin t source . Se e Section s 3. 2 an d 4 o f thi s pape r fo r a discussio n o f the exposur e period s use d i n the othe r exposur e pathway models
.
c / Thi s i s th e se t o f condition s assume d i n the calculatio n o f propose d RQ s presente d i n th e NPRM . d / I n Condition s 1 2 throug h15 , RQ s ar e calculate d simpl yb ytaking multiple s o f the inhalatio n an d ingestio n Annua l Limit s o f Intake
. Neithe r distanc e no r time , therefore , wer e considere d i n thes e calculations
.P. 7

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henc e woul d neve r serve a s the basi s fo r the RQs . Thi s determinatio n i s no t intende d t o impl ytha t human exposure s vi a the irrigation-vegetabl e rout e wil l alway s b e less , critica l than thos e tha t occur throughthe ingestion o f groun d water ; the Agencyrecognize s tha t exposure s throughirrigatio n coul d b e muc h mor e critica l than ground-wate r exposure s du e t o th e specifi c condition s surrounding the actua l releas e event . However , unde r the hypothetica l releas e an d exposur e scenario s examined , EPAfoun d ground-wate r exposure s alway s t o b e mor e critica l (se e Sectio n 4. 7 o f thi s pape r fo r a justificatio n fo r thi s conclusion)
. Therefore , a separat e calculatio n using th e irrigatio n pathway mode l wa s no t performed
. 3 . OVERVIE WO FCALCULATIONA L APPROACHE S
I n simples t terms , eacho f the model s use d t o calculat e radionuclid e RQ s i s intende d t o determin e tha t quantit yo f a radionuclid e that , i f release d int o the environmen t unde r a certai n se t o f conditions , coul d resul t i n an expose d individua l receiving a specifie d effective whol e bod ydose

equivalent
. T o mak e thi s determination , the model s defin e a hypothetica l releas e an

d exposur e scenari o i n which : (1 ) a radionuclid e i s assume d t o b e release d int o an environmenta l medium ; (2 ) th e radionuclid e i s transporte d fro mthe poin t o f releas e t o the poin t o f exposur e an d dilute d along the way ; an d (3 ) a perso n i s expose d (i.e. , inhales , ingests , o r come s int o direc t contact ) t o the release d radionuclid e ove r a certai n lengt ho f time
. Change s i n the assumption s wit hregard t o the distanc e betwee n th e poin t o f releas e an d the poin t o f exposure , the perio d o f exposure , the maximu mdose-equivalen t tha t the expose d individua l i s permitte d t o receive , an d th e exten t o f radioactive deca

ythroughou t thi s perio d wil l involve change s i n th e calculatio n method s an d results
. Thi s sectio n i s divide d int o four subsections
. Eac ho f the subsection s describ e i n genera l terms howal l the model s use d i n thi s analysi s wer e change d t o tak e int o accoun t variation s i n distance , variation s i n exposur e period , variation s i n dose-equivalen t limit , an d variation s i n the exten t o f radioactive decay
. 3. 1 Change s i

nModel s t

o Accommodat e Variation s i nDistanc e A s show n i n Exhibi t 1 , the distanc e fro mth e poin t o f releas e t o the poin t o f exposur e wa s varie d i n thi s analysi s betwee n 1 an d 3 0 meters . Th e onl y pathwaytha t wa s evaluate d assuming a 1 mete r distanc e wa s direc t exposur e t o a poin t source . Th e Agenc ybelieve s tha t assuming a 1 mete r distanc e fo r the othe r exposur e pathway s woul d b e generall yunrealisti c an d overl yconservative
. Th e mode l use d t o estimat e direc t exposur e t o a poin t sourc e assume s tha t an individua l reside s i n the vicinit yo f a radiatio n sourc e fo r a certai n lengt ho f time
. Th e distanc e betwee n th e poin t sourc e an d the expose d individua l i s an inpu t variabl e and , t o estimat e potentia l exposure s a t th e differen t distances , th e valu e o f thi s variabl e wa s simpl ychanged fro m3 0 meter s t o 1 meter .P. 8

Th e model s use d for bot hdistance s estimat e the dos e fro mgamm a radiatio n i n unit s o f rem . Bot hmodel s tak e int o accoun t gamm a ra yattenuatio n i n ai r betwee n the sourc e an d the receptor . Fo r the sak e o f simplicity , however , EPA decide d t o ignor e the possibl e direc t radiatio n dos e cause d b ybet a particles
. Thi s exclusio n i s technicall yvali d whe n considering a distanc e o f 3 0 meters ; the mea n rang e o f almos t al l bet a particle s i n ai r i s les s than 2 0 meters . Althoughnumerou s bet a particle s can trave l 1 mete r an d woul d resul t i n mor e biologica l damag e than i s being considere d i n thi s analysi s (i.e. , the consideratio n o f bet a particle s woul d resul t i n lowe r releas e value s base d o n the direc t exposur e pathway) , a release-to-exposur e distanc e o f 1 mete r i s highl yunlikel yi n reality
. Therefore , ignoring bet a particl e exposure s fo r the sak e o f simplicit yshoul d hav e littl e practica l effect
. 3. 2 Change s i n Model s t o Accommodat e Variation s i n Exposur e Perio d Th e perio d o f time tha t an individua l i s assume d t o b e expose d t o release d radionuclide s i s an inpu t variabl e t o mos t o f the pathwa ymodel s considere d i n thi s analysis
. I n the pathwaymode l considering direc t exposur e t o a poin t source , th e valu e o f thi s variabl e simpl ywa s varie d betwee n 1 da yan d 36 5 day s i n accordanc e wit hthe condition s show n i n Exhibi t 1
. A s discusse d below , however , the Agencyconclude d tha t ther e wa s adequat e justificatio n for no t varying the exposur e perio d i n the pathwaymodel s othe r than direc t exposure . Fo r th e inhalatio n exposur e pathway , th e calculate d inhalation releas e value s ar e independen t o f the assume d exposur e period
. Using the same atmospheri c relative concentratio n valu e (i.e. , X/Q ) t o represen t al l possibl e releas e periods , th e same quantit yo f radionuclide s release d t o the ai r wil l resul t i n th e same inhalatio n dos e regardles s o f whethe r the releas e last s 1 da yo r 1 year . Th e onl ydifferenc e betwee n thes e two case s woul d b e the lengt ho f time i t woul d tak e an individua l t o receive the dose
. Accordingly , the exposur e perio d i s no t a facto r i n th e inhalatio n pathwa ymode l an

d n o change s t o the mode l had t o b e mad e t o tak e int o accoun t variation s i n thi s parameter . Th e perio d o f exposur e i n th e ground-wate r ingestion mode l i s complicate d b ythe fac t tha t differen t radionuclide s migrat e i n groun d wate r a t differen t rate s an

d thu s maylinge r i n the vicinit yo f a drinking wate r wel l ove r differen t time periods
. Unde r the releas e an d ground-wate r transpor t characteristic s assume d i n the TBD , i t wa s estimate d tha t i t woul d tak e roughl y9 day s fo r a contaminate d groun d wate r plume t o pas s a wel l 3 0 meter s fro mthe poin t o f releas e i f the radionuclide s wer e no t sorbed t o soi l (se e Appendi xF o f th e TBD)
. However , i f a radionuclide' s sorption coefficien t i s 4 o r more , the time necessaryfor the radionuclid e t o reachan d pas s a wel l 3 0 meter s awa

yi s greate r than 36 5 days
. Base d o n thi s analysis , the Agenc y conclude d tha t the perio d o f exposur e i n the ground-wate r ingestion mode l i s a functio n o f th e propertie s o f the radionuclid e i n questio n an d coul d no t b e change d arbitraril ybetwee n 1 da yan d 36 5 days
. Therefore , the perio d o f ground-wate r ingestio n wa s no t varie d i n accordanc e wit hthe condition s show n i n Exhibi t 1 , bu t rathe r wa s varie d betwee n 9 an d 36 5 day s depending o n th e sorptio n coefficien t selecte d for eachradionuclide
.P. 9

Areleas e conceivabl ycoul d contaminat e a smal l quantit yo f vegetables ; fo r example , th e quantit ytha t a perso n migh t ea t i n on e da yo r less
. I t i s als o possible , however , fo r a releas e o f the same magnitud e t o contaminat e a muc hlarge r crop an d i t i s no t inconceivabl e tha t a perso n subsequentl ycoul d ea t fro mtha t crop fo r period s clos e t o a year . Consequently , rathe r than varying th e perio d o f ingestion betwee n 1 da yan d 36 5 days , the Agenc ydecide d t o adop t a singl e conservative , althoughno t worst-case , exposur e perio d tha t ha s some technica l basis
. I n particular , i t wa s assumed for al l th e set s o f condition s show

n i n Exhibi t 1 tha t a perso n ingest s contaminate d vegetable s ove r th e entir e vegetabl e growing season , generall yrecognize d t o b e 6 0 days
. Asimila r approac hwa s adopted for the mode l use d t o evaluat e exposur e vi a the ingestio n o f contaminate d milk
. Thi s mode l assume s tha t gras s i s contaminate d b

yan airborn e releas e o f radionuclides , the contaminate d gras s i s ingeste d b

ya cow , an

d radionuclide-bearing mil k produce d b yth e cowi s i n tur n ingeste d b

ya person . Bot hthe perio d o f time tha t th e cowgraze s fro m th e contaminate d pastur e an d the time ove r whic hthe expose d individua l drink s contaminate d mil k ar e completel yarbitrary
. Therefore , rathe r than simpl y varying the exposur e perio d i n thi s pathwaymode l betwee n 1 da yan d 36 5 days , th e Agenc yselecte d a singl e time period
. T o b e consisten t wit hth e vegetabl e ingestio n pathwa

ymodel , EPAassume d tha t the cowgraze d fo r a perio d o f 6 0 day s an d tha t the perso n subsequentl ydran k mil k fro

mthe cowove r thi s same period
. Th e mode l fo r submersio n i n an airborn e clou d assume s tha t nobl e gase s ar e release d t o the atmospher e (i.e. , no t containe d withi n a structure ) an d tha t th e clou

d travel s t o an exposur e poin t 3 0 meter s away . Unde r thi s scenario , the lengt ho f time tha t an individua l coul d b e submerse d i n th e clou d i s the same a s the perio d o f release
. RQ s ar e applicabl e t o release s tha t las t u p t o 1 day
. Therefore , a n exposur e perio d o f 1 da ywa s use d fo r al l th e condition s show n i n Exhibi t 1
. 3. 3 Change s i n Model s t o Accommodat e Variation s i n Dose-Equivalen tLimi t Al l o f th e model s use d i n thi s analysi s (regardles s o f th e exposur e pathwa ybeing evaluated ) requir e a s an inpu t variabl e the maximu m dose-equivalen t limi t tha t the hypotheticall yexpose d individua l i s allowe d t o receive
. Thi s variabl e take s th e for mo f th e Annua l Limi t o f Intak e (ALI ) o r Derive d Ai r Concentratio n (DAC ) presente d i n ICRP Publicatio n 3 0 divide d b yan adjustmen t factor
. Bot hthe AL I an d DA C ar e base d o n an expose d individual , ove r the cours e o f a year , receiving an effectiv e whol e bod ydose-equivalen t o f 5 rem . I n orde r t o calculat e RQ s base d o n an alternat e whol e bod ydos e limit , appropriat e adjustmen t factor s t o arrive a t the dos e limit s show n i n Exhibi t 1 wer e used
. Fo r example , i n thos e analyse s tha t assume a whol e bod y dos e limi t o f 0. 5 rem , th e AL I o r DA C i s divide d b

y10 ; th e AL I o r DAC i s divide d b

y5 0 fo r thos e analyse s wher e the dos e limi t i s 0. 1 rem .P.1 0

-8 -

3. 4 Change s i n Model s t o Incorporat e Radioactiv e Deca y I n the pathwaymodel s use d i n the NPRM , radioactive deca ywa s ignored fo r th e sak e o f conservatisman d simplicity
. Recognizing , however , tha t radioactive deca

yi s an intrinsi c propert yo f al l radionuclides , the Agency ha s analyze d wha t the propose d RQ s woul d b e i f deca ywer e take n int o account . Fo r the purpos e o f thi s analysis , th e tota l perio d o f time i n the hypothetica l releas e an d exposur e scenario s can b e divide d int o thre e segments : (1 ) th e time perio d ove r whic hthe releas e occurs ; (2 ) the time i t take s fo r th e radionuclid e t o trave l fro mth e poin t o f releas e t o th e poin t o f exposure ; an

d (3 ) th e perio d o f exposure . Radioactiv e decayove r thes e time period s i s take n int o accoun t differentl yi n the differen t exposur e pathway models
. Fo r the inhalation pathwa ymode l an

d th e direc t exposur e mode l tha t consider s submersio n i n an airborn e cloud , the Agencydecide d t o continu e t o ignor e the effect s o f radioactive deca yi n thi s analysis
. Bot ho f thes e pathwa ymodel s conside r exposure s t o an airborn e plume o f radionuclides
. A short-live d radionuclid e coul d underg o significan t decayi f th e releas e an d exposur e period s wer e severa l days , bu t deca ywoul d b e muc hles s i f a time perio d o f severa l hour s wa s considered
. Becaus e i t wa s no t possibl e t o establis hexac t bound s o n the rang e o f releas e an d exposur e periods , the Agencyassume d conservativel ytha t n o deca yoccur s ove r thes e periods
. EPA als o ignored deca

yove r the perio d o f radionuclid e transpor t t o the poin t o f inhalation o r submersio n i n a cloud
. Thi s approac hwa s adopte d becaus e decay during airborn e transpor t t o a recepto r jus t 3 0 meter s awa ywoul d b e negligibl e fo r al l bu t a handful l o f radionuclides
. I n the mode l use d t o evaluat e exposur e b yth e ingestio n o f groun d water , the releas e i s assume d conservativel yt o b e instantaneou s suc htha t n o decay ove r the perio d o f releas e coul d occur . Deca yove r the perio d o f transpor t an d perio d o f ingestion , however , i s considered
. Fo r the perio d o f transport , th e time tha t i t woul d tak e fo r a release d radionuclid e t o trave l t o a drinking wate r wel l i s firs t determine d assuming conservative transpor t characteristics
. Onc e th e time o f transpor t i s estimated , deca yove r thi s time i s take n int o accoun t using the exponentia l function :

A= Aexp(-Xt ) t o wher e A= activit ya t time t ; t A= activit ya t time t= o (i.e. , initia l activit yreleased) ; o_P_J 1

X= 0.693 , wher e T-l/ 2 = the radionuclid e half-life ; an d T-l/ 2 t = time tha t i t take s the release d radionuclid e t o trave l t o the receptor . T o conside r deca

yove r the perio d o f ingestion , i t wa s recognize d tha t an individua l woul d inges t smalle r quantitie s o f radioactivit ya t time s tha t ar e successivel ylonge r fro mthe time tha t the radionuclid e firs t arrive s a t th e poin t o f exposure . Accordingly , deca yove r the perio d o f exposur e wa s take n int o accoun t i n the ground-wate r mode l throughthe following integrate d exponentia l equation :

1 - exp(-Xte ) A= C * * IR t e t X wher e A= the quantit yo f radioactivit yingeste d ove r the perio d o f exposure ; t e C = the concentratio n o f radioactivit ytha t firs t arrive s a t the poin t t o f exposure ; t e = the perio d o f exposure ; X= 0.693 , wher e T-l/ 2 = the radionuclid e half-life ; an d T-l/ 2 IR = wate r ingestion rate . I n the model s use d t o evaluat e the ingestio n o f mil k an d the ingestio n o f vegetable s contaminate d b yairborn e deposition , the assumptio n wit hregard t o the perio d o f releas e an d airborn e depositio n follow s th e same approac huse d i n the inhalatio n an d clou d submersio n models
. Tha t is , deca yduring releas e an d depositio n wa s ignored
. Similarly , deca yduring airborn e transpor t t o vegetatio n located 3 0 meter s awa ywa s no t considere d becaus e i t woul d b e negligibl e for al l bu t a handfu l o f radionuclides
. Onc e the initia l quantit y o f radioactivit yi s deposite d o n th e vegetation , however , a significan t amoun t o f deca ycoul d occur befor e th e radionuclide s ar e actuall yconsume d b yma n (eithe r directl ythroughthe ingestion o f vegetable s o r indirectl ythroughth e ingestio n o f milk)
. Therefore , deca yove r the perio d o f ingestion wa s take n int o accoun t i n th e vegetabl e an d mil k ingestio n model s using an integrate d deca yexpressio n a s show n above
. Finally , onl ydeca

yove r the perio d o f exposur e wa s considere d i n the mode l use d t o evalaut e direc t exposure s t o a poin t source . Deca ywa s considere d i n thi s pathwaymode l b yusing an integrate d deca yterm , accounting fo r an individual' s cumulative exposur e ove r th e entir e perio d tha t the perso n remain s i n the vicinit yo f the poin t source . Th e Agencyconservativel y assume d an instantaneou s releas e (i.e. , n o deca yove r the perio d o f release)
.P.1 2

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Similarly , the Agencyconservativel yassume d tha t n o deca ytake s plac e during the time neede d fo r a release d sourc e t o come int o contac t wit han individual
. 4 . DERIVATIO N O FMODE L EQUATION S
Eac ho f th e specifi c equation s use d t o evaluat e exposure s unde r th e condition s show

n i n Exhibi t 1 i s derive d i n thi s section
. T o hel p illustrat e the change s mad e i n the variou s pathwa ymodel s i n going fro mon e se t o f condition s t o the next , al l o f the equation s use d t o evaluat e a particula r exposur e pathwayar e describe d togethe r i n separat e sections ; tha t is , al l th e inhalation pathwa

ymodel s acros s the variou s set s o f condition s ar e derive d i n Sectio n 4.1 , al l th e ground-wate r ingestion model s acros s the variou s set s o f condition s ar e derive d i n Sectio n 4.2 , an d s o on . Withi n eac hsection , th e equatio n use d t o calculat e RQ s unde r th e condition s assume d i n th e NPR Mi s presente d an

d briefl ydescribe d firs t (th e TB D shoul d b e reference d fo r mor e detai l o n th e equation s use d i n the NPRM)
. Th e equation s use d t o mode l th e pathway s unde r condition s 1 throug h1 8 (se e Exhibi t 1 ) are-'the n derived , wit h an emphasi s place d o n howth e equation s diffe r fro mth e on e use d i n th e NPRM . Tw o additiona l point s als o shoul d b e explaine d t o hel p introduc e the equation s tha t follow
. First , a s discusse d i n Section 3. 1 o f thi s paper , the onl yexposur e pathwaytha t wa s evaluate d assuming 1 mete r betwee n th e poin t o f releas e an

d the poin t o f exposur e wa s direc t exposur e t o a poin t source . Therefore , for thos e set s o f condition s involving a distanc e o f 1 mete r (i.e. , Condition s 3 , 6 , 7 , 10 , 1 1 an d 18) , n o equation s ar e derive d fo r the inhalation , ingestio n o f groun d water , ingestio n o f vegetables , ingestio n o f milk , an

d submersion-in-a-cloud pathways
. Second , eacho f the equation s tha t i s derive d belowi s fo r the calculatio n o f "releas e values, " no t RQs . Th e lowes t releas e valu e fo r a give n radionuclid e considering eac ho f the exposur e pathway s unde r th e define d se t o f condition s i s selecte d a s the RQ fo r tha t radionuclide
. 4. 1 Inhalatio n Pathwa yEquation s Equatio n Use d i n NPRM . As describe d o n pag e 4- 3 o f the TBD , the equatio n use d t o evaluat e the inhalation pathwa yi n suppor t o f the NPR Mis : (1 ) Inhalatio n Releas e Valu e = ALI/((10)*(R)*(X/Q)*(BR)*(lxl0 6 ) ) wher e AL I = Annua l Limi t o f Intak e for inhalation (microcuries) ;

1 0 = Facto r t o adjus t the dose-equivalen t limi t buil t int o th e ALI , 5 rem , t o a limi t o f 0. 5 rem ; R = Releas e Fraction ; X/ Q = Atmospheri c Relativ e Concentratio n Valu e (8. 4 x10- 1 3 day / cubi c cm) ;P.1 3

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B R = Breathing Rat e (2. 3 xIO 7 cubi c cm/day) ; an d 1 x10 s = Conversio n facto r betwee n microcurie s an d curies
. Whe n al l o f th e specifie d value s ar e plugge d int o Equatio n (1) , the equatio n simplifie s to : (2 ) Inhalatio n Releas e Valu e = AL I (inhalation)/(193.2*R ) Conditio n 1
. Exhibi t 1 show s tha t the onl ydifferenc e betwee n Conditio n 1 an d the se t o f condition s assume d i n th e NPR Mwa s a differen t whol e bod ydos e limi t (0.02 5 re

mrathe r than 0. 5 rem)
. Therefore , onl ythe dose-equivalen t limi t adjustmen t facto r i n Equatio n (1 ) neede d t o b e change d fro m1 0 t o a facto r o f 200
. Plugging thi s newfacto r i n Equatio n (1 ) wit hthe othe r value s show n fo r the equation , the revise d inhalatio n pathwa ymode l reduce d to : (3 ) Inhalatio n Releas e Valu e = AL I (inhalation)/(3864*R ) Conditio n 2
. Lik e the revisio n neede d i n Conditio n 1 , th e onl ychang e t o Equatio n (1 ) tha t wa s neede d t o accommodat e Conditio n 2 wa s a differen t dos e limi t adjustmen t factor
. Using a facto r o f 5 0 t o adjus t th e dos e limi t t o 0. 1 rem , Equatio n (1 ) became : (4 ) Inhalatio n Releas e valu e = AL I (inhalation)/(966*R ) Conditio n 4
. Th e onl ydifferenc e betwee n Conditio n 4 an d Conditio n 1 wa s tha t radioactive deca ywa s considere d i n Conditio n 4
. A s discusse d i n Sectio n 3. 4 o f thi s paper , however , the Agencydecide d t o ignor e the effect s o f radioactive deca

yi n al l inhalation pathwaymodels
. Therefore , the same inhalatio n pathwa

ymode l (Equation (3) ) use d for Conditio n (1 ) wa s use d unde r thi s se t o f conditions
. Conditio n 5
. Becaus e radioactive deca ywa s ignored i n the inhalatio n pathwa ymodels , the same equatio n use d unde r Conditio n 2 - - Equatio n (4 ) - - wa s used unde r Conditio n 5 (th e onl ydifferenc e betwee n Condition s 2 an d 5 wa s tha t Conditio n 5 consider s decay)
. Conditio n 8
. Thi s se t o f condition s i s the same a s tha t use d i n the NPR M excep t tha t i t assume d a 36 5 da yexposur e perio d rathe r than a 1 da yexposur e period
. A s discusse d i n Sectio n 3. 2 o f thi s paper , inhalation releas e valu e result s ar e independen t o f the perio d o f exposur e assume d i n the calculation
. Unde r th e conservative atmospheri c dispersio n condition s assume d i n thi s analysis , the same quantit yo f radionuclid e release d t o the ai r ove r differen t time period s woul d resul t i n the same tota l inhalatio n dose ; i t woul d jus t tak e differen t period s o f time t o receive thi s dose
. A s a result , th e inhalatio n pathwa

ymode l use d i n the NPR M(Equation (2) ) di d no t hav e t o b e modifie d t o accoun t fo r the differen t exposur e perio d assumed unde r thi s se t o f conditions
. Conditio n 9
. Th e onl ydifferenc e betwee n Conditio n 9 an d Conditio n 8 i s tha t Conditio n 9 considere d radioactive decay
. However , for the reason s give nP.1 4

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i n Sectio n 3. 4 o f thi s paper , the Agencydecide d t o continu e t o ignor e radioactive deca

yi n the inhalatio n pathwaymodels
. A s a result , the same inhalatio n pathwaymode l use d fo r Conditio n 8 , Equatio n (2) , wa s als o use d fo r thi s se t o f conditions
. Conditio n 12
. Th e ALI s fo r inhalatio n wer e use d directl ya s th e inhalatio n releas e value s for thi s condition
. Th e onl ymodification.t o th e ALI s tha t wa s neede d wa s t o conver t the mfro munit s o f microcurie s t o curie s using th e following equation : Inhalatio n AL I (i n microcuries ) (5 ) Inhalatio n Releas e Valu e (i n curies ) = 1 x10 s wher e 1 x10 p = Conversio n facto r betwee n microcurie s an d curies
. Conditio n 13
. Unde r thi s condition , th e inhalation releas e value s wer e calculate d simpl yb ytaking a multipl e o f th e inhalatio n ALIs . Specifically , the ALI s wer e multiplie d b y100 0 t o arrive a t ALI s base d o n 500 0 re ma s oppose d t o 5 rem . Combining thi s multiplicatio n wit hthe conversio n neede d t o calculat e releas e value s i n unit s o f curies , the inhalation pathwaymode l use d unde r thi s conditio n too k the form : 100 0 * Inhalation AL I (in microcuries ) (6 ) Inhalatio n Releas e Valu e =

(in curies ) 1 x10 s Inhalatio n AL I (i n microcuries )

1 xIO 3 wher e 100 0 = Facto r use d t o adjus t the ALI , base d o n a dos e limi t o f 5 rem , t o

an AL I base d o n 500 0 rem ; an d 1 x10 s = Conversio n facto r betwee n microcurie s an d curies
. Conditio n 14
. Thi s conditio n i s the same a s Conditio n 1 3 excep t tha t th e dos e limi t i n thi s cas e i s 2 5 re mrathe r tha n 500 0 rem . Accordingly , th e equatio n use d her e wa s the same a s Equatio n (6 ) excep t tha t a dos e adjustmen t facto r o f 5 wa s use d rathe r than a facto r o f 1000 , a s show n below : 5 * Inhalatio n AL I (in microcuries ) (7 ) Inhalatio n Releas e Valu e =

(i n curies ) 1 x10 s Inhalatio n AL I (i n microcuries )

2 x10 sP.1 5

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wher e 5 = Facto r use d t o adjus t the ALI , base d o n a dos e limi t o f 5 rem , t o

an AL I base d o n 2 5 rem ; an d 1 x10 s = Conversio n facto r betwee n microcurie s an d curies
. Conditio n 15
. Lik e Condition s 1 3 an d 14 , releas e value s unde r thi s conditio n wer e calculate d simpl yb ytaking a multipl e o f th e inhalatio n ALIs . I n thi s case , the dose-equivalen t limi t o f interes t wa s 50 0 rem , suchtha t releas e value s wer e calculate d using the following equation : 10 0 * Inhalation AL I (i n microcuries ) (8 ) Inhalatio n Releas e Valu e =

(in curies ) 1 x10 s Inhalatio n AL I (i n microcuries )

1 x10 * wher e 10 0 = Facto r use d t o adjus t the ALI , base d o n a dos e limi t o f 5 rem , t o

an AL I base d o n 50 0 rem ; an d 1 x10 s = Conversio n facto r betwee n microcurie s an d curies
. Conditio n 16
. Thi s se t o f condition s i s the same a s tha t use d i n the NPR M excep t tha t i t incorporate d th e effect s o f radioactiv e decay
. However , fo r th e reason s give n i n Sectio n 3. 4 o f thi s paper , EPAdecide d t o continu e t o ignor e radioactive deca yi n the inhalatio n pathwaymodels
. A s a result , the inhalatio n pathwaymode l use d i n suppor t o f th e NPR M(Equation (2) ) als o wa s use d i n th e calculatio n o f releas e value s unde r Conditio n 16
. Conditio n 17
. Ther e ar e two difference s betwee n thi s se t o f condition s an d the on e use d i n the NPRM : (1 ) an exposur e perio d o f 36 5 day s rathe r than 1 da ywa s assumed ; an

d (2 ) the dose-equivalen t limi t wa s 0. 1 re mrathe r than 0. 5 rem . However , becaus e th e inhalatio n releas e value s ar e independen t o f th e assume d exposur e perio d (se e Sectio n 3. 2 o f thi s paper) , the inhalatio n pathwayequatio n use d i n the NPR M(i.e. , Equatio n (1) ) di d no t hav e t o b e change d t o incorporat e th e differen t exposur e perio d assume d here
. Equatio n (1 ) di d hav e t o b e changed , however , t o accoun t fo r the revised dose-equivalen t limit
. Specifically , a facto r o f 5 0 (rathe r than a facto r o f 10 ) wa s use d t o adjus t th e dose-equivalen t t o 0. 1 rem . Plugging thi s differen t facto r int o Equatio n (1 ) along wit hth e othe r inpu t value s show n fo r tha t equation , the inhalatio n pathwa yequatio n use d for thi s conditio n reduce d to : (9 ) Inhalatio n Releas e Valu e = AL I (inhalation)/(966*R )P.1 6

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4. 2 Ground-Wate rIngestio n Pathwa yEquation s Releas e value s fo r the ground-wate r ingestio n pathwaywer e calculate d using the following basi c equatio n (se e Sectio n 4.2. 2 o f the TB D for mor e discussio n o n the derivatio n o f thi s equation) : (10 ) Ground-wate r Ingestio n = ALI/((AF)*(DF)*(CT)*(WC)*(lxl0 6 ) ) Releas e Valu e (curies ) wher e AL I = Annua l Limi t o f Intak e for ingestion fo r a particula r radionuclid e

(microcuries) ; A F = Dose-equivalen t adjustmen t facto r t o adjus t th e dose-equivalen t o n whic hthe AL I i s based , 5 rem , t o a dose-equivalen t limi t o f interest ; DF = Dilutio n factor , the concentratio n o f a radionuclid e a t a drinking

wate r wel l 3 0 meter s fro mthe poin t o f releas e pe r curi e release d (Ci/lite r pe r Ci , o r liter- 1 ) ; C T = Contac t time i n days , o r the numbe r o f day s an individua l drink s

the contaminate d water ; W C = Wate r consumptio n rat e o f referenc e ma n ( 2 liters/day) ; an d 1x10 s = Conversio n facto r betwee n microcurie s an d curies
. A s derive d i n Sectio n F. l o f the TBD , the dilutio n facto r use d i n Equatio n (10 ) wa s expresse d i n the following manner : (11 ) DF = 7. 6 xIO- 8 liters-'/R d wher e R d - = the radionuclid e retardatio n facto r (i.e. , a facto r tha t account s for the degre e t o whic hradionuclide s ar e sorbe d t o the aquife r medi a an d thu s slowe d i n movemen t relative t o the transporting water)
. Whe n a radionuclide' s sorptio n coefficien t equal s zero , the R d for tha t radionuclid e equal s one ; tha t is , the radionuclid e move s a t the same rat e a s the groun

d water . I n thi s situation , an d unde r the ground-wate r transpor t characteristic s assume d i n the TBD , the Agencyestimate d tha t i t woul d tak e approximatel y6 day s fo r the leadin g edg e o f th e contaminan t plume t o firs t reacha wel l 3 0 meter s awa yan d the n 9 day s fro

mthe time o f the firs t arriva l fo r the trailing edg e o f the plume t o pas s the well
. Therefore , the contac t time whe n R

d = 1 wa s estimate d t o b e 9 days
. A s sorptio n coefficient s ris e above 4 , the time necessaryfo r a radionuclid e t o reachan d pas s a wel l 3 0 meter s fro

mthe poin t o f releas e become s greate r than 36 5 days
. Becaus eP.1 7

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ALI s ar e concerne d wit hannua l limit s o f intake , however , EP Achos e t o limi t th e contac t tim e i n thes e situation s t o 36 5 days
. I t i s als o importan t t o clarif ytha t th e dilutio n facto r give n i n Equatio n (11 ) i s designe d t o yiel d th e maximumradionuclid e concentratio n tha t passe s th e drinkin g wate r well
. Therefore , radionuclid e los s du e t o radioactiv e deca yove r th e tim e o f transpor t ha s no t bee n factore d int o th e dilutio n facto r use d i n th e NPRM . Suc hcorrection s fo r decay , ove r bot hth e tim e o f transpor t an d th e perio d o f ingestion , ar e carrie d ou t throug hseparat e deca y term s a s explaine d belo wunde r Condition s 4 , 5 , 9 , an d 16
. Equation s Use d i n th e NPRM . I n th e NPRM , a valu e o f 1 0 wa s use d fo r A F t o adjus t th e dose-equivalen t limi t fro m5 re m t o 0. 5 rem . Substitutin g thi s valu e alon g wit hC T = 9 day s fo r radionuclide s wit ha R d = 1 int o Equatio n (10) , th e equatio n simplifie d to : (12 ) Ground-wate r Ingestio n = ALI/(1. 4 x10 1 ) Releas e Valu e Whe n R d > 1 , th e contac t tim e wa s assume d t o b e 36 5 days
. Usin g 36 5 a s th e valu e fo r C T whil e keepin g R d a s a variable , Equatio n (10 ) became : (13 ) Ground-wate r Ingestio n = ((ALI ) * (Rd))/(5. 5 x10 2 ) Releas e Valu e Conditio n 1
. Th e equation s use d fo r thi s conditio n wer e derive d differentl yfro mthos e use d i n th e NPR Monl ybecaus e o f th e us e o f a different dose-equivalen t adjustmen t factor
. Specifically , a valu e o f A F = 20 0 wa s use d rathe r tha n 1 0 t o arriv e a t a dose-equivalen t limi t o f 0.02 5 re mrathe r tha n 0. 5 rem . Pluggin g thi s valu e int o Equatio n (10 ) an d followin g th e sam e rational e a s presente d abov e fo r th e NPR Mequations , th e equation s use d i n thi s cas e were : (14 ) Ground-wate r Ingestio n = ALI/(2. 7 x10 2 ) Releas e Valu e whe n R d = 1 , an d (15 ) Ground-wate r Ingestio n = ((ALI)*(Rd))/(1. 1 x10" ) Releas e Valu e whe n R d > 1
. Conditio n 2
. Lik e Conditio n 1 , Conditio n 2 differ s fro mth e condition s assume d i n th e NPR Monl ybyassumin g a different dose-equivalen t limi t (0. 1 re mrathe r tha n 0. 5 rem)
. Accordingly , th e appropriat e dose-equivalen t adjustmen t facto r fo r thi s conditio n i s 50
. Pluggin g thi s valu e fo r A F int o Equatio n (10) , th e equatio n becomes : (16 ) Ground-wate r Ingestio n = ALI/(6. 8 x10 1 ) Releas e Valu eP.1 8

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whe n R d = 1 , an d (17 ) Ground-wate r Ingestio n = ((ALI)*(Rd))/(2. 8 xIO 3 ) Releas e Valu e whe n R d > 1
. Conditio n 4
. Unde r thi s se t o f conditions , th e appropriat e valu e fo r A F wa s 20 0 i n orde r t o adjus t th e dose-equivalent limi t fro m5 re mt o 0.02 5 rem . I n addition , becaus e thi s se t o f condition s include d th e effect s o f radioactiv e decay , Equatio n (10 ) neede d t o b e modifie d t o includ e tw o deca y terms . First , a ter mt o accoun t fo r radioactiv e deca ydurin g th e perio d o f transpor t fro mth e poin t o f releas e t o th e poin t o f exposur e ha d t o b e included
. Thi s ter mtoo k th e form : (18 ) exp (-Xt ) wher e X= 0.693/T-1/2 , wher e T-l/ 2 = radionuclid e half-lif e i n days ;

an d
t = tim e tha t i t take s fo r th e contaminan t plum e t o firs t reac ha drinkin g wate r wel l 3 0 meter s fromth e point o f releas e (estimate d t o b e 6 day s whe n R d =1 ; se e AppendixF o f th e TBD )
. Th e secon d deca yter mtha t wa s neede d wa s t o accoun t fo r radioactiv e deca y ove r th e perio d o f ingestion
. Thi s deca yter mtoo k th e form : (19 ) 1 - exp (-XCT )

wher e X= 0.693/T-1/2, wher e T-l/ 2 = radionuclid e half-lif e i n days ;

an d
C T = contac t time , rangin g anywher e fro m9 day s whe n R d = 1 t o u p

t o 36 5 day s whe n R d > 1
. Pluggin g thes e tw o deca yterm s int o Equatio n (10) , th e equatio n fo r ground-wate r ingestio n releas e value s incorporatin g th e effect s o f radioactiv e deca ybecame : (20 ) Ground-wate r AL I Ingestio n = (AF)*(DF)*(exp(-Xt))*(WC)*(lxlO s ) * (l-exp(-XCT) ) Releas e Valu e

T o accommodat e th e se t o f condition s assume d unde r Conditio n 4 , a valu e o f A F = 20 0 wa s inserte d int o Equatio n (20 ) an d th e equatio n simplifie d t o th e followin g whe n R d = 1 :P.1 9

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(21 ) Ground-wate r AL I * (2. 3 xIO- 2 ) Ingestio n Releas e Valu e (exp(-4.2/T-l/2))*(T-l/ 2 - T-l/ 2 exp(-6.2/T-l/2) ) wher e T-l/ 2 = radionuclid e half-lif e i n days
. Whe n R d > 1 , i t take s a significantl ylonge r time for th e release d radionuclide s t o migrat e t o an d pas s the wel l point
. Incorporating radioactive deca

yi n thi s scenari o ha s the effec t o f "removing " a larg e portio n o f th e radionuclide s befor e theycan b e ingested
. A s a result , the calculate d releas e valu e i s significantl ylarge r than the releas e valu e assuming R

d = 1 and , i n fact , become s muc hlarge r i n compariso n wit hthe othe r releas e value s calculate d fo r th e othe r exposur e pathways
. I t i s recognized , therefore , tha t th e ground-wate r ingestio n releas e valu e whe n R d > 1 woul d neve r driv e the R Q fo r a give n radionuclid e and , accordingly , the Agencydi d no t develop separat e ground-wate r ingestio n equation s for situation s wher e R d > 1
. Conditio n 5
. Th e equatio n use d unde r thi s conditio n wa s derive d i n exactl ythe same manne r a s the equatio n use d unde r Conditio n 4 excep t tha t an AF valu e o f 5 0 wa s use d instead o f 200
. Making thi s substitutiona l chang e i n Equatio n (20 ) an

d following the same rational e a s outline d fo r Conditio n 4 , th e equatio n use d i n thi s cas e became : (22 ) Ground-wate r AL I * (9. 1 x10- 2 ) Ingestion = Releas e Valu e (exp(-4.2/T-l/2))*(T-l/ 2 - T-l/ 2 exp(-6.2/T-1/2) ) wher e R d = 1 an

d T-l/ 2 = half-lif e i n days
. Again , n o equatio n wa s derive d fo r situation s wher e R d > 1 becaus e the resulting releas e valu e woul d b e significantl yhighe r than the releas e valu e calculate d for the othe r exposur e pathways
. Conditio n 8
. Th e onl ydifferenc e betwee n thi s conditio n an d th e condition s assume d i n the NPR Mi s tha t i t assume d a 365-da yexposur e perio d fo r the direc t exposur e t o a poin t sourc e release
. As discusse d i n Sectio n 3. 2 o f thi s paper , however , the Agencydecide d no t t o var ythe exposur e perio d i n the ground-wate r ingestio n mode l betwee n 1 da yan d 36 5 day s a s show

n i n Exhibi t 1 , bu t rathe r t o us e exposur e period s tha t ar e consisten t wit hth e ground-wate r transpor t characteristic s define d fo r thi s analysi s (i.e. , 9 day s t o 36 5 day s depending o n a radionuclide' s Rd value)
. Wit hthi s approach , ther e wer e n o difference s i n the NPR Mcondition s an

d Conditio n 8 fo r th e ground-wate r ingestio n model , an d th e same equation s use d i n the NPR M(i.e. , Equation s (12 ) an

d (13) ) wer e use d here
. Conditio n 9
. Th e equatio n use d fo r thi s se t o f condition s wa s derive d b y using Equatio n (20 ) an d al l the inpu t value s specifie d for tha t equatio n (se e discussio n above for Conditio n 4 ) except , rathe r than using a valu e o f AF = 200 , a valu e o f AF = 1 0 wa s used
. Again , th e 365-da yexposur e perio d assume d fo r Conditio n 9 wa s applicabl e onl yt o the pathwaymode l concerning direc t exposur e t o a poin t source ; the exposur e perio d use d i n the ground-wate rP.2 0

-18

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ingestio n mode l varie d fro m9 day s t o 36 5 day s depending o n the radionuclide' s Rd
. Therefore , for case s wher e R d = 1 , the equatio n use d fo r thi s conditio n was : (23 ) Ground-wate r AL I * (4. 5 x10- x )

Ingestio n Releas e Valu e (exp(-4.2/T-l/2))*(T-l/ 2 - T-l/ 2 exp(-6.2/T-1/2) ) wher e T-l/ 2 = radionuclid e half-lif e i n days
. Aseparat e equatio n wa s no t derive d for case s wher e R d > 1 because , a s describe d above , the releas e value s calculate d i n thes e case s woul d b e relativel yhighan

d inconsequentia l i n the adjustmen t o f RQs . Condition s 12-15
. Th e ground-wate r ingestion equation s use d unde r thes e condition s wer e derive d i n exactl ythe same waya s th e inhalation equation s fo r Condition s 12-15
. Th e onl ydifferenc e betwee n the two set s o f equation s wa s tha t the AL I fo r ingestio n wa s use d her e rathe r th e inhalatio n AL I a s use d i n the inhalation pathwayequations
. Refe r t o th e derivatio n o f thes e individua l equation s give n i n Sectio n 4. 1 o f thi s paper . Conditio n 16
. Th e onl ydifferenc e betwee n thi s se t o f condition s an d the on e use d i n the NPR Mwa s tha t i t incorporate d the effect s o f radioactive decay
. Therefore , the equatio n use d i n thi s cas e wa s derive d b yusing Equatio n (20 ) an

d substituting th e following values : AF = 10 ; DF = 7. 6 x IO- 8 liter-VRd ; t = 6 days ; WC = 2 liters/day , an d C T = 9 day s (when R d = 1)
. Whe n thes e value s wer e used , Equatio n (20 ) reduce d to : (24 ) Ground-wate r AL I * (4. 6 x10- x ) Ingestio n Releas e Valu e (exp(-4.2/T-l/2))*(T-l/ 2 - T-l/ 2 exp(-6.2/T-1/2) ) wher e T-l/ 2 = radionuclid e half-lif e i n days
. Conditio n 17
. Becaus e the 365-da yexposur e perio d specifie d fo r Conditio n 1 7 wa s onl yfo r the evaluatio n o f direc t exposur e t o a poin t source , ther e wa s n o differenc e betwee n thi s conditio n an d Conditio n 2 fo r the ground-wate r ingestio n pathwa

ymodel
. Therefore , the same equation s use d for Conditio n 2

- - Equation s (16 ) an d (17 ) - - als o wer e use d here
. 4. 3 Equation s fo rth e Ingestio n o fVegetable s Contaminate d b yAirborn e Depositio n Equatio n Base d o n Condition s Assume d i n the NPRM . I n suppor t o f the NPRM , th e basi c equatio n use d for the calculatio n o f releas e value s base d o n the consumptio n o f vegetable s wa s (se e pag e F-3 6 o f the TBD) :

Vegetabl e Ingestion (25 ) Releas e Valu e = ALI/((10)*(DF)*(FC)*(CT)*(R)*( 1 x10 s ) )

(i n curies )P.2 1

-19

-

wher e AL I = Annua l Limi t o f Intak e fo r ingestion (microcuries) ;

1 0 = Facto r t o adjus t the dose-equivalen t limi t buil t int o the ALI , 5 rem , t o a limi t o f 0. 5 rem ; D F = Dilutio n facto r accounting for the transfe r o f radionuclide s fro mai r t o vegetatio n (curies/kg o f vegetable s a t the poin t o f exposur e pe r curi e release d t o the atmosphere) ; F C = Foo d (i.e. , leafyvegetable ) consumptio n rat e o f referenc e man (0.17 5 kg/day) ; C T = Contac t time , o r the numbe r o f day s ove r whic hcontaminate d vegetable s ar e ingested ; R = Airborn e releas e fraction ; an d 1 x10 s = Conversio n facto r betwee n microcurie s an d curies
.
Sectio n F. 3 o f the TB D supporting the NPR Mdescribe s two alternat e model s fo r calculating the dilutio n facto r accounting fo r the transfe r o f radionuclide s fro

mai r t o vegetation
. On e o f th e model s i s presente d b ythe Nuclea r RegulatoryCommissio n i n RegulatoryGuid e 1.109 3 an d the othe r i s presente d b

ythe Nationa l Counci l o n Radiatio n Protectio n an d Measurement s (NCRP ) i n NCR P Commentar yNo . 3. * Th e two model s ar e basicall ythe same i n tha t theybot haccoun t for radionuclid e depositio n fro mth e air , radionuclid e los s du e t o weathering an d radioactive decay , an d radionuclid e buildu p i n an d uptak e fro

msoil
. Th e principa l differenc e betwee n the two model s lie s i n the waytheyaccoun t for the depositio n velocit yo f the radionuclid e i n question
. Briefly , t o determin e the depositio n velocity , the Nuclea r Regulatory Commissio n mode l relie s o n a relative depositio n ter mtha t consider s radionuclid e dispersio n an d depletio n whil e i n transi t fro mthe poin t o f releas e t o the poin t o f exposure . Th e NCR P model , o n the othe r hand , use s a singl e depositio n velocit ydefaul t valu e tha t i s invarian t t o the radionuclid e i n question , the atmospheri c dispersio n characteristics , an d the distanc e betwee n the poin t o f releas e an d th e poin t o f deposition
.

S U.S . Nuclea r RegulatoryCommission , Calculatio n o f Annua l Dose s t o Ma n fro mRoutin e Release s o f Reacto r Effluent s for the Purpos e o f Evaluating Complianc e wit h1 0 CFR Par t 50 , Appendi xI , RegulatoryGuid e 1.109 , Revisio n 1 , Octobe r 1977
. "Nationa l Counci l o n Radiatio n Protectio n an d Measurements , Screening Technique s fo r Determining Complianc e wit hEnvironmenta l Standards : Release s o f Radionuclide s t o the Atmosphere , NCR P Commentar yNo . 3 , 1986
.•20

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A s discusse d i n th e TBD , EP Apreviousl yha d selecte d th e Nuclea r Regulator yCommissio n mode l fo r us e i n th e adjustmen t o f RQs . Thi s selectio n wa s base d principall yo n th e belie f tha t th e depositio n defaul t valu e use d b y th e NCR P (100 0 meters/day ) wa s highl yconservative , resultin g i n needlessl y lo wRQs . Sinc e publishin g th e NPR Man d TBD , however , EP Aha s gaine d additiona l informatio n tha t point s t o th e NCR P mode l a s bein g mor e appropriat e fo r th e purpos e o f R Q adjustments
. I n particular , EP Aha s sinc e recognize d that : (1 ) th e derivatio n o f th e depositio n velocit yi n th e Nuclea r Regulator y Commissio n mode l i s incorrect ; an d (2 ) tha t th e NCR P default valu e o f 100 0 meters/da y(1. 2 cm/sec ) i s no t overl yconservativ e bu t rathe r i s i n th e rang e o f commonl yaccepte d value s frequentl yuse d i n environmenta l assessments . Accordingly , fo r thi s analysis , EP Aha s use d instea d th e NCR P equatio n wit ha depositio n velocit yo f 100 0 meters/da yt o calculat e th e dilutio n factor
. Thi s equatio n i s a s follows :

(26 ) D F = V

C d ai r 'r[ l - exp(- Xt ) ] B [ 1 - exp(- Xt )] ' E i e i vi b 

### + YXP X vE i i exp(- Xt ) i h

wher e
D F = Dilutio n factor; tha t is , th e concentratio n o f radionuclid e i n an d

o n vegetatio n pe r curi e o f radionuclid e release d t o th e atmospher e (Ci/k g pe r Ci ; o r kg- 1 )
V = Depositio n velocit yfo r wet an d dr ydepositio n (100 0 meters/day) ; d C = Concentratio n o f radionuclid e i n ai r a t th e locatio n o f growin g ai r vegetable s

= (Radionuclid e releas e rate)*(X/Q )

= (Ci/day)*(8. 4 xIO- 7 day/m 3 )

= 8. 4 xIO- 7 Ci/m 3 ;

r = Fractio n o f deposite d activit yretaine d o n crop s (0.25 , dimensionless) ;
Y= Agricultura l productivit y( 2 kg/m 2 ) ; v X= Effectiv e remova l rat e constan t fo r radionuclid e i fro mcrop s E i (i n day- 1 ) , wher e X= X+ X; E i i w X= 0.693/T-1/2 , wher e T-l/ 2 = half-lif e i n days ; iP.2 3

-21

-

X= Remova l rat e constan t fo r physica l los s b yweathering , calculate d wo n th e basi s o f a weathering half-lif e o f 1 4 days , suchtha t X= 0.693/1 4 day s = 0.0495/day ; w t = Time perio d tha t the crop s ar e expose d t o contaminatio n during th e e growing seaso n (assigned a valu e o f 1 da ybecaus e the maximu mperio d o f release , an

d henc e th e maximu

mperio d o f airborn e deposition , applicabl e t o RQ s i s 1 day) ; B = Concentratio n facto r fo r uptak e o f radionuclid e i fro msoi l b

y ivedibl e part s o f crops ; P = Effectiv e surfac e densit yfo r soi l (24 0 kg/m 2 , dr yweight) ; t = Time perio d ove r whic hthe soi l i s expose d t o contaminatio n b(assigned a valu e o f 1 da yfollowing the same reasoning give n above for t ) ; an

d e t = Time interva l betwee n harves t an d consumptio n o f vegetable s h(conservativel yassume d t o b e zer o days)
. Assuming n o radioactive deca y(i.e.
. X=0 ) becaus e the time perio d

i betwee n the time o f releas e an d contac t wit hthe vegetable s i s sufficientl y short , an

d plugging al l o f the above value s int o Equatio n (12) , the expressio n fo r DF reduced to : (27 ) D F = ( 1 x10- * + 3. 5 xIO- 6 B )kg- x iv Th e onl yremaining valu e neede d t o determin e the vegetabl e ingestio n releas e valu e i s a valu e for CT , the contac t time
. A s discusse d i n Sectio n 3. 2 o f thi s paper , the Agencyconservativel yassume d tha t an individua l ingest s the contaminate d vegetable s ove r the entir e lengt ho f the growing season , 6 0 days
. Thi s perio d mus t b e adjusted , however , t o accoun t fo r radionuclid e los s du e t o weathering ove r the 6 0 da yseason . Th e dilutio n facto r outline d above , whe n applie d t o th e quantit yo f radionuclid e release d i n 1 day , yield s the concentratio n o f radionuclid e i n an d o n vegetatio n afte r 1 da y(conservativel yassume d t o b e the firs t da yo f the growing season)
. Ove r the nex t 6 0 days , the radionuclid e concentratio n wil l progressivel y decreas e a s mor e an d mor e o f the contaminatio n i s los t du e t o weathering
. T o accoun t fo r thi s los s i n determining an individual' s cumulative intak e ove r the 6 0 da

yperiod , the "equivalent " contac t time wa s calculate d i n the following manner :

1 - exp(- Xt ) 1 - exp(-0.0495/da y* 6 0 days ) w (28 ) C T = X0.0495/da y w

= 1 9 day sP.2 4

-22

-

Pluggin g al l th e appropriat e value s int o Equatio n (25) , th e equatio n use d t o evaluat e th e ingestio n o f vegetable s contaminate d b yairborn e depositio n unde r th e se t o f condition s assume d i n th e NPR Mbecame :
(29 ) Vegetabl e Ingestio n Releas e Valu e AL I (ingestion ) (3. 3 xIO 3 + 1. 2 xIO 2 B ) * R i v Conditio n 1
. Conditio n 1 wa s exactl yth e sam e a s th e se t o f condition s assume d i n th e NPR Mexcep t tha t i t limite d th e dose-equivalen t t o 0.02 5 re m rathe r tha n 0. 5 rem . Accordingly , th e onl ydifferenc e i n th e equatio n use d her e an d Equatio n (25 ) wa s tha t a facto r o f 20 0 (rathe r tha n a facto r o f 10 ) wa s use d t o mak e th e appropriat e adjustmen t t o th e ALI . Usin g thi s ne w adjustmen t facto r wit hth e othe r inpu t value s specifie d abov e fo r Equatio n (25) , th e equatio n use d i n thi s conditio n became :
(30 ) Vegetabl e Ingestio n Releas e Valu e = AL I (ingestion ) (6. 7 x10 * + 2. 3 xIO 3 B ) * R i v Conditio n 2
. Lik e Conditio n 1 , Conditio n 2 differe d fro mth e se t o f condition s use d i n th e NPR Monl ybyassumin g a differen t dose-equivalen t limit , 0. 1 re mrathe r tha n 0. 5 rem . Pluggin g th e revise d adjustmen t factor , 50 , int o Equatio n (25 ) alon g wit hth e othe r inpu t variables , th e equatio n reduce d to :
(31 ) Vegetabl e Ingestio n Releas e Valu e = AL I (ingestion ) (1. 7 x10 * + 5. 8 x10 2 B ) * R i v Conditio n 4
. Unlik e th e preceediri g conditions , thi s conditio n incorporate d th e effect s o f radioactiv e decay
. A s describe d i n Sectio n 3. 4 o f thi s paper , th e Agenc ydecide d t o conside r deca yove r th e perio d o f ingestion , bu t t o ignor e deca yove r th e perio d o f releas e and depositio n (becaus e thes e tim e period s coul d b e ver yshort , prohibitin g significan t decay ) an d t o ignor e deca ydurin g transpor t t o th e vegetable s (becaus e transpor t t o a poin t 3 0 meter s awa ywoul d b e s o rapi d tha t deca ywoul d b e negligibl e fo r al l bu t a handfu l o f radionuclides)
. Wit hthi s approach , Equatio n (27 ) fo r calculatin g D F unde r th e condition s assume d i n th e NPR Mals o wa s applicabl e here
. Th e contac t tim e derive d i n Equatio n (28) , however , neede d t o b e revise d t o incorporat e a radioactiv e deca yterm . Specifically , th e contac t tim e neede d t o b e derive d i n th e followin g manner :

1 - exp(- Xt )

E i (32 ) C T = X

E iP.2 5

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1 - exp(-( X+ X) * t )

i w C T = X+ X

i w 1 - exp(-((0.693/T-l/2 ) + 0.0495/day ) * 6 0 days ) C T = (0.693/T-1/2 ) + 0.0495/da y 1 - exp-((41.6/T-l/2 ) + 3 ) C T = (0.693/T-1/2 ) + 0.049 5

wher e T-l/ 2 = radionuclid e half-lif e i n days
. Plugging thi s revise d expressio n fo r C T int o Equatio n (25 ) alon g wit ha dose-equivalen t adjustmen t facto r o f 20 0 (t o arrive a t a dos e limi t o f 0.02 5 re mrathe r than 0. 5 rem) , the equatio n use d unde r thi s se t o f condition s simplifie d to : (33 ) Vegetabl e Ingestion AL I (ingestion )

Releas e Valu e = (3. 5 xIO 3 + 1. 2 x10 2 B ) * (R ) * (CT ) iv wher e C T wa s calculate d using Equatio n (32)
. Conditio n 5
. Exhibi t 1 show s tha t thi s conditio n differe d fro mthe se t o f condition s assume d i n th e NPR Mi n two respects . First , i t assume d a differen t dose-equivalen t limit ; an d secon d i t incorporate d radioactive decay
. Thes e difference s wer e accounte d fo r her e b yusing a differen t dose-equivalen t adjustmen t facto r (5 0 rathe r than 10 ) an d b ycalculating C T using Equatio n (32 ) rathe r than Equatio n (28)
. Incorporating thes e change s int o Equatio n (25) , the equatio n use d fo r thi s conditio n became : (34 ) Vegetabl e Ingestio n AL I (ingestion )

Releas e Valu e = (8. 8 xIO 2 + 3. 1 x10 1 B ) * (R ) * (CT ) iv wher e C T wa s calculate d using Equatio n (32)
. Conditio n 8
. Thi s se t o f condition s differe d fro mtha t assume d i n th e NPR Mb yassuming a 365-da yexposur e perio d fo r the direc t exposur e t o a poin t sourc e pathway
. A s discusse d i n Sectio n 3. 2 o f thi s paper , however , the Agencydecide d no t t o var ythe exposur e perio d i n the analysi s o f vegetable s contaminate d b

yairborn e deposition
. Accordingly , the same equatio n use dP.2 6

•24

-

unde r the se t o f condition s use d i n the NPR M(i.e. , Equatio n (29) ) wa s used i n thi s situation
. Conditio n 9
. I n orde r t o accommodat e thi s se t o f conditions , th e equatio n use d unde r the NPR

Mcondition s onl yneede d t o b e modifie d t o incorporat e radioactive decay
. Thi s chang e yield s the following revised equatio n use d unde r Conditio n 9 : (35 ) Vegetabl e Ingestio n AL I (ingestion )

Releas e Valu e = (1.7 5 xIO 2 + 6. 1 B ) * (R ) * (CT ) iv wher e C T wa s calculate d using Equatio n (32)
. Condition s 12-15
. Becaus e th e same ingestio n ALI s ar e applicabl e regardles s o f whethe r wate r o r vegetable s ar e ingested , the same equation s derive d t o evaluat e ground-wate r ingestio n unde r thes e condition s wer e applicabl e t o th e ingestio n o f vegetables
. Refe r t o Sectio n 4. 2 fo r th e specifi c derivatio n o f eac ho f thes e equations
. Conditio n 16
. Becaus e the Agencydi d no t varythe exposur e perio d assumed i n th e vegetabl e ingestio n mode l (se e Sectio n 3. 2 o f thi s paper) , thi s conditio n wa s identica l t o Conditio n 9
. Accordingly , Equatio n (35 ) derive d above als o wa s use d here
. Conditio n 17
. Fo r the vegetabl e ingestio n pathwaymodel , ther e wa s n o differenc e betwee n Conditio n 1 7 an d Conditio n 2 (thes e two set s o f condition s differe d onl yi n th e perio d o f exposur e assume d i n th e mode l evaluating direc t exposur e t o a poin t source)
. Therefore , the same equatio n use d fo r Conditio n 2 - - Equatio n (31 ) - - wa s use d unde r thi s se t o f conditions
. 4. 4 Equation s fo rDirec tExposur e t o a Poin tSourc e Equatio nUse di nth eNPRM

. Th ebasi c equatio nuse dt o evaluat edirec t exposur et o apoin t sourc ei nsuppor t

o f th eNPR

M wa s a s follow s (referenc e Sectio n4.2. 3 i nth eTBD) : (36 ) Direc t

Exposur e= (6.41xl0- 5 ) * (Dn ) * (S 2 ) Releas eValu e (E) * ( u) * (T ) * (ex p (- uS) ) l aa wher e Dn = Dose-equivalen t i n rem ;

S = Distanc e betwee n th e poin t sourc e an d the receptor ; E = Th e su

mo f the product s o f the gamm a ra yenergie s (MeV ) an d 1 th e gamm

a ra yfractions ;P.2 7

-25

-

u = Linea r energ

yabsorptio n coefficien t fo r gamm a rays i n ai r a (assumed t o b e 3. 7 x10- 5 /cmfo r al l radionuclides) ; T = Duratio n o f exposur e (hours) ; an d exp(- u S ) = Attenuatio n factor , a Unde r th e condition s assume d i n the NPRM , the exposed individua l i s 3 0 meter s fro

mthe poin t source , i s a t thi s location fo r 2 4 hours , an d receive s a maximu mwhol e bod

ydos e o f 0. 5 rem . Plugging thes e value s int o Equatio n (36) , the equatio n became : (37 ) Direc t Exposur e Releas e Valu e = 3. 6 x10 X / E 1 Conditio n 1
. Th e onl ydifferenc e betwee n thi s se t o f condition s an d the on e assume d i n the NPR Mi s tha t the expose d individua l receive s a dos e o f 0.02 5 re

mrathe r than 0. 5 rem . Plugging thi s revise d dose-equivalen t limi t int o Equatio n (36 ) along wit hthe othe r value s specifie d above , the equatio n simplifie d to : (38 ) Direc t Exposur e Releas e Valu e = 1.8/ E 1 Conditio n 2
. T o accommodat e thi s se t o f conditions , a dos e limi t o f 0. 1 re mrathe r than 0. 5 re m wa s plugge d int o Equatio n (36) ; al l th e othe r value s specifie d fo r tha t equatio n wer e kep t the same . Therefore , the direc t exposur e equatio n fo r thi s cas e reduce d to : (39 ) Direc t Exposur e Releas e Valu e = 7.3/ E 1 Conditio n 3
. A s show n i n Exhibi t 1 , thi s se t o f condition s differe d fro m tha t assume d i n th e NPR Mi n two respects : the distanc e betwee n the poin t o f releas e an

d the poin t o f exposur e (S ) wa s 1 mete r rathe r than 3 0 meters ; an d th e dose-equivalen t limi t (Dn ) wa s 0. 1 re mrathe r than 0. 5 rem . Substituting thes e value s fo r the one s use d i n suppor t o f the NPRM , Equatio n (36 ) reduce d to : (40 ) Direc t Exposur e Releas e Valu e = 7. 2 x10- 3 / E 1 Conditio n 4
. Thi s se t o f condition s wa s differen t fro mthe on e assume d i n th e NPR Mi n tha t i t assume s a dose-equivalen t limi t o f 0.02 5 re man d incorporate d th e effect s o f radioactive decay
. As discusse d i n Sectio n 3. 4 o f thi s paper , th e Agencydecide d t o evaluat e deca yonl yove r the perio d o f exposur e (i.e. , deca yove r the releas e perio d an d deca yove r the time betwee n releas e an

d th e star t o f an individual' s exposur e wa s neglected)
. T o incorporat e deca

yove r the exposur e period , Equatio n (36 ) wa s modifie d t o includ e an exponentia l deca yter ma s show

n below :-26

-

(41 ) Direc t Exposur e = (6.41xl0- 5 ) * (Dn ) * (S 2 ) Releas e Valu e ( E ) * ( u ) * (T ) * (exp(- u S) ) * (l-exp(-Xt) ) l a a
wher e t = Perio d o f exposur e i n days ; an d \ = 0.693/T-1/2 , wher e T-l/ 2 = radionuclid e half-lif e i n days
. Substituting the value s D n = 0.02 5 rem , S = 3 0 meters , T = 2 4 hours , an d t = 1 da yint o Equatio n (41 ) a s called fo r unde r Conditio n 4 , th e equatio n reduce d to : (42 ) Direc t Exposur e = 1.2 6

Releas e Valu e ( E ) * (T-l/ 2 - T-l/ 2 exp(-.693/T-l/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
. Conditio n 5
. Thi s conditio n wa s exactl ythe same a s Conditio n 4 excep t tha t i t assume d a dose-equivalen t limi t o f 0. 1 re mrathe r than 0.02 5 rem . Plugging thi s revise d valu e int o Equatio n (41 ) bu t keeping al l the othe r paramete r value s specifie d i n Conditio n 4 , the equatio n became : (43 ) Direc t Exposur e = 5.0 3 Releas e Valu e ( E ) * (T-l/ 2 - T-l/ 2 exp(-.693/T-1/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
. Conditio n 6
. Th e onl ydifferenc e betwee n thi s se t o f condition s an d the on e assume d i n the NPR Mi s tha t i t assume d the expose d individua l wa s 1 mete r rathe r than 3 0 meter s fro mthe poin t source . Therefore , using Equatio n (36 ) an d al l the value s specifie d fo r i t i n accordanc e wit hthe NPR Mcondition s excep t a revise d valu e o f 1 mete r fo r S , th e equatio n used in thi s cas e became : (44 ) Direc t Exposur e Releas e Valu e = 3. 6 x10- 2 / E 1 Conditio n 7
. Thi s conditio n wa s the same a s Conditio n 4 above excep t tha t i t considere d a distanc e o f 1 meter . Therefore , using Equatio n (41 ) an d substituing the value s Dn = 0.02 5 rem , S = 1 meter , T = 2 4 hours , an d t = 1 day , the equatio n fo r thi s conditio n became : (45 ) Direc t Exposur e = 1.2 5 xIO- 3 Releas e Valu e ( E ) * (T-l/ 2 - T-l/ 2 exp(-.693/T-l/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
.P.2 9

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Conditio n 8
. Thi s se t o f condition s wa s th e sam e a s th e on e assume d i n th e NPR Mexcep t tha t i t assume d a n exposur e perio d o f 36 5 days
. Therefore , usin g Equation
. (36 ) and substitutin g th e value s D n = 0. 5 rem , S = 3 0 meters , an d T = 2 4 hour s * 36 5 day s = 876 0 hours , th e equatio n use d fo r thi s conditio n reduce d to : (46 ) Direct Exposur e Releas e Valu e = 0.1/ E 1 Conditio n 9
. Becaus e thi s conditio n considere d radioactiv e decay , th e equatio n use d her e wa s derive d fro mEquatio n (41 ) (se e discussio n fo r Conditio n 4 above)
. Pluggin g th e value s D n = 0. 5 rem , S = 3 0 meters , T = 2 4 hours , an d t = 36 5 day s int o Equatio n (41) , th e equatio n became : (47 ) Direc t Exposur e = _ _2 5
. 1 Releas e Valu e ( E )
. * (T-l/ 2 - T-l/ 2 exp(-253/T-l/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
. Condi t io n 10
. Th e equatio n use d unde r thi s se t o f condition s wa s derive d b yusin g Equatio n (41 ) (se e discussio n fo r Conditio n 4 above ) and pluggin g i n th e value s D n = 2 5 rem , S = 1 meter , T = 2 4 hours , an d t = 1 day : (48 ) Direct Exposur e = 1.2 5 Releas e Valu e ( E ) * (T-l/ 2 - T-l/ 2 exp(-.693/T-1/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
. Conditio n 11
. Th e equatio n fo r thi s conditio n wa s derive d i n th e sam e wa y a s describe d fo r Conditio n 1 0 excep t tha t a valu e o f D n = 0. 5 re mwa s use d rathe r tha n 2 5 rem . Thi s substitutiona l chang e yielde d th e followin g equation : (49 ) Direct Exposur e = 2. 5 x10- 2 Releas e Valu e ( E ) * (T-l/ 2 - T-l/ 2 exp(-.693/T-l/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
. Condition s 12-15
. Thes e condition s wer e concerne d onl ywit hth e ingestio n an d inhalatio n pathways
. Therefore , n o direc t exposur e calculation s wer e performe d unde r thes e conditions
. Conditio n 16
. Thi s se t o f condition s wa s identica l t o th e on e assume d unde r Conditio n 4 excep t tha t i t assume d a dos e limi t o f 0. 5 re mrathe r tha n 0.02 5 rem . Accordingly , th e equatio n use d i n thi s cas e wa s derive d byusin g Equatio n (41 ) an d pluggin g i n th e value s D n = 0. 5 rem , S = 3 0 meters , T = 24 hours , an d t = 1 day
. Thi s proces s yielde d th e followin g equation :-28

-

(50 ) Direc t Exposur e = 25. 1 Releas e Valu e ( E ) * (T-l/ 2 - T-l/ 2 exp(-.693/T-1/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
. Conditio n 17
. Thi s se t o f condition s differe d fro mthe on e assume d i n the NPR Mi n two respects . First , i t assume d an exposur e perio d o f 36 5 day s rathe r than 1 da

yand , second , i t assume d a dose-equivalen t limi t o f 0. 1 re mrathe r than 0. 5 rem . Accordingly , th e equatio n use d i n thi s cas e wa s derive d b y using Equatio n (36 ) an d plugging i n the value s Dn = 0. 1 rem , S = 3 0 meters , an d T = 2 4 hour s * 36 5 day s = 876 0 hour s t o yield : (51 ) Direc t Exposur e Releas e Valu e = 0.02/ E 1 Conditio n 18
. Th e equatio n fo r thi s conditio n wa s derive d b yusing Equatio n (41 ) (se e discussio n fo r Conditio n 4 above ) an d plugging i n the value s Dn = 0. 1 rem , S = 1 meter , T = 2 4 hours , an d t = 1 day
. Thi s yielde d th e following equation : (52 ) Direc t Exposur e = 5 x10- 2 Releas e Valu e ( E ) * (T-l/ 2 - T-l/ 2 exp(-.693/T-l/2) ) 1 wher e T-l/ 2 = radionuclid e half-lif e i n days
. 4. 5 Equation s fo rDirec tExposur e b ySubmersio n i n a Clou d Equatio n Use d i n the NPRM . Sectio n 4.2. 3 o f the TBD outline s the rational e for an

d provide s a derivatio n o f the basi c equatio n use d i n the NPR M t o evaluat e submersio n i n a clou d o f nobl e gas . Thi s equatio n i s reprinte d below : (53 ) Submersio n Releas e = (83 ) * (DAC ) * (T ) Valu e (i n curies ) (AF ) * (X/Q ) * (1x10 s ) wher e DA

C = Derive d Airborn e Concentratio n fo r a particula r radionuclid e (microcuries/cm 3 ) ; T = Duratio n o f exposur e (assumed t o b e 1 da yi n al l case s becaus e the maximu mairborn e releas e perio d applicabl e t o RQs , an d henc e th e maximu mperio d tha t a perso n can b e submerse d i n a clou d fo r the purpos e o f thi s analysis , i s 1 day) ; X/ Q = Atmospheri c relative concentratio n valu e a t 3 0 meter s (8. 4 x 10- 1 3 day/cm 3 ) ;P.3 1

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AF =•Dose-equivalen t limi t adjustmen t facto r t o conver t the dose

equivalen t buil t int o the DAC , 5 rem , t o a dose-equivalen t limi t of.interest ; 8 3 = Time perio d conversio n facto r t o conver t the exposur e perio d considere d i n the DAC , 200 0 hours , t o a 2 4 hour exposur e perio d (i.e. , 200 0 hour s * 2 4 hours) ; an d 1x10 s = Conversio n facto r betwee n microcurie s an d curies
. Unde r the se t o f condition s assume d i n th e NPRM , AF = 1 0 (i.e. , the assume d dose-equivalen t i s 0. 5 rem)
. Plugging thi s valu e int o Equatio n (53 ) along wit hthe othe r value s spelled.ou t above , the equatio n simplifie d to : (54 ) Submersio n Releas e Valu e = DAC/( 1 xIO- 7 ) Conditio n 1
. Becaus e thi s conditio n differe d fro mtha t assume d i n th e NPR Monl yb

yassuming a differen t dose-equivalen t limi t (0.02 5 re mrathe r than 0. 5 rem) , the equatio n fo r thi s conditio n wa s derive d b yusing Equatio n (53 ) bu t wit ha valu e o f 20 0 for AF . B ymaking thi s substitutiona l change , th e equatio n use d fo r thi s conditio n became : (55 ) Submersio n Releas e Valu e = DAC/( 2 x10- 6 ) Conditio n 2
. The
. equatio n fo r thi s se t o f condition s wa s derive d b yusing Equatio n (53 ) alon

g wit hal l th e paramete r value s specifie d fo r tha t equation , excep t tha t a valu e o f 5 0 wa s used for AF rathe r than 10
. Thi s chang e wa s neede d t o arrive a t a differen t dos e limit ; 0. 1 re mrathe r than 0. 5 rem . B y using thi s revise d A F valu e i n Equatio n (53) , the equatio n became : (56 ) Submersio n Releas e Valu e = DAC/(5.lxlO- 7 ) Conditio n 4
. Thi s se t o f condition s differe d fro mthe on e assume d i n the NPR Mi n two respects . First , thi s conditio n assume d a dose-equivalen t limi t o f 0.02 5 re

mrathe r than 0. 5 rem . T o mak e thi s change , a dose-equivalen t adjustmen t facto r o f 20 0 wa s used
. Second , thi s conditio n incorporate d the effect s o f radioactive decay
. As describe d i n Sectio n 3. 4 o f thi s paper , however , the Agencydecide d no t t o conside r radioactive deca yin thi s exposur e pathwaymodel
. Accordingly , th e equatio n use d her e wa s derive d b yusing Equatio n (53 ) an

d substituting A

F = 20 0 along wit hthe othe r inpu t value s specifie d above fo r tha t equation : (57 ) Submersio n Releas e Valu e = DAC/(2xlO- 6 ) Conditio n 5
. Becaus e the Agencydecide d t o neglec t the consideratio n o f radioactive deca

yi n thi s pathwa

ymodel , thi s se t o f condition s for submersio n i n a clou

d wa s the same a s thos e assumed unde r Conditio n 2
. Accordingly , Equatio n (56 ) derive d above fo r Conditio n 2 wa s als o use d fo r thi s case .P.3 2

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Conditio n 8
. A s show n i n Exhibi t 1 , the onl ydifferenc e betwee n thi s conditio n an

d the se t o f condition s assume d i n the NPR Mwa s tha t a 36 5 da y exposur e perio d wa s assume d here
. However , a s describe d i n Sectio n 3. 2 o f thi s paper , the maximu mperio d o f time tha t a perso n can b e submerse d i n an airborn e clou

d fo r the purpos e o f thi s analysi s i s 1 day
. Recognizing thi s fact , ther e wa s n o differenc e betwee n thi s conditio n an d the se t o f condition s use d i n the NPRM , an d Equatio n (53 ) (derived above ) als o wa s use d fo r Conditio n 8
. Conditio n 9
. Th e equatio n use d unde r thi s se t o f condition s wa s als o the same equatio n use d i n the NPR M(i.e. , Equatio n (53))
. Thi s equatio n coul d be use d agai n her e becaus e the two difference s betwee n the NPR Mcondition s an

d Conditio n 9 - - differen t exposur e period s an d differen t deca

yconsideration s

- - wer e no t take n int o accoun t i n the submersion-in-a-clou d analysis
. Refe r t o Section s 3. 2 an

d 3. 4 i n thi s pape r fo r an explanatio n o f wh ythe exposur e perio d an

d th e approac ht o modeling decaywer e no t varie d i n th e equation s for modeling thi s exposur e pathway
. Condition s 12-15
. Thes e condition s wer e concerne d onl ywit hthe inhalatio n an

d ingestio n exposur e pathway s and , therefore , direc t exposur e b y submersio n i n an airborn e clou d wa s no t evaluate d unde r thes e conditions
. Conditio n 16
. Thi s se t o f condition s wa s the same a s tha t assume d i n th e NPR Mexcep t tha t i t incorporate d radioactive decay
. Fo r the reason s give n i n Sectio n 3. 4 o f thi s paper , however , th e Agencydecide d t o ignor e radioactive decayi n the analysi s o f direc t exposur e b ysubmersio n i n a cloud
. Accordingly , the same equatio n use d fo r the NPR Mconditions , Equatio n (53) , wa s als o use d unde r thi s se t o f conditions
. Conditio n 17
. Becaus e th e maximu mexposur e perio d considere d b yth e Agencyi n analyzing thi s exposur e pathwaywa s 1 day , the 365-da yexposur e perio d specifie d for Conditio n 1 7 wa s no t considere d i n the submersio n pathway model
. Th e dose-equivalen t limi t o f 0. 1 re mwa s take n int o account , however , b yusing a dose-equivalen t adjustment ' facto r o f 5 0 i n Equatio n (53 ) along wit h th e othe r inpu t variable s use d fo r the NPRM . Using A F = 5 0 i n Equatio n (53) , the equatio n simplifie d to : (58 ) Submersio n Releas e Valu e = DAC/(5.lxlO- 7 ) 4. 6 Mil kIngestionPathwa y Equation s I n th e TBD supporting the NPR Mo n radionuclides , EP Adi d no t perfor

ma specifi c analysi s o f exposur e throughth e ingestio n o f contaminate d milk
. Thi s exposur e pathwaywa s analyze d a s par t o f thi s analysis , however , t o se e howthe propose d RQ s woul d hav e varie d i f suchexposure s had bee n take n int o account . Conceptually , the Agencyassume d i n thi s mode l tha t radionuclide s ar e release d t o ai r ove r a perio d o f on e day
. Twenty-fou r hour s i s the timeframe fo r whic hRQ s ar e applicable
. Th e release d radionuclide s wer e assume d t oP.3 3

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b e transporte d i n an airborn e plume t o a pastur e approximatel y3 0 meter s away , wher e theyar e deposite d o n soi l an d growing gras s for the time tha t i t too k the plume t o pas s (i.e. , on e day)
. Thi s gras s wa s assume d t o b e the onl yfood sourc e fo r a grazing cow , whic hstarte d eating th e gras s the da yafte r i t wa s contaminate d an

d continue d t o ea t i t for a perio d o f 6 0 days. 5 I t wa s finall y assume d tha t an individua l ingested the cow' s contaminate d milk , for a perio d o f 6 0 days
. Th e mil k ingeste d b ythe perso n wa s assume d t o b e produce d b ythe cowtwo day s earlier. 6 Th e basi c equatio n tha t EPAuse d t o calculat e releas e value s assuming thi s cow-milk-man exposur e scenari o i s presente d below : (59 ) Mil k Ingestio n = AL I Releas e Valu e (AF)*(DF)*(MC)*(CT)*(R)*(lxlO s ) (i n curies ) wher e AL I = Annua l Limi t o f Intak e fo r ingestio n (microcuries) ;
i AF = Dose-equivalen t limi t adjustmen t facto r t o conver t th e

dose-equivalen t buil t int o th e ALI , 5 rem , t o a dose-equivalen t limi t o f interest ; DF = Dilutio n facto r accounting for th e transfe r o f radionuclide s fro m ai r t o gras s an

d fro mgras s t o mil k (curies/lite r o f mil k a t th e poin t o f exposur e pe r curi e release d t o the atmosphere) ; MC = Mil k consumptio n rat e o f referenc e man (0.8 5 liter/day);
. C T = Contac t time , o r the numbe r o f day s ove r whic hcontaminate d mil k

i s ingested ; R = Airborn e releas e fraction ; an d 1x10 s = Conversio n facto r betwee n microcurie s an d curies
. Th e value s use d for D F an d C T i n Equatio n (59) , a s wel l a s the method s use d t o deriv e thos e values , warran t furthe r explanation
. Th e valu e fo r D F

5 Thi s perio d o f time wa s selecte d t o b e consisten t wit hthe vegetabl e ingestio n pathwaymodel
. 6 Mil k consumptio n delaytime use d i n AIRDOS-EPAgeneri c sit e assessments . See : U.S . Environmenta l Protectio n Agency , Radionuclides : Backgroun

d Informatio n Documen t for Fina l Rules , Volume II , Offic e o f Radiatio n Programs , EP A520/1-84-022-2 , 1984
.P.3 4

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wa s derive d using the following equatio n use d i n AIRDOS-EPA , an EPAmode l use d t o calculat e environmenta l concentration s resulting fro mradionuclid e emission s int o air: 7 (60 ) D F = Q F C

f mv wher e D F = Dilutio n factor ; tha t is , the concentratio n o f radionuclid e i n

mil k pe r curi e o f radionuclid e release d t o th e atmospher e (Ci/lite r pe r Ci ; o r liter- 1 ) ; Q = Cowfeed consumptio n rat e (15. 6 kg/da yo n a dr

ybasis) ; f F - = Equilibriu

mtransfe r facto r accounting for th e transfe r o f mradionuclide s ingeste d b ya cowt o the cow r s mil k (day/liter) ; an d C = Concentratio n o f radionuclid e i n forag e pe r curi e release d t o vthe atmospher e (Ci/k g pe r Ci ; o r kg- 1 )
. Th e valu e o f F i n Equatio n (60 ) i s radionuclide-specific
. Wher e

m available , EP

Ause d for thi s analysi s the F value s develope d for th e m AIRDOS-EPAcompute r code. 8 F value s wer e no t available , however , i n the m AIRDOS-EPAdocumentatio n fo r a majorit yo f radionuclides
. Fo r thos e radionuclides , EPAuse d an F defaul t valu e base d o n availabl e F value s mm for radionuclide s fro mthe same serie s i n th e periodi c chart
. Th e valu e for C i n Equatio n (60 ) wa s derive d basicall yfro mth e same v equatio n used t o calculat e the concentratio n o f radionuclide s i n vegetable s in the vegetabl e ingestio n pathwa ymode l (se e Equatio n (26 ) describe d i n Sectio n 4. 3 o f thi s paper)
. Thi s equation , adapte d fro man equatio n presente d b ythe NCR P i n NCR P CommentaryNo . 3 (se e footnot e 4 o f thi s paper) , i s show n below : r[ l - exp(- Xt ) ] B [ 1 - exp(- Xt )] '

E i e ivi b + (26)
. C = V

C vd ai r YP X vi exp(- Xt ) i h

r U.S . Environmenta l Protectio n Agency , Radionuclides : Backgroun d Informatio n Documen t fo r Fina l Rules , Volume I , Offic e o f Radiatio n Programs , EPA520/1-84-022-1 , 1984
. "Bae s III , CF . an

d R.D . Sharp , ADirectoryo f Parameter s Use d i n a Serie s o f Assessmen t Application s o f th e AIRDOS-EPAan d DARTA B Compute r Codes , eftN L for the U.S . Environmenta l Protectio n Agency , ORNL-5710 , 1981
.P.3 5

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wher e C = Concentratio n o f radionuclid e i n forag e pe r curi e o f radionuclid e

vrelease d t o th e atmospher e (kg- 1 ) ;
V = Depositio n velocit yfo r wet an d dr ydepositio n (100 0 meters/day) ; d C = Concentratio n o f radionuclid e i n ai r a t th e locatio n o f growin g ai r vegetable s

= (Radionuclid e releas e rate)*(X/ Q a t 3 0 meters )

= (Ci/day)*(8. 4 xIO- 7 day/m 3 )

= 8. 4 xIO- 7 Ci/m 3 ;

r = Fractio n o f deposite d activit yretaine d o n crop s (0.25 , dimensionless) ;
Y= Pastur e productivit y(0.28 0 kg/m 2 , o n a dr ybasis) ; v X= Effectiv e remova l rat e constan t fo r radionuclid e i fro mgras s E i (i n day- 1 ) , wher e X= X+ X; E i i w X= 0.693/T-1/2 , wher e T-l/ 2 = half-lif e i n days ; i
X= Remova l rat e constan t fo r physica l los s byweathering , calculate d wo n th e basi s o f a weatherin g half-lif e o f 1 4 days , suc htha t X= 0.693/1 4 day s = 0.0495/days ; w t = Tim e perio d tha t th e grass ; i s expose d t o contaminatio n durin g th e e growin g seaso n (assigne d a valu e o f 1 da ybecaus e th e maximumperio d o f release , an d henc e th e maximu mperio d o f airborn e deposition , applicabl e t o RQ s i s 1 day) ;
B = Concentratio n facto r fo r uptak e o f radionuclid e i fro msoi l b y i vvegetation ;
P = Effectiv e surfac e densit yfo r soi l (24 0 kg/m 2 , dr yweight) ;
t = Tim e perio d ove r whic hth e soi l i s expose d t o contaminatio n b(assigne d a valu e o f 1 da yfollowin g th e sam e reasonin g give n abov e fo r t ) ; an d e
t = Tim e interva l betwee n th e tim e tha t th e mil k i s produce d byth e co w ht o th e tim e tha t th e expose d individua l consume s th e mil k ( 2 days)
.P.3 6

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Assuming n o radioactive deca ybetwee n th e poin t o f releas e an d contac t wit hthe gras s (i.e. , X=0 ) an d plugging al l o f the i above-specifie d value s int o Equatio n (61) , the expressio n for C becomes : v (62 ) C = (7. 3 x10- * + 3. 5 xIO- 6 B )kg- J viv Inputting thi s equatio n fo r C int o Equatio n (60 ) along wit hthe valu e o f v Q =15. 6 kg/day , the equatio n for D F becomes : f (63 ) D F = ( F ) * (1. 1 xIO- 2 + 5. 5 xIO- 5 B )

miv Th e valu e for the contac t time , CT , use d i n Equatio n (59 ) varied , depending o n whethe r radioactive deca ywa s take n int o account . A s state d above , the expose d individua l wa s assume d t o inges t mil k ove r a 6 0 da yperio d following the airborn e depositio n o f radionuclide s afte r 1 day
. T o accoun t fo r radionuclid e los s fro mthe gras s du e t o weathering and/o r radioactiv e decayove r the 60-da yingestion period , an "equivalent " contac t time wa s derive d using the following equation : (64 ) C T = 1 - exp(- Xt ) E i X E i wher e t = 6 0 days ; X= \ + X= (0.693/T-1/2 ) + (0.693/1 4 days ) = (0.693/T-1/2 ) + E i i w (0.049 5 day- 1 ) , wher e T-l/ 2 = radionuclid e half-lif e i n days
. Fo r thos e set s o f assumption s i n whic hradioactive deca ywa s neglecte d (i.e. , X=0) , th e contac t time wa s derive d i n the following way : i (65 ) C T = 1 - exp(-(0.0495/day ) * (6 0 days) ) = 1 9 day s 0.0495/da

y Fo r thos e set s o f assumption s i n whic hradioactive deca ywa s incorporate d int o th e model , th e contac t time wa s derive d i n the following manner : (66 ) C T = 1 - exp(-((0.693/T-l/2 ) + (0.0495) ) * (60) ) (0.693/T-1/2 ) + (0.0495 )

= 1 - ex

p - ((41.6/T-1/2 ) + (3) ) (0.693/T-1/2 ) + (0.0495 ) wher e T-l/ 2 = radionuclid e half-lif e i n days
.-35

-

I n summary , therefore , mil k ingestio n releas e value s wer e calculate d usin g th e followin g expressio n derive d bypluggin g Equatio n (63 ) fo r D F int o Equatio n (59):

- (67 ) Mil k Ingestio n = AL I Releas e Valu e (AF)*( F )*(9.69xl0 3 + 4.59xlO x B )*(CT)*(R ) mi v wher e C T wa s eithe r 1 9 days , unde r condition s wher e radioactiv e deca ywa s neglected , o r calculate d usin g Equatio n (66 ) wher e radioactiv e deca ywa s take n int o account . Equatio n Base d o n Condition s Assume d i n th e NPRM . A s show n i n Exhibi t 1 , th e se t o f assumption s use d i n th e NPR Minclude d a dose-equivalen t limi t o f 0. 5 re m

and n o consideratio n o f radioactiv e decay
. Accordingly , th e dose-equivalen t adjustmen t facto r (AF ) unde r thes e assumption s wa s 1 0 (t o adjus t th e 5 re mdose-equivalen t considere d i n th e AL I t o a dose-equivalen t o f 0. 5 rem ) an d th e contac t tim e (CT ) wa s 1 9 day s a s derive d i n Equatio n (65)
. Pluggin g thes e value s int o Equatio n (67) , th e equatio n simplifie d to : (68 ) Mil k Ingestio n = AL I Releas e Valu e ( F )*(R)*(1.8x10 s + 8.72xl0 3 B ) mi v Conditio n 1
. Unde r thi s se t o f assumptions , a dose-equivalen t adjustmen t facto r o f 20 0 wa s use d t o g o fro mth e 5 re mo n whic hth e AL I i s base d t o 0.02 5 rem . Also , becaus e radioactiv e deca ywa s neglecte d i n thi s case , C T = 1 9 day s a s show n i n Equatio n (65)
. Pluggin g thes e value s int o Equatio n (67) , th e equatio n use d her e became : (69 ) Mil k Ingestio n = AL I Releas e Valu e ( F )*(R)*(3.68xl0 7 + 1.74xl0 5 B ) mi v Conditio n 2
. Th e onl ydifferenc e betwee n thi s se t o f assumption s an d th e on e use d i n th e NPR Mi s tha t a dose-equivalent limi t o f 0. 1 re mwa s use d rathe r tha n a 0. 5 re mlimit
. T o accommodat e thi s difference , th e appropriat e valu e fo r A F unde r Conditio n 2 wa s 5 0 ( 5 rem/5 0 =0. 1 rem)
. Pluggin g thi s valu e int o Equatio n (67 ) alon g wit ha contac t tim e o f 1 9 day s (decayals o wa s neglecte d here) , th e equatio n reduce d to : (70 ) Mil k Ingestio n = AL I Releas e Valu e ( F )*(R)*(9.2x10 s + 4.36xl0* B ) mi v Conditio n 4
. Unlik e th e preceedin g set s o f conditions , th e effect s o f radioactiv e deca ywer e take n int o accoun t unde r Conditio n 4
. Therefore , th e valu e fo r C T i n thi s cas e wa s calculate d usin g Equatio n (66)
. Usin g tha t equatio n alon g wit ha n A F valu e o f 20 0 (t o arriv e a t a dose-equivalen t limi t o f 0.02 5 rem , i.e. , 5 rem/20 0 = 0.02 5 rem ) i n Equatio n (67) , th e equatio n use d t o calculat e releas e value s unde r th e se t o f condition s assume d her e became :-36

-

(71 ) Mil k Ingestio n = AL I Releas e Valu e (CT)*( F )*(R)*(1.93x10 * + 9.2xl0 3 B ) mi v wher e C T wa s calculate d usin g Equatio n (66)
. Conditio n 5
. T o calculat e releas e value s unde r thi s se t o f assumptions , th e valu e o f C T wa s calculate d usin g Equatio n (66 ) (becaus e radioactiv e deca y wa s incorporated ) an d th e valu e fo r A F wa s 5 0 (t o adjus t th e 5 re mo n whic h th e AL I i s base d t o 0. 1 rem)
. Th e equatio n use d i n thi s case , show n below , wa s derive d byinputtin g thes e value s int o Equatio n (67) : (72 ) Mil k Ingestio n = AL I Releas e Valu e (CT)*( F )*(R)*(4.84x10 s + 2.29xl0 3 B ) mi v wher e C T wa s calculate d usin g Equatio n (66)
. Conditio n 8
. Th e onl ydifferenc e fro mth e condition s assume d i n thi s cas e an d thos e assume d i n th e NPR Mwa s tha t a 365-da yexposur e perio d wa s use d unde r Conditio n 8 i n th e evaluatio n o f direc t exposur e t o a point source . However , becaus e a 365-da yexposur e perio d wa s no t use d i n th e mil k ingestio n pathwa ymode l (se e Sectio n 3. 2 o f thi s paper) , th e sam e equatio n use d unde r th e NPR Mcondition s (i.e. , Equatio n 68) ) als o wa s use d here
. Conditio n 9
. A s describe d i n Sectio n 3. 2 o f thi s paper , th e Agenc y assume d a 365-da yexposur e perio d onl yi n th e evaluatio n o f direc t exposur e t o a poin t source . Th e exposur e period , o r contac t time , i n th e mil k ingestio n pathwa ymode l wa s determine d usin g eithe r Equatio n (65 ) o r (66 ) dependin g o n whethe r radioactiv e deca ywa s take n int o account . Becaus e th e effect s o f deca ywer e considere d unde r thi s se t o f assumptions , th e contac t tim e i n thi s cas e wa s determine d usin g Equatio n (66)
. Usin g thi s expressio n fo r CT , a valu e o f A F = 1 0 a s use d unde r th e NPR Mconditions , and Equatio n (67) , th e equatio n use d fo r Conditio n 9 reduce d to : (73 ) Mil k Ingestio n = AL I Releas e Valu e (CT)*( F )*(R)*(4.84xl0 5 + 2.29xl0 3 B ) mi v wher e C T wa s calculate d usin g Equatio n (66)
. Condition s 12-15
. Becaus e th e ingestio n ALI s ar e applicabl e regardles s o f whethe r radionuclide s ar e ingeste d i n water , vegetables , o r milk , th e sam e equation s use d i n th e ground-wate r ingestio n an d vegetabl e ingestio n model s unde r thes e set s o f assumption s als o ar e applicabl e here
. Thes e equation s wer e derive d i n exactl yth e sam e wa ya s th e inhalatio n equation s fo r Condition s 12-15
. Th e onl ydifferenc e betwee n th e tw o set s o f equation s i s tha t th e AL I fo r ingestio n wa s use d her e rathe r tha n th e inhalatio n AL I a s use d i n th e inhalatio n pathwa yequations
. Refe r t o th e derivatio n o f thes e individua l equation s give n i n Sectio n 4. 1 o f thi s paper .-37

-

Conditio n 16
. Fo r the mil k ingestion pathway , ther e wa s n o differenc e betwee n the se t o f condition s assume d her e an d tha t assume d unde r Conditio n 9
. Therefore , the same equatio n derive d for Conditio n 9 (i.e. , Equatio n (73) ) als o wa s use d for Conditio n 16
. Conditio n 17
. As discusse d i n Sectio n 3. 2 o f thi s paper , EP Adi d no t conside r a 365-da

yexposur e perio d i n the evaluatio n o f contaminate d milk
. Accordingly , ther e wa s n o differenc e betwee n Conditio n 1 7 an d Conditio n 2 fo r th e mil k ingestio n pathwa ymodel , an

d the same equatio n use d unde r tha t se t o f assumption s - - Equatio n (70 ) - - als o wa s use d here
. 4. 7 Analysi s o fth e Ingestio n o fVegetable s Contaminate d B yIrrigatio n As par t o f thi s analysis , EP Aconsidere d potentia l exposure s throughthe ingestio n o f vegetable s contaminate d b yirrigation
. Equation s fo r th e calculatio n o f releas e value s fo r thi s exposur e pathwaywer e develope d but , base d o n the rang e o f value s t o b e use d i n thi s equation , i t wa s determine d tha t releas e value s for the irrigation-vegetabl e pathwa ywoul d b e highe r for al l radionuclide s than th e releas e value s for the ground-wate r ingestio n pathway
. Tha t is , th e irrigation-vegetabl e pathwa yi s alway s les s critica l tha n the ground-wate r ingestion pathway
. Th e Agencyrecognize s tha t th e ingestio n o f vegetable s contaminate d b yirrigation wate r actuall ycoul d b e mor e critica l than th e ingestio n o f groun d wate r unde r certai n scenario s (e.g. , unde r scenario s wher e groun d wate r i s no t use d fo r drinking) ; the Agency' s conclusio n abou t the relative significanc e o f thes e exposur e pathway s i s base d onl yo n the releas e an d exposur e scenario s considere d i n thi s analysis
. Base d o n thi s conclusion , EPAdecide d tha t i t wa s no t necessaryt o develop separat e equation s an d t o calculat e releas e value s for the irrigation-vegetabl e ingestion pathwa yunde r eachse t o f assumption s show n i n Exhibi t 1
. Th e specifi c rational e supporting thi s approac hi s outline d below
. Conceptually , the releas e an d environmenta l transpor t characteristic s assume d i n the irrigation pathwa ymode l wer e identica l t o thos e assume d i n the ground-wate r ingestio n mode l (se e Sectio n F.l. l o f th e TBD)
. Specifically , i t wa s assumed tha t radionuclide s ar e instantaneousl yrelease d t o groun d water , theythe n migrat e 3 0 meter s downgradient , an d contaminat e a

n irrigation well
. Contaminate d wate r wa s assume d t o b e extracte d fro mthe wel l an

d applie d t o vegetable s fo r the perio d o f time tha t i t take s the contaminan t plume t o pas s the well
. A s describe d i n Sectio n 4. 2 o f thi s pape r an d i n Sectio n F.l. l o f th e TBD , EPAestimate d tha t thi s perio d o f time varie d fro m9 day s t o u

p t o 36 5 days , depending o n the retardatio n facto r for the radionuclid e i n question
. Regardles s o f the perio d o f time ove r whic hthe crop wa s irrigate d wit hcontaminate d water , i t wa s assume d tha t an individua l eat s vegetable s fro mthe crop for 6 0 days , the entir e lengt ho f the vegetabl e growing season . Finally , i t wa s assume d tha t th e vegetable s ar e eate n immediatel yafte r they ar e harvested ; tha t is , the vegetable s ar e no t store d betwee n the time they ar e harveste d an

d th e time theyar e eaten . Th e following equatio n wa s develope d t o calculat e releas e value s base d o n th e exposur e scenari o outline d above :P.4 0

-38

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(74 ) Irrigatio n Releas e = AL I Valu e (in curies ) (AF)*(DF)*(FC)*(CT)*(lxlO s ) wher e AL I = Annua l limi t o f intak e fo r ingestio n fo r a particula r radionuclide ; D F = Dilutio n factor , the concentratio n o f a radionuclid e i n an d o n vegetable s pe r curi e release d t o groun d wate r (Ci/k

g pe r Ci ; o r kg- 1 ) ; F C = Foo d (i.e. , leafyvegetable ) consumptio n rat e o f referenc e ma n (0.17 5 kg/day) ; C T = Contac t time , o r the numbe r o f day s ove r whic hcontaminate d vegetable s ar e ingested ; an d 1x10 s = Conversio n facto r betwee n microcurie s an d curies
. T o determin e the valu e for the dilutio n factor , DF , i n Equatio n (74) , EPA adapte d an equatio n fro mthe Nuclea r RegulatoryCommission' s RegulatoryGuid e 1.109
. Thi s equatio n i s show n below : r[l-exp(- Xt ) ] f B [l-exp(- Xt ) ]

E i e i ivi b + YXP X vE i i (75 ) D F = C I

w exp(- Xt ) i h

wher e DF = Dilutio n factor , tha t is , the concentratio n o f radionuclid e i n an d o n edibl e portio n o f vegetatio n pe r curi e o f radionuclid e release d t o groun

d wate r (Ci/k

g per-Ci ; o r kg- 1 ) ; C = Concentratio n o f radionuclid e i n irrigatio n wate r pe r curi e o f wradionuclid e release d t o groun d wate r (Ci/lite r pe r Ci ; o r liter- 1 ) ; I = Averag e irrigation rat e (2. 5 l/m 2 -day) ; f = Fractio n o f yea r crop s ar e irrigate d wit hcontaminate d water ; an d i al l the othe r parameter s an d value s ar e a s define d for Equatio n (26 ) i n Sectio n 4. 3 o f thi s paper . Th e valu e for C use d i n Equatio n (75 ) wa s the same concentratio n

w calculate d fo r th e ground-wate r ingestio n pathwaymodel , (7.6xl0- 8 /Rd ) liter- 1 (se e Sectio n F.l. l o f the TBD fo r th e derivatio n o f thi s value)
.P.4 1

-39

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T o determin e the valu e o f the contac t time , CT , i n Equatio n (74) , i t wa s recognize d tha t weathering and/o r radioactive deca yove r th e perio d o f ingestio n woul d resul t i n some radionuclid e loss
. A n "equivalent " contac t time , therefore , wa s calculate d using the following equation : (76 ) C T = l-exp(- Xt ) E i X E i wher e t = exposur e perio d (6 0 days) ; an d
X= X+ X= (0.693/T-1/2 ) + (0.693/1 4 days ) = (0.693/T-1/2 ) + E i i w (0.049 5 day- 1 ) , wher e T-l/ 2 = radionuclid e half-lif e i n

days
. Unde r condition s involving n o radionuclid e retardatio n during ground-wate r transpor t (i.e. , R

d = 1 ) an

d n o radioactive deca y(i.e. , X= 0 ) , th e

i expressio n fo r DF reduce d to : (77 ) D F = (1. 7 x10- 7 + 1. 9 xlO-^ B )kg- x iv
an d th e valu e for CT , using Equatio n (76) , wa s calculate d t o b e 1 9 days
. I f th e secon

d ter mi n the expressio n fo r DF i s droppe d fo r the sak e o f simplicit y (i t i s approximatel yfour order s o f magnitud e lowe r than the firs t ter man d therefor e doe s no t significantl yaffec t th e releas e valu e results) , plugging a valu e o f D F = 1.7xl0- 7 int o Equatio n (74 ) along wit hthe value s AF = 1 0 (for example) , F C = 0.17 5 kg/day , an d C T = 1 9 days , the equatio n for irrigatio n releas e value s reduced to : (78 ) Irrigatio n Releas e Valu e (in curies ) = AL I (i n microcuries)/5. 6 Equatio n (78 ) can b e compare d t o Equatio n (12) , whic hrepresent s th e releas e valu e for the ingestion o f groun d wate r unde r the same se t o f assumption s use d t o derive Equatio n (78) : (12 ) Ground-wate r Ingestio n Releas e Valu e = ALI/1 4 Base d o n thi s comparison , i t i s eviden t tha t the ground-wate r releas e valu e wil l b e lowe r than the irrigatio n releas e valu e whe n R d = 1 an

d radioactive deca yi s neglected
. A s th e valu e fo r R d i s increased (i.e. , whe n radionuclide s wit hhig hsorptio n coefficient s ar e considered) , the ground-wate r releas e valu e become s eve n smalle r whe n compare d t o the irrigatio n releas e value
. Thi s chang e i s the resul t o f the chang e i n th e exposur e perio d i n the two models
. I n th e ground-wate r ingestio n model , the exposur e perio d increase s t o 36 5 day s whe n R d i s greate r than one , suchtha t th e equatio n became (se e derivatio n o f Equatio n (13)) :P.4 2

-40

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(79 ) Ground-wate r Ingestio n Releas e Valu e = ((ALI)*(Rd))/(550 )
I n the irrigation pathwa ymodel , however , the exposur e perio d remain s 6 0 day s regardles s o f the valu e for Rd
. Equatio n (78 ) als o remain s applicabl e whe n RD -t 1 excep t tha t a valu e for Rd need s t o b e include d i n th e numerato r a s follows : (80 ) Irrigation Releas e Valu e = ((ALI)*(Rd))/5. 6 Consequently , comparing Equation s (79 ) an d (80 ) show s tha t the ground-wate r ingestio n releas e valu e als o wil l b e smalle r than the irrigatio n releas e valu e whe n R d > 1
. Fo r bot hthe ground-wate r ingestion an d irrigation models , the calculate d releas e value s ar e ver ylarg e i n compariso n t o the othe r exposur e pathway model s whe n radioactive deca yi s considered
. Result s fro mthes e two models , therefore , di d no t have t o b e evaluate d an d compare d for situation s i n whic h deca yi s incorporated
. 5 . SUMMAR YO F RESULT S Thi s sectio n summarize s the RQ result s calculate d for eachse t o f condition s considere d i n thi s analysis
. Refe r t o the Superfun d docke t supporting the radionuclid e rul e (Superfun d Docke t No . 102RQ-RN ) fo r the ra w result s obtaine d from-eac hcalculation , including a lis t o f pathway-specifi c releas e value s an

d RQ s calculate d fo r the 75 7 radionuclide s identifie d i n th e NPRM . Exhibi t 2 summarize s for eachse t o f condition s the numbe r o f radionuclide s calculate d t o hav e an R Q o f a give n size
. Th e firs t rowi n thi s exhibi t identifie s the se t o f modeling condition s assume d i n the NPR M(5 2 FR 8172 , Marc h16 , 1987 ) an d present s th e distributio n o f RQ s propose d i n th e NPRM . Th e distributio n o f RQ s presente d i n the secon d rowo f Exhibi t 2 i s base d o n the same se t o f condition s assume d i n the NPRM ; however , the RQ s wer e calculate d using a revise d vegetabl e ingestion pathwa ymodel
. Specifically , the vegetabl e ingestion mode l use d t o calculat e the RQ s show n in the secon

d rowi n Exhibi t 2 relie d o n a revise d depositio n velocit yaccounting fo r the transfe r o f radionuclide s fro mai r t o vegetatio n (se e th e detaile d discussio n o f thi s modeling chang e i n Sectio n 4. 3 o f thi s paper)
. Comparing the firs t an d secon d row s i n thi s exhibi t show s tha t th e chang e i n depositio n velocit y di d no t hav e a significan t effec t o n the overal l distributio n o f RQs , although (as demonstrate d b

ydat a i n the docket ) th e specifi c RQ s calculate d for severa l radionuclide s di d chang e a s a resul t o f the revise d vegetabl e ingestion model
. I n general , the chang e i n the vegetabl e ingestio n mode l resulte d i n a sligh t lowering o f th e RQs ; fewe r radionuclide s wer e calculate d t o have RQ s o f 10 0 C i an d 100 0 C i whe n compare d t o the distributio n propose d i n the NPRM , whil e mor e radionuclide s wer e calculate d t o hav e an R Q o f 1 0 C i o r less
. Al l the RQ s fo r Condition s 1 throug h1 8 wer e calculate d using th e revised vegetabl e ingestio n model
. Exhibi t 2 als o serve s t o demonstrat e the relative effect s o f certai n variabl e change s o n the overal l distributio n o f RQs . Fo r example , a s woul d b eEXHIBI T 2 DISTRIBUTION S O F RQ s FO RTH E SET S O F CONDITION S CONSIDERE DI N THI S ANALYSI S

Cond i t io n Numbe r

NPR M (5 2 f_

R 8172 ) NPR M (revised ) 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1* 4 1 5 1 6 1 7 1 8 b / D i stanc e

Exposur e Poin t (meters )

a / 3 0 3 0 3 0 3 0 1 3 0 3 0 1 1 3 0 3 0 1 1 £ / £ / £ / £ / 3 0 3 0 1 Assume d Con d t o Perio d o f D i rec t Exposur e (days )
1 1 1 1 1 1 1 1 1 36 5 36 5 1 1 £ / £ / £ / £ / 1 36 5 1 i t ion s Dos e Limi t ( rem )
0. 5 0. 5 0.02 5 0. 1 0. 1 0.02 5 0
. 1 0. 5 0.02 5 0. 5 0. 5 2 5 0. 5 5 500 0 2 5 50 0 0. 5 0. 1 0. 1 Ra d ioactiv e

Deca y Con s idered ?
No N o No No N o Ye s Ye s No Ye s No Ye s Ye s Ye s No No N o N o Ye s No Ye s - 7

<1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 5 6 2 4 1 2 4 0 0 0 Numbe r o f

- 6 - 4 1 0 -1 0
0 0 1 5 7 0 1 2 5 0 2 1 1 1 0 0 20 9 5 4 10 4 5 6 1 7 0 Rad ionuc I ide s

- 3 - 2 1 0 1 0
6 2 5 7 3 1 3 6 6 8 2 9 3 2 20 6 24 6 3 7 4 3 2 8 2 5 2 29 5 19 6 20 8 1 0 18 3 9 4 6 0 0 0 14 9 23 7 21 7 2 4 4 6 16 6 22 9 4 6 13 9 9 2 9 7 4 34 2 8 5 21 3 Havin q

- 1 1 0
2 4 2 8 16 2 8 6 10 2 9 4 6 4 19 2 11 0 29 5 6 8 2 3 214 3 5 13 9 18 8 23 7 3 8 16 8 17 5 a n R Q

1
3 5 4 5 35 3 28 7 2 6 23 0 14 3 7 9 3 6 13 2 10 0 19 1 15 0 2 23 7 2 9 21 7 6 3 7 5 7 8 (i n curies ) o f

1 0
34 2 41 3 9 6 24 5 1 1 19 4 23 1 1 4 2 6 5 9 15 2 21 0 4 7 1 21 7 0 3 5 20 8 4 0 1 0 10 0
23 6 17 9 2 4 5 7 1 9 9 8 16 2 1 6 1 4 3 3 17 4 11 1 3 1 0 3 5 1 2 21 5 1 7 2 3 100 0

8 9 5 4 3 1 4 8 4 9 9 9 2 0 7 4 4 20 7 8 3 2 7 0 3 0 1 19 4 3 4 1 3

a / Thi s i s th e assume dse t o f condition s an dpropose ddistributio no f RQ s inth e NPR M publishe do nMarc h16 , 198 7 (5 2 £ R8172) . b / Th e distributio no f RQ s inthi s ro w wa s calculate dusin gth e sam e se t o f condition s assume di nth e NPRM ; however , th e mode l fo r calculatin greleas e value s fo r th e vegetabl e ingestio npathwa y wa s revise dt o incorporat e a differen t airborn e depositio n velocit y

tha ntha t assume dinth e NPR M (se e Sectio n4. 3 o f thi s paper) . c / InCondition s 1 2 throug h15 , RQ s wer e calculate dsimpl y b y takin gmultiple s o f th e inhalatio nan dingestio nAnnua l Limit s o f Intake . Neithe r distanc e no r time , therefore , wer e considere di nthes e calculations .p » -42

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expected , the exhibi t show s tha t lowerin g the dose-equivalen t limi t whil e keeping al l othe r variable s constan t resulte d i n a genera l lowering o f RQ s (e.g. , compar e the distributio n o f RQ s for Condition s 1 an d 2 , an d th e distributio n fo r Condition s 4 an d 5)
. Similarly , keeping al l othe r variable s constan t bu t incorporating radioactive deca yint o the pathwaymodel s resulte d in highe r RQ s (e.g. , compar e the distributio n o f RQ s for Condition s 1 an d 4 , an d for Condition s 8 an d 9)
. Trend s associate d wit hchange s i n the exposur e perio d an d th e distanc e fro mthe releas e poin t ar e mor e difficul t t o identif ybecause : (1 ) thes e variable s wer e change d onl yfo r th e pathwaymode l considering direc t exposur e t o a poin t source ; an d (2 ) onl ydirec t exposur e t o a poin t sourc e an d gamm a emitting radionuclide s wer e considere d fo r thos e set s o f condition s assuming a distanc e o f 1 mete r (not e ther e ar e RQ s for 618 , no t 757 , radionuclide s for Condition s 3 , 6 , 7 , 10 , 11 , an d 1 8 becaus e 13 9 o f the radionuclide s neve r emi t gamm a rays)
. Nevertheless , Exhibi t 2 doe s illustrat e the lowering o f RQ s tha t woul d resul t i f a direc t exposur e perio d o f 36 5 day s rathe r than 1 da ywer e assume d (compar e the result s for Conditio n 8 an d thos e i n the revised NPRM)
. Additionally , i t i s importan t t o clarif ytha t the result s for Condition s 3 , 6 , 7 , 10 , 11 , an

d 1 8 ar e onl yreleas e value s for the direc t exposur e pathway ; thes e value s wer e no t compare d wit hreleas e value s for othe r exposur e pathway s t o determin e RQs . I t i s possibl e tha t the releas e value s fo r th e exposur e pathway s othe r than direc t exposur e woul d b e lowe r than thos e show n i n Exhibi t 2 , resulting i n lowe r RQ s than ar e presente d i n Condition s 3 , 6 , 7 , 10 , 11 , an d 18
. Finally , Exhibi t 2 show s tha t the lowes t RQs , a s a group , wer e calculate d for Condition s 1 2 through15 , wit hConditio n 1 2 yielding the lowes t RQs . A s describe d i n Sectio n 4 o f thi s paper , RQ s wer e calculate d unde r thes e set s o f condition s simpl yb ytaking multiple s o f the radionuclid e ALIs , whic hi n effect , doe s no t accoun t fo r an ydispersio n o r dilutio n tha t woul d occu r betwee n the poin t o f releas e an d the poin t o f exposure . Whe n al l exposur e pathway s considere d i n thi s analysi s wer e take n int o accoun t (i.e. , whe n a distanc e o f 3 0 meter s wa s assumed) , the highes t grou p o f RQ s wa s calculate d unde r Condition s 9 an d 16
. Exhibi t 3 summarize s the numbe r o f radionuclide s whos e calculate d RQ s ar e base d o n the differen t exposur e pathway s considere d i n thi s analysis
. A s i n Exhibi t 2 , the firs t ro wi n Exhibi t 3 present s the condition s an d limiting exposur e pathway s publishe d i n th e NPRM , whil e the result s i n th e secon d row ar e fo r the same se t o f condition s bu t ar e base d o n a revise d vegetabl e ingestio n model
. A s discusse d i n Sectio n 4. 3 o f thi s paper , th e revise d vegetabl e ingestio n mode l considere d a greate r transfe r o f radionuclide s fro m ai r t o vegetatio n whe n compare d t o th e mode l use d i n the NPR Mand , accordingly , Exhibi t 3 show s tha t thi s revisio n resulte d i n a significantl y large r numbe r o f RQ s being base d o n the vegetabl e ingestion pathway
. Exhibi t 3 demonstrate s severa l usefu l point s abou t the waythe limiting pathway s generall yshifte d whe n differen t set s o f condition s wer e assumed
. First , regardles s o f the combinatio n o f distance , exposur e period , dos e limit , an d modeling approac hfo r radioactive decay , th e direc t exposur e pathwaymode l use d i n thi s analysi s yielde d the lowes t releas e value s for th e majorit yo fEXHIBI T 3 NUMBE RO F PROPOSE DRQ s BASE DO N PARTICULA REXPOSUR E PATHWAY S

Cond itio n Numbe r
NPRM(5 2 F

R NPRM( re vi s

i 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 8172 ) 2d ) £ / Assume d Cond

Distanc e t o Exposur e Poin t (meters )
b / 3 0 3 0 3 0 3 0 1 3 0 3 0 1 1 3 0 3 0 1 1 e / § / £ / £ / 3 0

•• • 3 0 1 Pe i

D ~io d o f rec t Exposur e ( c lays )
1 1 1 1 1 1 1 1 1 36 5 36 5 1 1 § / e / £ / e / 1 36 5 1 t ion s

Dos e Limi t ( rem )
0. 5 0. 5 0.02 5 0. 1 0
. 1 0.02 5 0. 1 0. 5 0.02 5 0. 5 0. 5 2 5 0. 5 5 500 0 2 5 50 0 0. 5 0. 1 0. 1 Rad ioactiv e

Deca y Con s idered ?
N o N o N o No No Ye s Ye s No Ye s No Ye s Ye s Ye s No No No No Ye s No Ye s M i Ik

Ingestio n

20 7 20 7 13 0 13 0
7 0 9 5

13 0 7 0 Numbe r

Veget a o f RQ s
bl e Ingestio n
4 26 6 14 3 14 3 8 1 8 1
3 8

. 4 4

8 1 3 8 Base d o n

Ground

Wate r Ingestio n
11 3 3 1 2 5 2 5 1 1
1 4 0
47 5 47 5 47 5 47 5 1 1 4 

### £ / 1 / £ / £ / a n Expo ;

sur e

1nhala t ion
18 4 10 4 9 4 9 4 15 7 15 7
7 2 14 3
33 0 33 0 33 0 33 0 15 7 7 2 fl/ 9 / fl/ fl/ Pa thwa y

D i rec t Exposur e a. /
45 6 35 6 28 8 28 8 61 8 38 8 38 8 61 8 61 8 56 3 47 5 61 8 61 8

38 8 56 3 61 8 d / 

### fl7 d /
d / d /

d /

a / Include s direc t exposur e t o a poin t sourc e an dsubmersio nina nairborn e cloud . b / Thi s i s th e assume dse t o f condition s an dpropose ddistributio no f RQ s inth e NPR M publishe do nMarc h16 , 198 7 (5 2 £ R8172) . c / Th e distributio no f RQ s i nthi s row

wa s calculate dusin gth e sam e se t o f condition s assume dinth e NPRM ; however , th e mode l fo r calculatin greleas e value s fo r th e vegetabl e ingestio npathwa y wa s revise dt o incorporat e a differen t airborn e depositio n velocit y

tha ntha t assume dinth e NPR M (se e Sectio n4. 3 o f thi s paper) . d / Thi s tota l i s 61 8 rathe r tha n75 7 because : (1 ) a distanc e o f 1 mete r betwee nth e poin t o f releas e an dth e poin t o f exposur e wa s assume donl y i nth e direc t exposur e pathwa y model ; an d(2 ) 13 9 o f th e radionuclide s o f interes t t o thi s analysi s d o no t emi t gamm a ray s (exposure s t o bet a particle s 1 mete r awa y fro m th e poin t o f releas e wer e no t considere di nthi s analysis) . Thes e value s ar e releas e value s fo r th e direc t exposur e t o a poin t sourc e pathway ; the y wer e no t compare dt o th e releas e value s fo r othe r exposur e pathway s unde r thes e condition s fo r th e determinatio no f RQs . I f suc ha compariso nha dbee nmade , however , othe r exposur e pathway s ma y hav e bee nfoun dt o b e mor e limitin gtha nth e direc t exposur e t o a poin t source . e / InCondition s 1 2 throug h15 , RQ s wer e calculate dsimpl y by takin gmultiple s o f th e inhalatio nan dingestio nAnnua l Limit s o f Intake . Neithe r distanc e no r time , therefore , wer e considere di nthes e calculations . £ / Thi s i s th e numbe r o f radionuclide s whos e RQ s ar e base do nth e ALI s fo r ingestion , whic har e th e sam e regardles s o f whethe r th e radionuclide s ar e ingeste di ngroun dwater , vegetables , o r milk . Therefore , whil e thi s numbe r i s displaye dabov e inth e ground-wate r ingestio npathwa y column , ground-wate r ingestio nwa s no t determine dt o b e necessaril y mor e critica l tha nmil ko r vegetabl e ingestio nunde r Condition s 1 2 throug h15 . g / Unde r Condition s 1 2 throug h15 , th e releas e value s an dinhalatio n(i.e. , fo r thos e radionuclides , th e lowes t inhalatio nno r ingestio ncoul db e counte da s th e limitin g o f thi s exhibit , ar e state dt o b e base do nbot hingestio n fo r 4 8 radionuclide s wer e calculate dt o b e th e sam e fo r bot hingestio n ingestio nAL I equal s th e lowes t inhalatio nALI) . Accordingly , neithe r exposur e pathwa y

fo r thes e radionuclide s an dthei r RQs , fo r th e purpos e an dinhalation . Thi s result s i na "doubl e counting " o f RQ s fo r 4 8 radionuclide s suc htha t th e tota l numbe r o f radionuclide s accounte dfo r i nCondition s 1 2 throug h1 5 i s 805 , rathe r tha n757 .P.46
_

-44

-

radionuclide s whe n compare d t o the releas e value s calculate d b yth e othe r exposur e pathwaymodels
. I t i s importan t t o clarify , however , tha t onl y direc t exposur e t o a poin t sourc e wa s considere d whe n a distanc e o f 1 mete r wa s assume d and , thus , the result s show n for Condition s 3 , 6 , 7 , 10 , 11 , an d 1 8 ar e direc t exposur e releas e value s rathe r than RQs . Had releas e value s for the othe r exposur e pathway s unde r thes e set s o f condition s bee n compare d t o thos e for direc t exposure , othe r exposur e pathway s ma yhav e bee n foun

d t o b e mor e limiting
. In addition , a s mentione d previously , the tota l numbe r o f releas e value s for Condition s 3 , 6 , 7 , 10 , 11 , an d 1 8 equa l 61 8 rathe r than 75 7 becaus e 13 9 o f the radionuclide s o f interes t do no t emi t gamm a ray s an

d wer e exclude d fro

mthe direc t exposur e pathwayanalysis
. Second , Exhibi t 3 demonstrate s howthe relative significanc e o f th e ground-wate r ingestio n pathwa ydecrease d whe n radioactive deca ywa s take n int o account . Fo r example , not e howth e numbe r o f RQ s base d o n the ground-wate r ingestio n pathwa

ydecrease d i n going fro mthe origina l NPR

Mresult s t o the result s fo r Conditio n 16 , an d i n going fro

mthe result s for Conditio n 1 t o thos e for Conditio n 4
. Thi s shif t wa s th e resul t o f radionuclid e los s du e t o deca yduring the slowmigratio n o f radionuclide s t o a wel l located 3 0 meter s downgradien t fro

mthe poin t o f release
. Finally , Exhibi t 3 illustrate s that , wit hon e exception , change s onl yi n the dose-equivalen t limi t di d no t chang e the relative significanc e o f the variou s exposur e pathways
. Tha t is , whil e change s i n the dose-equivalen t limi t resulte d in a shif t in the magnitud e o f RQ s (se e Exhibi t 2) , the exposur e pathway s tha t wer e limitin g unde r the assumptio n o f on e dose

equivalen t leve l wer e the same a s the limitin g pathway s unde r anothe r level
. Thi s i s evident , for example , whe n the result s for Condition s 1 an d 2 , an d the result s fo r Condition s 4 , 5 , an d 1 6 ar e compared
. Th e on e exceptio n t o thi s finding i s that , base d o n the pathwa ymodel s use d i n thi s analysis , the mil k ingestio n pathwaywa s no t limitin g whe n a dose-equivalen t o f 0. 5 re mo r highe r wa s assumed
.