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\02RQ.-Rti-S'm. 

SUPPLEMENTARY TECHNICAL BACKGROUND DOCUMENT TO 

SUPPORT THE ADJUSTMENT OF 

RADIONUCLIDE REPORTABLE QUANTITIES: 

METHODS AND RESULTS FOR CALCULATIONS OF 

RADIONUCLIDE REPORTABLE QUANTITIES 

UNDER VARYING SETS OF CONDITIONS 

EMERGENCY RESPONSE DIVISION 

Office of Emergency and Remedial Response 

U.S. Environmental Protection Agency 

June 18, 1987 
P.3 

METHODS AND RESULTS FOR CALCULATIONS OF RADIONUCLIDE 

REPORTABLE QUANTITIES UNDER VARYING SETS OF CONDITIONS 

1. BACKGROUND 

The Comprehensive Environmental Response, Compensation, and Liability Act 

(CERCLA) requires immediate notification to the National Response Center when 

a hazardous substance designated under CERCLA is released into the environment 

in an amount equal to or greater than the reportable quantity (RQ) for that 

substance. Radionuclides are designated hazardous substances under CERCLA and 

the current RQ for radionuclides, established by Section 102(b) of CERCLA, is 

one pound. CERCLA, however, authorizes the Environmental Protection Agency 

(EPA) to adjust statutory RQs by regulation if deemed appropriate. 

Recognizing that a one-pound RQ is not appropriate for all radionuclides, 

EPA recently has published a Notice of Proposed Rulemaking (NPRM) to adjust 

the statutory RQ for radionuclides (52 FR 8172, March 16, 1987). The Agency 

proposed specific RQ adjustments for the 757 radionuclides for which the 

International Commission on Radiation Protection (ICRP) has provided metabolic 

data and recommended intake limits in ICRP Publication 30.l All 

radionuclides not listed by the ICRP were grouped into a generic class of 

"radionuclides," with one proposed RQ for the entire class. All of the 

proposed RQs are in units of curies. 

As discussed in the Technical Background Document (TBD) supporting the 

proposed RQ rulemaking,2 the proposed radionuclide RQs were developed by 

determining the quantity of radionuclides that, if released under a set of 

conservative exposure conditions, could result in an individual receiving an 

effective whole body dose-equivalent of 500 millirem. The Agency considered 

hypothetical releases into various environmental media and human exposures via 

three pathways: inhalation; ingestion of contaminated ground water; and 

direct exposure. Using a set of conservative assumptions to analyze each 

exposure pathway, the pathway that was found to be the most critical for a 

radionuclide (i.e., the one that yielded the lowest release value) was used as 

the basis for the RQ adjustment for that radionuclide. 

The equations or models used to examine possible exposure via the abovementioned pathways rely on several parameters and defined exposure conditions. 

Four conditions or parameters that have a significant bearing on the RQ 

1International Commission on Radiation Protection, Annals of the ICRP: 

Limits for Intakes of Radionuclides by Workers, ICRP Publication 30, 1980. 

2U.S. Environmental Protection Agency, Technical Background Document to 

Support Proposed Rulemaking Pursuant to Section 102 of CERCLA: Radionuclides, 

Emergency Response Division, Office of Emergency and Remedial Response, 1986. 
P.4 

m 

-2-

results are: (1) the distance between the point of release and the point of 

exposure; (2) the dose-equivalent limit that the hypothetically-exposed 

individual is permitted to receive; (3) the extent of radioactive decay during 

transport to the point of exposure and over the period of exposure; and (4) 

the time period over which an individual is exposed. The models used to 

calculate the proposed RQs in the NPRM assume that: the distance from the 

point of release to the point of exposure is 30 meters; the dose-equivalent 

limit is 500 millirem effective whole body dose; and there is no radioactive 

decay (for the sake of conservatism and simplicity). For the period of 

exposure, the models used in the NPRM assume that persons are exposed for one 

day for inhalation and direct exposure, but that persons are exposed for 

longer periods through the ingestion pathway in order to account for the slow 

movement of radionuclides in ground water. 

Since publishing the NPRM, EPA has analyzed how the proposed RQ 

adjustments would vary if different assumptions are used with regard to the 

distance to the exposure point, dose-equivalent limit, extent of radioactive 

decay, and exposure period. This paper derives the models used to calculate 

radionuclide RQs under several alternate sets of assumptions and summarizes 

the results of these alternate calculations. The raw results obtained from 

each calculation can be found in the Superfund docket supporting the 

radionuclide rule (Superfund Docket No. 102RQ-RN). 

The remainder of this paper is divided into four main sections. In 

Section 2, the sets of alternate conditions used to calculate radionuclide RQs 

are defined. Including the set of model conditions used to derive the 

proposed RQs in the NPRM, a total of 19 different sets of conditions involving 

variations in the exposure-point distance, dose-equivalent limit, extent of 

radioactive decay, and exposure period were evaluated. In Section 3, an 

overview of the approaches used to calculate the RQs under the various sets of 

conditions is provided. While Section 3 presents the general rationale and 

concepts used to take into account the various conditions, the particular 

equations and values for parameters used in the different calculations are not 

derived until Section 4. Finally, Section 5 presents the summary and raw 

results obtained from the equations derived in Section 4. 

2. CALCULATIONS PERFORMED FOR THIS ANALYSIS 

Radionuclide RQs were calculated using different assumptions regarding: 

• distances between the point of radionuclide release 

and the point of exposure; 

• durations of exposure to the radionuclide release for 

a hypothetical individual; 

• dose-equivalent limits that the exposed individual is 

permitted to receive; and 
P.5 

• assumptions with regard to the extent of radioactive 

decay from the time that the radionuclide is released to 

the end of the time that a person is exposed to the 

release. 

The various combinations of these assumptions that define the calculations 

performed for this analysis are listed in Exhibit 1. 

The first set of assumptions shown in Exhibit 1 is the one used to 

calculate the radionuclide RQs proposed in the NPRM. The methods used to 

calculate RQs under this set of conditions, as well as the results from these 

calculations, are summarized here to permit comparison with the alternate sets 

of assumptions defined by condition numbers 1 through 18. 

All of the RQ adjustments in the NPRM were determined by one of the 

following exposure pathways: inhalation; ingestion of ground water; direct 

exposure to a point source; and direct exposure by submersion in an airborne 

cloud. Other ingestion pathways (i.e., ingestion of vegetables contaminated 

by airborne deposition and ingestion of surface water) also were evaluated 

but, under the set of assumptions evaluated in the NPRM, were found to be less 

critical for most radionuclides as compared to the ingestion of ground water. 

It is recognized, however, that changes in the exposure conditions (most 

notably, a different assumption with regard to the extent of radioactive 

decay) could increase significantly the relative importance of the vegetable 

ingestion pathway. In addition, EPA recognizes that exposure pathways other 

than the ones considered previously also exist and could in fact be more 

critical (i.e., lead to lower RQs) for some radionuclides. For example, the 

ingestion of contaminated milk is a possible exposure pathway that could lead 

to lower RQs for some radionuclides. 

For this analysis, therefore, EPA has expanded the approach used in the 

NPRM to consider additional exposure pathways in greater detail. For each set 

of assumptions shown in Exhibit 1 that involves a distance of 30 meters, a 

separate calculation was performed to evaluate exposures through the following 

pathways: inhalation, ingestion of ground water, ingestion of vegetables 

contaminated by airborne deposition, ingestion of milk, and direct exposure. 

Direct exposure to a point source was evaluated for all radionuclides except 

the isotopes of the noble gases argon, krypton, and xenon; for these 

radionuclides, direct exposure by submersion in a cloud was evaluated. For 

those sets of assumptions involving a distance of 1 meter, the only exposure 

pathway that was evaluated was direct exposure to a point source. An analysis 

assuming a distance of 1 meter for the other exposure pathways was not 

performed because such a close distance for the other pathways generally would 

be unrealistic and would yield overly conservative results. 

The Agency also considered in this analysis the potential exposure 

resulting from the ingestion of vegetables contaminated by radionuclide-bearing 

irrigation water. An equation to calculate release values for this exposure 

pathway was developed, but based on the range of input values to be used in 

this equation, EPA determined that release values for the irrigation pathway 

always would be higher than those for the ground-water ingestion pathway and 
P.6 

EXHIBIT 1 

COMBINATIONS OF ASSUMPTIONS DEFINING THE 

RADIONUCLIDE RQ CALCULATIONS 

Condition 

Number 

NPRM c/ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

Distance from 

Rel 

to 

ease Point 

Exposure 

Point (Meters) a/ 

30 

30 

30 

1 

30 

30 

1 

1 

30 

30 

1 

1 

d/ 

d/ 

d/ 

_y 

30 

30 

1 

Period of 

Direct 

Exposure 

(Days) b/ 

1 

1 

1 

1 

1 

1 

1 

1 

365 

365 

1 

1 

d/ 

d/ 

d/ 

d/ 

1 

365 

1 

Whole Body 

Dose Limit 

(Rem) 

0.5 

0.025 

0.1 

0.1 

0.025 

0.1 

0.5 

0.025 

0.5 

0.5 

25 

0.5 

5 

5000 

25 

500 

0.5 

0.1 

0.1 

Radioactive 

Decay 

Considered? 

No 

No 

No 

No 

Yes 

Yes 

No 

Yes 

No 

Yes 

Yes 

Yes 

No 

No 

No 

No 

Yes 

No 

Yes 

a/ For each set of conditions involving a distance of 30 meters, a 

separate calculation was performed to evaluate radionuclide releases and 

exposures through all the pathways considered in this analysis; for each set 

of conditions involving a distance of 1 meter, however, only direct exposures 

to a point source were evaluated. 

b/ The periods of exposure listed here were used only in the evaluation 

of direct exposures to a point source. See Sections 3.2 and 4 of this paper 

for a discussion of the exposure periods used in the other exposure pathway 

models. 

c/ This is the set of conditions assumed in the calculation of proposed 

RQs presented in the NPRM. 

d/ In Conditions 12 through 15, RQs are calculated simply by taking 

multiples of the inhalation and ingestion Annual Limits of Intake. Neither 

distance nor time, therefore, were considered in these calculations. 
P.7 

-5-

hence would never serve as the basis for the RQs. This determination is not 

intended to imply that human exposures via the irrigation-vegetable route will 

always be less, critical than those that occur through the ingestion of ground 

water; the Agency recognizes that exposures through irrigation could be much 

more critical than ground-water exposures due to the specific conditions 

surrounding the actual release event. However, under the hypothetical release 

and exposure scenarios examined, EPA found ground-water exposures always to be 

more critical (see Section 4.7 of this paper for a justification for this 

conclusion). Therefore, a separate calculation using the irrigation pathway 

model was not performed. 

3. OVERVIEW OF CALCULATIONAL APPROACHES 

In simplest terms, each of the models used to calculate radionuclide RQs 

is intended to determine that quantity of a radionuclide that, if released 

into the environment under a certain set of conditions, could result in an 

exposed individual receiving a specified effective whole body doseequivalent. To make this determination, the models define a hypothetical 

release and exposure scenario in which: (1) a radionuclide is assumed to be 

released into an environmental medium; (2) the radionuclide is transported 

from the point of release to the point of exposure and diluted along the way; 

and (3) a person is exposed (i.e., inhales, ingests, or comes into direct 

contact) to the released radionuclide over a certain length of time. Changes 

in the assumptions with regard to the distance between the point of release 

and the point of exposure, the period of exposure, the maximum dose-equivalent 

that the exposed individual is permitted to receive, and the extent of 

radioactive decay throughout this period will involve changes in the 

calculation methods and results. 

This section is divided into four subsections. Each of the subsections 

describe in general terms how all the models used in this analysis were 

changed to take into account variations in distance, variations in exposure 

period, variations in dose-equivalent limit, and variations in the extent of 

radioactive decay. 

3.1 Changes in Models to Accommodate Variations in Distance 

As shown in Exhibit 1, the distance from the point of release to the point 

of exposure was varied in this analysis between 1 and 30 meters. The only 

pathway that was evaluated assuming a 1 meter distance was direct exposure to 

a point source. The Agency believes that assuming a 1 meter distance for the 

other exposure pathways would be generally unrealistic and overly conservative. 

The model used to estimate direct exposure to a point source assumes that 

an individual resides in the vicinity of a radiation source for a certain 

length of time. The distance between the point source and the exposed 

individual is an input variable and, to estimate potential exposures at the 

different distances, the value of this variable was simply changed from 30 

meters to 1 meter. 
P.8 

The models used for both distances estimate the dose from gamma radiation 

in units of rem. Both models take into account gamma ray attenuation in air 

between the source and the receptor. For the sake of simplicity, however, EPA 

decided to ignore the possible direct radiation dose caused by beta 

particles. This exclusion is technically valid when considering a distance of 

30 meters; the mean range of almost all beta particles in air is less than 20 

meters. Although numerous beta particles can travel 1 meter and would result 

in more biological damage than is being considered in this analysis (i.e., the 

consideration of beta particles would result in lower release values based on 

the direct exposure pathway), a release-to-exposure distance of 1 meter is 

highly unlikely in reality. Therefore, ignoring beta particle exposures for 

the sake of simplicity should have little practical effect. 

3.2 Changes in Models to Accommodate Variations in Exposure Period 

The period of time that an individual is assumed to be exposed to released 

radionuclides is an input variable to most of the pathway models considered in 

this analysis. In the pathway model considering direct exposure to a point 

source, the value of this variable simply was varied between 1 day and 365 

days in accordance with the conditions shown in Exhibit 1. As discussed 

below, however, the Agency concluded that there was adequate justification for 

not varying the exposure period in the pathway models other than direct 

exposure. 

For the inhalation exposure pathway, the calculated inhalation release 

values are independent of the assumed exposure period. Using the same 

atmospheric relative concentration value (i.e., X/Q) to represent all possible 

release periods, the same quantity of radionuclides released to the air will 

result in the same inhalation dose regardless of whether the release lasts 1 

day or 1 year. The only difference between these two cases would be the 

length of time it would take an individual to receive the dose. Accordingly, 

the exposure period is not a factor in the inhalation pathway model and no 

changes to the model had to be made to take into account variations in this 

parameter. 

The period of exposure in the ground-water ingestion model is complicated 

by the fact that different radionuclides migrate in ground water at different 

rates and thus may linger in the vicinity of a drinking water well over 

different time periods. Under the release and ground-water transport 

characteristics assumed in the TBD, it was estimated that it would take 

roughly 9 days for a contaminated ground water plume to pass a well 30 meters 

from the point of release if the radionuclides were not sorbed to soil (see 

Appendix F of the TBD). However, if a radionuclide's sorption coefficient is 

4 or more, the time necessary for the radionuclide to reach and pass a well 30 

meters away is greater than 365 days. Based on this analysis, the Agency 

concluded that the period of exposure in the ground-water ingestion model is a 

function of the properties of the radionuclide in question and could not be 

changed arbitrarily between 1 day and 365 days. Therefore, the period of 

ground-water ingestion was not varied in accordance with the conditions shown 

in Exhibit 1, but rather was varied between 9 and 365 days depending on the 

sorption coefficient selected for each radionuclide. 
P.9 

A release conceivably could contaminate a small quantity of vegetables; 

for example, the quantity that a person might eat in one day or less. It is 

also possible, however, for a release of the same magnitude to contaminate a 

much larger crop and it is not inconceivable that a person subsequently could 

eat from that crop for periods close to a year. Consequently, rather than 

varying the period of ingestion between 1 day and 365 days, the Agency decided 

to adopt a single conservative, although not worst-case, exposure period that 

has some technical basis. In particular, it was assumed for all the sets of 

conditions shown in Exhibit 1 that a person ingests contaminated vegetables 

over the entire vegetable growing season, generally recognized to be 60 days. 

A similar approach was adopted for the model used to evaluate exposure via 

the ingestion of contaminated milk. This model assumes that grass is 

contaminated by an airborne release of radionuclides, the contaminated grass 

is ingested by a cow, and radionuclide-bearing milk produced by the cow is in 

turn ingested by a person. Both the period of time that the cow grazes from 

the contaminated pasture and the time over which the exposed individual drinks 

contaminated milk are completely arbitrary. Therefore, rather than simply 

varying the exposure period in this pathway model between 1 day and 365 days, 

the Agency selected a single time period. To be consistent with the vegetable 

ingestion pathway model, EPA assumed that the cow grazed for a period of 60 

days and that the person subsequently drank milk from the cow over this same 

period. 

The model for submersion in an airborne cloud assumes that noble gases are 

released to the atmosphere (i.e., not contained within a structure) and that 

the cloud travels to an exposure point 30 meters away. Under this scenario, 

the length of time that an individual could be submersed in the cloud is the 

same as the period of release. RQs are applicable to releases that last up to 

1 day. Therefore, an exposure period of 1 day was used for all the conditions 

shown in Exhibit 1. 

3.3 Changes in Models to Accommodate Variations in Dose-Equivalent Limit 

All of the models used in this analysis (regardless of the exposure 

pathway being evaluated) require as an input variable the maximum 

dose-equivalent limit that the hypothetically exposed individual is allowed to 

receive. This variable takes the form of the Annual Limit of Intake (ALI) or 

Derived Air Concentration (DAC) presented in ICRP Publication 30 divided by an 

adjustment factor. Both the ALI and DAC are based on an exposed individual, 

over the course of a year, receiving an effective whole body dose-equivalent 

of 5 rem. In order to calculate RQs based on an alternate whole body dose 

limit, appropriate adjustment factors to arrive at the dose limits shown in 

Exhibit 1 were used. For example, in those analyses that assume a whole body 

dose limit of 0.5 rem, the ALI or DAC is divided by 10; the ALI or DAC is 

divided by 50 for those analyses where the dose limit is 0.1 rem. 
P.10 

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3.4 Changes in Models to Incorporate Radioactive Decay 

In the pathway models used in the NPRM, radioactive decay was ignored for 

the sake of conservatism and simplicity. Recognizing, however, that 

radioactive decay is an intrinsic property of all radionuclides, the Agency 

has analyzed what the proposed RQs would be if decay were taken into account. 

For the purpose of this analysis, the total period of time in the 

hypothetical release and exposure scenarios can be divided into three 

segments: (1) the time period over which the release occurs; (2) the time it 

takes for the radionuclide to travel from the point of release to the point of 

exposure; and (3) the period of exposure. Radioactive decay over these time 

periods is taken into account differently in the different exposure pathway 

models. 

For the inhalation pathway model and the direct exposure model that 

considers submersion in an airborne cloud, the Agency decided to continue to 

ignore the effects of radioactive decay in this analysis. Both of these 

pathway models consider exposures to an airborne plume of radionuclides. A 

short-lived radionuclide could undergo significant decay if the release and 

exposure periods were several days, but decay would be much less if a time 

period of several hours was considered. Because it was not possible to 

establish exact bounds on the range of release and exposure periods, the 

Agency assumed conservatively that no decay occurs over these periods. EPA 

also ignored decay over the period of radionuclide transport to the point of 

inhalation or submersion in a cloud. This approach was adopted because decay 

during airborne transport to a receptor just 30 meters away would be 

negligible for all but a handfull of radionuclides. 

In the model used to evaluate exposure by the ingestion of ground water, 

the release is assumed conservatively to be instantaneous such that no decay 

over the period of release could occur. Decay over the period of transport 

and period of ingestion, however, is considered. For the period of transport, 

the time that it would take for a released radionuclide to travel to a 

drinking water well is first determined assuming conservative transport 

characteristics. Once the time of transport is estimated, decay over this 

time is taken into account using the exponential function: 

A = A exp(-Xt) 

t o 

where 

A = activity at time t; 

t 

A = activity at time t=o (i.e., initial activity released); 

o 
_P_J1 

X = 0.693, where T-l/2 = the radionuclide half-life; and 

T-l/2 

t = time that it takes the released radionuclide to travel to the receptor. 

To consider decay over the period of ingestion, it was recognized that an 

individual would ingest smaller quantities of radioactivity at times that are 

successively longer from the time that the radionuclide first arrives at the 

point of exposure. Accordingly, decay over the period of exposure was taken 

into account in the ground-water model through the following integrated 

exponential equation: 

1 - exp(-Xte) 

A = C * * IR 

te t X 

where 

A = the quantity of radioactivity ingested over the period of exposure; 

te 

C = the concentration of radioactivity that first arrives at the point 

t of exposure; 

te = the period of exposure; 

X = 0.693, where T-l/2 = the radionuclide half-life; and 

T-l/2 

IR = water ingestion rate. 

In the models used to evaluate the ingestion of milk and the ingestion of 

vegetables contaminated by airborne deposition, the assumption with regard to 

the period of release and airborne deposition follows the same approach used 

in the inhalation and cloud submersion models. That is, decay during release 

and deposition was ignored. Similarly, decay during airborne transport to 

vegetation located 30 meters away was not considered because it would be 

negligible for all but a handful of radionuclides. Once the initial quantity 

of radioactivity is deposited on the vegetation, however, a significant amount 

of decay could occur before the radionuclides are actually consumed by man 

(either directly through the ingestion of vegetables or indirectly through the 

ingestion of milk). Therefore, decay over the period of ingestion was taken 

into account in the vegetable and milk ingestion models using an integrated 

decay expression as shown above. 

Finally, only decay over the period of exposure was considered in the 

model used to evalaute direct exposures to a point source. Decay was 

considered in this pathway model by using an integrated decay term, accounting 

for an individual's cumulative exposure over the entire period that the person 

remains in the vicinity of the point source. The Agency conservatively 

assumed an instantaneous release (i.e., no decay over the period of release). 
P.12 

•10-

Similarly, the Agency conservatively assumed that no decay takes place during 

the time needed for a released source to come into contact with an individual. 

4. DERIVATION OF MODEL EQUATIONS 

Each of the specific equations used to evaluate exposures under the 

conditions shown in Exhibit 1 is derived in this section. To help illustrate 

the changes made in the various pathway models in going from one set of 

conditions to the next, all of the equations used to evaluate a particular 

exposure pathway are described together in separate sections; that is, all the 

inhalation pathway models across the various sets of conditions are derived in 

Section 4.1, all the ground-water ingestion models across the various sets of 

conditions are derived in Section 4.2, and so on. Within each section, the 

equation used to calculate RQs under the conditions assumed in the NPRM is 

presented and briefly described first (the TBD should be referenced for more 

detail on the equations used in the NPRM). The equations used to model the 

pathways under conditions 1 through 18 (see Exhibit 1) are-'then derived, with 

an emphasis placed on how the equations differ from the one used in the NPRM. 

Two additional points also should be explained to help introduce the 

equations that follow. First, as discussed in Section 3.1 of this paper, the 

only exposure pathway that was evaluated assuming 1 meter between the point of 

release and the point of exposure was direct exposure to a point source. 

Therefore, for those sets of conditions involving a distance of 1 meter (i.e., 

Conditions 3, 6, 7, 10, 11 and 18), no equations are derived for the 

inhalation, ingestion of ground water, ingestion of vegetables, ingestion of 

milk, and submersion-in-a-cloud pathways. Second, each of the equations that 

is derived below is for the calculation of "release values," not RQs. The 

lowest release value for a given radionuclide considering each of the exposure 

pathways under the defined set of conditions is selected as the RQ for that 

radionuclide. 

4.1 Inhalation Pathway Equations 

Equation Used in NPRM. As described on page 4-3 of the TBD, the equation 

used to evaluate the inhalation pathway in support of the NPRM is: 

(1) Inhalation Release Value = ALI/((10)*(R)*(X/Q)*(BR)*(lxl06)) 

where 

ALI = Annual Limit of Intake for inhalation (microcuries); 

10 = Factor to adjust the dose-equivalent limit built into the 

ALI, 5 rem, to a limit of 0.5 rem; 

R = Release Fraction; 

X/Q = Atmospheric Relative Concentration Value (8.4 x 10-13 day/ 

cubic cm); 
P.13 

-11-

BR = Breathing Rate (2.3 x IO7 cubic cm/day); and 

1 x 10s = Conversion factor between microcuries and curies. 

When all of the specified values are plugged into Equation (1), the equation 

simplifies to: 

(2) Inhalation Release Value = ALI (inhalation)/(193.2*R) 

Condition 1. Exhibit 1 shows that the only difference between Condition 1 

and the set of conditions assumed in the NPRM was a different whole body dose 

limit (0.025 rem rather than 0.5 rem). Therefore, only the dose-equivalent 

limit adjustment factor in Equation (1) needed to be changed from 10 to a 

factor of 200. Plugging this new factor in Equation (1) with the other values 

shown for the equation, the revised inhalation pathway model reduced to: 

(3) Inhalation Release Value = ALI (inhalation)/(3864*R) 

Condition 2. Like the revision needed in Condition 1, the only change to 

Equation (1) that was needed to accommodate Condition 2 was a different dose 

limit adjustment factor. Using a factor of 50 to adjust the dose limit to 0.1 

rem, Equation (1) became: 

(4) Inhalation Release value = ALI (inhalation)/(966*R) 

Condition 4. The only difference between Condition 4 and Condition 1 was 

that radioactive decay was considered in Condition 4. As discussed in Section 

3.4 of this paper, however, the Agency decided to ignore the effects of 

radioactive decay in all inhalation pathway models. Therefore, the same 

inhalation pathway model (Equation (3)) used for Condition (1) was used under 

this set of conditions. 

Condition 5. Because radioactive decay was ignored in the inhalation 

pathway models, the same equation used under Condition 2 -- Equation (4) --

was used under Condition 5 (the only difference between Conditions 2 and 5 was 

that Condition 5 considers decay). 

Condition 8. This set of conditions is the same as that used in the NPRM 

except that it assumed a 365 day exposure period rather than a 1 day exposure 

period. As discussed in Section 3.2 of this paper, inhalation release value 

results are independent of the period of exposure assumed in the calculation. 

Under the conservative atmospheric dispersion conditions assumed in this 

analysis, the same quantity of radionuclide released to the air over different 

time periods would result in the same total inhalation dose; it would just 

take different periods of time to receive this dose. As a result, the 

inhalation pathway model used in the NPRM (Equation (2)) did not have to be 

modified to account for the different exposure period assumed under this set 

of conditions. 

Condition 9. The only difference between Condition 9 and Condition 8 is 

that Condition 9 considered radioactive decay. However, for the reasons given 
P.14 

-12-

in Section 3.4 of this paper, the Agency decided to continue to ignore 

radioactive decay in the inhalation pathway models. As a result, the same 

inhalation pathway model used for Condition 8, Equation (2), was also used for 

this set of conditions. 

Condition 12. The ALIs for inhalation were used directly as the 

inhalation release values for this condition. The only modification.to the 

ALIs that was needed was to convert them from units of microcuries to curies 

using the following equation: 

Inhalation ALI (in microcuries) 

(5) Inhalation Release Value (in curies) = 

1 x 10s 

where 

1 x 10p = Conversion factor between microcuries and curies. 

Condition 13. Under this condition, the inhalation release values were 

calculated simply by taking a multiple of the inhalation ALIs. Specifically, 

the ALIs were multiplied by 1000 to arrive at ALIs based on 5000 rem as 

opposed to 5 rem. Combining this multiplication with the conversion needed to 

calculate release values in units of curies, the inhalation pathway model used 

under this condition took the form: 

1000 * Inhalation ALI (in microcuries) 

(6) Inhalation Release Value = 

(in curies) 1 x 10s 

Inhalation ALI (in microcuries) 

1 x IO3 

where 

1000 = Factor used to adjust the ALI, based on a dose limit of 5 rem, to 

an ALI based on 5000 rem; and 

1 x 10s = Conversion factor between microcuries and curies. 

Condition 14. This condition is the same as Condition 13 except that the 

dose limit in this case is 25 rem rather than 5000 rem. Accordingly, the 

equation used here was the same as Equation (6) except that a dose adjustment 

factor of 5 was used rather than a factor of 1000, as shown below: 

5 * Inhalation ALI (in microcuries) 

(7) Inhalation Release Value = 

(in curies) 1 x 10s 

Inhalation ALI (in microcuries) 

2 x 10s 
P.15 

-13-

where 

5 = Factor used to adjust the ALI, based on a dose limit of 5 rem, to 

an ALI based on 25 rem; and 

1 x 10s = Conversion factor between microcuries and curies. 

Condition 15. Like Conditions 13 and 14, release values under this 

condition were calculated simply by taking a multiple of the inhalation ALIs. 

In this case, the dose-equivalent limit of interest was 500 rem, such that 

release values were calculated using the following equation: 

100 * Inhalation ALI (in microcuries) 

(8) Inhalation Release Value = 

(in curies) 1 x 10s 

Inhalation ALI (in microcuries) 

1 x 10* 

where 

100 = Factor used to adjust the ALI, based on a dose limit of 5 rem, to 

an ALI based on 500 rem; and 

1 x 10s = Conversion factor between microcuries and curies. 

Condition 16. This set of conditions is the same as that used in the NPRM 

except that it incorporated the effects of radioactive decay. However, for 

the reasons given in Section 3.4 of this paper, EPA decided to continue to 

ignore radioactive decay in the inhalation pathway models. As a result, the 

inhalation pathway model used in support of the NPRM (Equation (2)) also was 

used in the calculation of release values under Condition 16. 

Condition 17. There are two differences between this set of conditions 

and the one used in the NPRM: (1) an exposure period of 365 days rather than 

1 day was assumed; and (2) the dose-equivalent limit was 0.1 rem rather than 

0.5 rem. However, because the inhalation release values are independent of 

the assumed exposure period (see Section 3.2 of this paper), the inhalation 

pathway equation used in the NPRM (i.e., Equation (1)) did not have to be 

changed to incorporate the different exposure period assumed here. Equation 

(1) did have to be changed, however, to account for the revised 

dose-equivalent limit. Specifically, a factor of 50 (rather than a factor of 

10) was used to adjust the dose-equivalent to 0.1 rem. Plugging this 

different factor into Equation (1) along with the other input values shown for 

that equation, the inhalation pathway equation used for this condition reduced 

to: 

(9) Inhalation Release Value = ALI (inhalation)/(966*R) 
P.16 

-14-

4.2 Ground-Water Ingestion Pathway Equations 

Release values for the ground-water ingestion pathway were calculated 

using the following basic equation (see Section 4.2.2 of the TBD for more 

discussion on the derivation of this equation): 

(10) Ground-water Ingestion = ALI/((AF)*(DF)*(CT)*(WC)*(lxl06)) 

Release Value (curies) 

where 

ALI = Annual Limit of Intake for ingestion for a particular radionuclide 

(microcuries); 

AF = Dose-equivalent adjustment factor to adjust the dose-equivalent on 

which the ALI is based, 5 rem, to a dose-equivalent limit of 

interest; 

DF = Dilution factor, the concentration of a radionuclide at a drinking 

water well 30 meters from the point of release per curie released 

(Ci/liter per Ci, or liter-1); 

CT = Contact time in days, or the number of days an individual drinks 

the contaminated water; 

WC = Water consumption rate of reference man (2 liters/day); and 

1x10s = Conversion factor between microcuries and curies. 

As derived in Section F.l of the TBD, the dilution factor used in Equation 

(10) was expressed in the following manner: 

(11) DF = 7.6 x IO-8 liters-'/Rd 

where Rd -= the radionuclide retardation factor (i.e., a factor that accounts 

for the degree to which radionuclides are sorbed to the aquifer media and thus 

slowed in movement relative to the transporting water). 

When a radionuclide's sorption coefficient equals zero, the Rd for that 

radionuclide equals one; that is, the radionuclide moves at the same rate as 

the ground water. In this situation, and under the ground-water transport 

characteristics assumed in the TBD, the Agency estimated that it would take 

approximately 6 days for the leading edge of the contaminant plume to first 

reach a well 30 meters away and then 9 days from the time of the first arrival 

for the trailing edge of the plume to pass the well. Therefore, the contact 

time when Rd = 1 was estimated to be 9 days. As sorption coefficients rise 

above 4, the time necessary for a radionuclide to reach and pass a well 30 

meters from the point of release becomes greater than 365 days. Because 
P.17 

•15-

ALIs are concerned with annual limits of intake, however, EPA chose to limit 

the contact time in these situations to 365 days. 

It is also important to clarify that the dilution factor given in Equation 

(11) is designed to yield the maximum radionuclide concentration that passes 

the drinking water well. Therefore, radionuclide loss due to radioactive 

decay over the time of transport has not been factored into the dilution 

factor used in the NPRM. Such corrections for decay, over both the time of 

transport and the period of ingestion, are carried out through separate decay 

terms as explained below under Conditions 4, 5, 9, and 16. 

Equations Used in the NPRM. In the NPRM, a value of 10 was used for AF to 

adjust the dose-equivalent limit from 5 rem to 0.5 rem. Substituting this 

value along with CT = 9 days for radionuclides with a Rd = 1 into Equation 

(10), the equation simplified to: 

(12) Ground-water Ingestion = ALI/(1.4 x 101) 

Release Value 

When Rd > 1, the contact time was assumed to be 365 days. Using 365 as the 

value for CT while keeping Rd as a variable, Equation (10) became: 

(13) Ground-water Ingestion = ((ALI) * (Rd))/(5.5 x 102) 

Release Value 

Condition 1. The equations used for this condition were derived 

differently from those used in the NPRM only because of the use of a different 

dose-equivalent adjustment factor. Specifically, a value of AF = 200 was used 

rather than 10 to arrive at a dose-equivalent limit of 0.025 rem rather than 

0.5 rem. Plugging this value into Equation (10) and following the same 

rationale as presented above for the NPRM equations, the equations used in 

this case were: 

(14) Ground-water Ingestion = ALI/(2.7 x 102) 

Release Value 

when Rd = 1, and 

(15) Ground-water Ingestion = ((ALI)*(Rd))/(1.1 x 10") 

Release Value 

when Rd > 1. 

Condition 2. Like Condition 1, Condition 2 differs from the conditions 

assumed in the NPRM only by assuming a different dose-equivalent limit (0.1 

rem rather than 0.5 rem). Accordingly, the appropriate dose-equivalent 

adjustment factor for this condition is 50. Plugging this value for AF into 

Equation (10), the equation becomes: 

(16) Ground-water Ingestion = ALI/(6.8 x 101) 

Release Value 
P.18 

•16-

when Rd = 1, and 

(17) Ground-water Ingestion = ((ALI)*(Rd))/(2.8 x IO3) 

Release Value 

when Rd > 1. 

Condition 4. Under this set of conditions, the appropriate value for AF 

was 200 in order to adjust the dose-equivalent limit from 5 rem to 0.025 rem. 

In addition, because this set of conditions included the effects of 

radioactive decay, Equation (10) needed to be modified to include two decay 

terms. First, a term to account for radioactive decay during the period of 

transport from the point of release to the point of exposure had to be 

included. This term took the form: 

(18) exp (-Xt) 

where X = 0.693/T-1/2, where T-l/2 = radionuclide half-life in days; 

and 

t = time that it takes for the contaminant plume to first reach a 

drinking water well 30 meters from the point of release 

(estimated to be 6 days when Rd =1 ; see Appendix F of the 

TBD) . 

The second decay term that was needed was to account for radioactive decay 

over the period of ingestion. This decay term took the form: 

(19) 1 - exp (-XCT) 

where X = 0.693/T-1/2, where T-l/2 = radionuclide half-life in days; 

and 

CT = contact time, ranging anywhere from 9 days when Rd = 1 to up 

to 365 days when Rd > 1. 

Plugging these two decay terms into Equation (10), the equation for 

ground-water ingestion release values incorporating the effects of radioactive 

decay became: 

(20) Ground-water ALI 

Ingestion = (AF)*(DF)*(exp(-Xt))*(WC)*(lxlOs)* (l-exp(-XCT)) 

Release Value 

To accommodate the set of conditions assumed under Condition 4, a value of 

AF = 200 was inserted into Equation (20) and the equation simplified to the 

following when Rd = 1: 
P.19 

-17-

(21) Ground-water ALI * (2.3 x IO-2) 

Ingestion 

Release Value (exp(-4.2/T-l/2))*(T-l/2 - T-l/2 exp(-6.2/T-l/2)) 

where T-l/2 = radionuclide half-life in days. 

When Rd > 1, it takes a significantly longer time for the released 

radionuclides to migrate to and pass the well point. Incorporating 

radioactive decay in this scenario has the effect of "removing" a large 

portion of the radionuclides before they can be ingested. As a result, the 

calculated release value is significantly larger than the release value 

assuming Rd = 1 and, in fact, becomes much larger in comparison with the other 

release values calculated for the other exposure pathways. It is recognized, 

therefore, that the ground-water ingestion release value when Rd > 1 would 

never drive the RQ for a given radionuclide and, accordingly, the Agency did 

not develop separate ground-water ingestion equations for situations where Rd 

> 1. 

Condition 5. The equation used under this condition was derived in 

exactly the same manner as the equation used under Condition 4 except that an 

AF value of 50 was used instead of 200. Making this substitutional change in 

Equation (20) and following the same rationale as outlined for Condition 4, 

the equation used in this case became: 

(22) Ground-water ALI * (9.1 x 10-2) 

Ingestion = 

Release Value (exp(-4.2/T-l/2))*(T-l/2 - T-l/2 exp(-6.2/T-1/2)) 

where Rd = 1 and T-l/2 = half-life in days. Again, no equation was derived 

for situations where Rd > 1 because the resulting release value would be 

significantly higher than the release value calculated for the other exposure 

pathways. 

Condition 8. The only difference between this condition and the 

conditions assumed in the NPRM is that it assumed a 365-day exposure period 

for the direct exposure to a point source release. As discussed in Section 

3.2 of this paper, however, the Agency decided not to vary the exposure period 

in the ground-water ingestion model between 1 day and 365 days as shown in 

Exhibit 1, but rather to use exposure periods that are consistent with the 

ground-water transport characteristics defined for this analysis (i.e., 9 days 

to 365 days depending on a radionuclide's Rd value). With this approach, 

there were no differences in the NPRM conditions and Condition 8 for the 

ground-water ingestion model, and the same equations used in the NPRM (i.e., 

Equations (12) and (13)) were used here. 

Condition 9. The equation used for this set of conditions was derived by 

using Equation (20) and all the input values specified for that equation (see 

discussion above for Condition 4) except, rather than using a value of AF = 

200, a value of AF = 10 was used. Again, the 365-day exposure period assumed 

for Condition 9 was applicable only to the pathway model concerning direct 

exposure to a point source; the exposure period used in the ground-water 
P.20 

-18-

ingestion model varied from 9 days to 365 days depending on the radionuclide's 

Rd. Therefore, for cases where Rd = 1, the equation used for this condition 

was: 

(23) Ground-water ALI * (4.5 x 10-x) 

Ingestion 

Release Value (exp(-4.2/T-l/2))*(T-l/2 - T-l/2 exp(-6.2/T-1/2)) 

where T-l/2 = radionuclide half-life in days. 

A separate equation was not derived for cases where Rd > 1 because, as 

described above, the release values calculated in these cases would be 

relatively high and inconsequential in the adjustment of RQs. 

Conditions 12-15. The ground-water ingestion equations used under these 

conditions were derived in exactly the same way as the inhalation equations 

for Conditions 12-15. The only difference between the two sets of equations 

was that the ALI for ingestion was used here rather the inhalation ALI as used 

in the inhalation pathway equations. Refer to the derivation of these 

individual equations given in Section 4.1 of this paper. 

Condition 16. The only difference between this set of conditions and the 

one used in the NPRM was that it incorporated the effects of radioactive 

decay. Therefore, the equation used in this case was derived by using 

Equation (20) and substituting the following values: AF = 10; DF = 7.6 x 

IO-8 liter-VRd; t = 6 days; WC = 2 liters/day, and CT = 9 days (when Rd = 

1). When these values were used, Equation (20) reduced to: 

(24) Ground-water ALI * (4.6 x 10-x) 

Ingestion 

Release Value (exp(-4.2/T-l/2))*(T-l/2 - T-l/2 exp(-6.2/T-1/2)) 

where T-l/2 = radionuclide half-life in days. 

Condition 17. Because the 365-day exposure period specified for Condition 

17 was only for the evaluation of direct exposure to a point source, there was 

no difference between this condition and Condition 2 for the ground-water 

ingestion pathway model. Therefore, the same equations used for Condition 2 

-- Equations (16) and (17) -- also were used here. 

4.3 Equations for the Ingestion of Vegetables Contaminated by Airborne 

Deposition 

Equation Based on Conditions Assumed in the NPRM. In support of the NPRM, 

the basic equation used for the calculation of release values based on the 

consumption of vegetables was (see page F-36 of the TBD): 

Vegetable Ingestion 

(25) Release Value = ALI/((10)*(DF)*(FC)*(CT)*(R)*(1 x 10s)) 

(in curies) 
P.21 

-19-

where 

ALI = Annual Limit of Intake for ingestion (microcuries); 

10 = Factor to adjust the dose-equivalent limit built into the ALI, 

5 rem, to a limit of 0.5 rem; 

DF = Dilution factor accounting for the transfer of radionuclides 

from air to vegetation (curies/kg of vegetables at the point of 

exposure per curie released to the atmosphere); 

FC = Food (i.e., leafy vegetable) consumption rate of reference man 

(0.175 kg/day); 

CT = Contact time, or the number of days over which contaminated 

vegetables are ingested; 

R = Airborne release fraction; and 

1 x 10s = Conversion factor between microcuries and curies. 

Section F.3 of the TBD supporting the NPRM describes two alternate models 

for calculating the dilution factor accounting for the transfer of 

radionuclides from air to vegetation. One of the models is presented by the 

Nuclear Regulatory Commission in Regulatory Guide 1.1093 and the other is 

presented by the National Council on Radiation Protection and Measurements 

(NCRP) in NCRP Commentary No. 3.* The two models are basically the same in 

that they both account for radionuclide deposition from the air, radionuclide 

loss due to weathering and radioactive decay, and radionuclide buildup in and 

uptake from soil. The principal difference between the two models lies in the 

way they account for the deposition velocity of the radionuclide in question. 

Briefly, to determine the deposition velocity, the Nuclear Regulatory 

Commission model relies on a relative deposition term that considers 

radionuclide dispersion and depletion while in transit from the point of 

release to the point of exposure. The NCRP model, on the other hand, uses a 

single deposition velocity default value that is invariant to the radionuclide 

in question, the atmospheric dispersion characteristics, and the distance 

between the point of release and the point of deposition. 

SU.S. Nuclear Regulatory Commission, Calculation of Annual Doses to Man 

from Routine Releases of Reactor Effluents for the Purpose of Evaluating 

Compliance with 10 CFR Part 50, Appendix I, Regulatory Guide 1.109, Revision 

1, October 1977. 

"National Council on Radiation Protection and Measurements, Screening 

Techniques for Determining Compliance with Environmental Standards: Releases 

of Radionuclides to the Atmosphere, NCRP Commentary No. 3, 1986. 
•20-

As discussed in the TBD, EPA previously had selected the Nuclear 

Regulatory Commission model for use in the adjustment of RQs. This selection 

was based principally on the belief that the deposition default value used by 

the NCRP (1000 meters/day) was highly conservative, resulting in needlessly 

low RQs. Since publishing the NPRM and TBD, however, EPA has gained 

additional information that points to the NCRP model as being more appropriate 

for the purpose of RQ adjustments. In particular, EPA has since recognized 

that: (1) the derivation of the deposition velocity in the Nuclear Regulatory 

Commission model is incorrect; and (2) that the NCRP default value of 1000 

meters/day (1.2 cm/sec) is not overly conservative but rather is in the range 

of commonly accepted values frequently used in environmental assessments. 

Accordingly, for this analysis, EPA has used instead the NCRP equation with a 

deposition velocity of 1000 meters/day to calculate the dilution factor. This 

equation is as follows: 

(26) DF = V C 

d air 

'r[l - exp(-X t )] B [1 - exp(-X t )]' 

Ei e iv i b 

+ 

Y X PX 

v Ei i 

exp(-X t ) 

i h 

where 

DF = Dilution factor; that is, the concentration of radionuclide in and 

on vegetation per curie of radionuclide released to the atmosphere 

(Ci/kg per Ci; or kg-1) 

V = Deposition velocity for wet and dry deposition (1000 meters/day); 

d 

C = Concentration of radionuclide in air at the location of growing 

air vegetables 

= (Radionuclide release rate)*(X/Q) 

= (Ci/day)*(8.4 x IO-7 day/m3) 

= 8.4 x IO-7 Ci/m3; 

r = Fraction of deposited activity retained on crops (0.25, 

dimensionless); 

Y = Agricultural productivity (2 kg/m2 ); 

v 

X = Effective removal rate constant for radionuclide i from crops 

Ei (in day-1 ), where X = X + X ; 

Ei i w 

X = 0.693/T-1/2, where T-l/2 = half-life in days; 

i 
P.23 

-21-

X = Removal rate constant for physical loss by weathering, calculated 

w on the basis of a weathering half-life of 14 days, such that 

X = 0.693/14 days = 0.0495/day; 

w 

t = Time period that the crops are exposed to contamination during the 

e growing season (assigned a value of 1 day because the maximum period 

of release, and hence the maximum period of airborne deposition, 

applicable to RQs is 1 day); 

B = Concentration factor for uptake of radionuclide i from soil by 

iv edible parts of crops; 

P = Effective surface density for soil (240 kg/m2, dry weight); 

t = Time period over which the soil is exposed to contamination 

b (assigned a value of 1 day following the same reasoning given above 

for t ); and 

e 

t = Time interval between harvest and consumption of vegetables 

h (conservatively assumed to be zero days). 

Assuming no radioactive decay (i.e.. X =0 ) because the time period 

i 

between the time of release and contact with the vegetables is sufficiently 

short, and plugging all of the above values into Equation (12), the expression 

for DF reduced to: 

(27) DF = (1 x 10-* + 3.5 x IO-6 B )kg-x 

iv 

The only remaining value needed to determine the vegetable ingestion 

release value is a value for CT, the contact time. As discussed in Section 

3.2 of this paper, the Agency conservatively assumed that an individual 

ingests the contaminated vegetables over the entire length of the growing 

season, 60 days. This period must be adjusted, however, to account for 

radionuclide loss due to weathering over the 60 day season. The dilution 

factor outlined above, when applied to the quantity of radionuclide released 

in 1 day, yields the concentration of radionuclide in and on vegetation after 

1 day (conservatively assumed to be the first day of the growing season). 

Over the next 60 days, the radionuclide concentration will progressively 

decrease as more and more of the contamination is lost due to weathering. To 

account for this loss in determining an individual's cumulative intake over 

the 60 day period, the "equivalent" contact time was calculated in the 

following manner: 

1 - exp(-X t) 1 - exp(-0.0495/day * 60 days) 

w 

(28) CT = 

X 0.0495/day 

w 

= 19 days 
P.24 

-22-

Plugging all the appropriate values into Equation (25), the equation used 

to evaluate the ingestion of vegetables contaminated by airborne deposition 

under the set of conditions assumed in the NPRM became: 

(29) Vegetable Ingestion Release Value 

ALI (ingestion) 

(3.3 x IO3 + 1.2 x IO2 B ) * R 

iv 

Condition 1. Condition 1 was exactly the same as the set of conditions 

assumed in the NPRM except that it limited the dose-equivalent to 0.025 rem 

rather than 0.5 rem. Accordingly, the only difference in the equation used 

here and Equation (25) was that a factor of 200 (rather than a factor of 10) 

was used to make the appropriate adjustment to the ALI. Using this new 

adjustment factor with the other input values specified above for Equation 

(25), the equation used in this condition became: 

(30) Vegetable Ingestion Release Value = 

ALI (ingestion) 

(6.7 x 10* + 2.3 x IO3 B ) * R 

iv 

Condition 2. Like Condition 1, Condition 2 differed from the set of 

conditions used in the NPRM only by assuming a different dose-equivalent 

limit, 0.1 rem rather than 0.5 rem. Plugging the revised adjustment factor, 

50, into Equation (25) along with the other input variables, the equation 

reduced to: 

(31) Vegetable Ingestion Release Value = 

ALI (ingestion) 

(1.7 x 10* + 5.8 x 102 B ) * R 

iv 

Condition 4. Unlike the preceedirig conditions, this condition 

incorporated the effects of radioactive decay. As described in Section 3.4 of 

this paper, the Agency decided to consider decay over the period of ingestion, 

but to ignore decay over the period of release and deposition (because these 

time periods could be very short, prohibiting significant decay) and to ignore 

decay during transport to the vegetables (because transport to a point 30 

meters away would be so rapid that decay would be negligible for all but a 

handful of radionuclides). With this approach, Equation (27) for calculating 

DF under the conditions assumed in the NPRM also was applicable here. The 

contact time derived in Equation (28), however, needed to be revised to 

incorporate a radioactive decay term. Specifically, the contact time needed 

to be derived in the following manner: 

1 - exp(-X t) 

Ei 

(32) CT = 

X 

Ei 
P.25 

-23-

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

i w 

CT = 

X + X 

i w 

1 - exp(-((0.693/T-l/2) + 0.0495/day) * 60 days) 

CT = 

(0.693/T-1/2) + 0.0495/day 

1 - exp-((41.6/T-l/2) + 3) 

CT = 

(0.693/T-1/2) + 0.0495 

where 

T-l/2 = radionuclide half-life in days. 

Plugging this revised expression for CT into Equation (25) along with a 

dose-equivalent adjustment factor of 200 (to arrive at a dose limit of 0.025 

rem rather than 0.5 rem), the equation used under this set of conditions 

simplified to: 

(33) Vegetable Ingestion ALI (ingestion) 

Release Value = 

(3.5 x IO3 + 1.2 x 102 B ) * (R) * (CT) 

iv 

where CT was calculated using Equation (32). 

Condition 5. Exhibit 1 shows that this condition differed from the set of 

conditions assumed in the NPRM in two respects. First, it assumed a different 

dose-equivalent limit; and second it incorporated radioactive decay. These 

differences were accounted for here by using a different dose-equivalent 

adjustment factor (50 rather than 10) and by calculating CT using Equation 

(32) rather than Equation (28). Incorporating these changes into Equation 

(25), the equation used for this condition became: 

(34) Vegetable Ingestion ALI (ingestion) 

Release Value = 

(8.8 x IO2 + 3.1 x 101 B ) * (R) * (CT) 

iv 

where CT was calculated using Equation (32). 

Condition 8. This set of conditions differed from that assumed in the 

NPRM by assuming a 365-day exposure period for the direct exposure to a point 

source pathway. As discussed in Section 3.2 of this paper, however, the 

Agency decided not to vary the exposure period in the analysis of vegetables 

contaminated by airborne deposition. Accordingly, the same equation used 
P.26 

•24-

under the set of conditions used in the NPRM (i.e., Equation (29)) was used in 

this situation. 

Condition 9. In order to accommodate this set of conditions, the equation 

used under the NPRM conditions only needed to be modified to incorporate 

radioactive decay. This change yields the following revised equation used 

under Condition 9: 

(35) Vegetable Ingestion ALI (ingestion) 

Release Value = 

(1.75 x IO2 + 6.1 B ) * (R) * (CT) 

iv 

where CT was calculated using Equation (32). 

Conditions 12-15. Because the same ingestion ALIs are applicable 

regardless of whether water or vegetables are ingested, the same equations 

derived to evaluate ground-water ingestion under these conditions were 

applicable to the ingestion of vegetables. Refer to Section 4.2 for the 

specific derivation of each of these equations. 

Condition 16. Because the Agency did not vary the exposure period assumed 

in the vegetable ingestion model (see Section 3.2 of this paper), this 

condition was identical to Condition 9. Accordingly, Equation (35) derived 

above also was used here. 

Condition 17. For the vegetable ingestion pathway model, there was no 

difference between Condition 17 and Condition 2 (these two sets of conditions 

differed only in the period of exposure assumed in the model evaluating direct 

exposure to a point source). Therefore, the same equation used for Condition 

2 -- Equation (31) -- was used under this set of conditions. 

4.4 Equations for Direct Exposure to a Point Source 

Equation Used in the NPRM. The basi c equation used t o evaluat e direc t 

exposure t o a point source in support of the NPRM was as follows (referenc e 

Section 4.2. 3 in th e TBD): 

(36) Direc t Exposure = (6.41xl0- 5) * (Dn) * (S2) 

Release Value 

(E ) * (u ) * (T) * (exp (-u S)) 

l a a 

where 

Dn = Dose-equivalent in rem; 

S = Distance between the point source and the receptor; 

E = The sum of the products of the gamma ray energies (MeV) and 

1 

the gamma ray fractions; 
P.27 

-25-

u = Linear energy absorption coefficient for gamma rays in air 

a (assumed to be 3.7 x 10-5/cm for all radionuclides); 

T = Duration of exposure (hours); and 

exp(-u S) = Attenuation factor, 

a 

Under the conditions assumed in the NPRM, the exposed individual is 30 

meters from the point source, is at this location for 24 hours, and receives a 

maximum whole body dose of 0.5 rem. Plugging these values into Equation (36), 

the equation became: 

(37) Direct Exposure Release Value = 3.6 x 10X/E 

1 

Condition 1. The only difference between this set of conditions and the 

one assumed in the NPRM is that the exposed individual receives a dose of 

0.025 rem rather than 0.5 rem. Plugging this revised dose-equivalent limit 

into Equation (36) along with the other values specified above, the equation 

simplified to: 

(38) Direct Exposure Release Value = 1.8/E 

1 

Condition 2. To accommodate this set of conditions, a dose limit of 0.1 

rem rather than 0.5 rem was plugged into Equation (36); all the other values 

specified for that equation were kept the same. Therefore, the direct 

exposure equation for this case reduced to: 

(39) Direct Exposure Release Value = 7.3/E 

1 

Condition 3. As shown in Exhibit 1, this set of conditions differed from 

that assumed in the NPRM in two respects: the distance between the point of 

release and the point of exposure (S) was 1 meter rather than 30 meters; and 

the dose-equivalent limit (Dn) was 0.1 rem rather than 0.5 rem. Substituting 

these values for the ones used in support of the NPRM, Equation (36) reduced 

to: 

(40) Direct Exposure Release Value = 7.2 x 10-3/E 

1 

Condition 4. This set of conditions was different from the one assumed in 

the NPRM in that it assumes a dose-equivalent limit of 0.025 rem and 

incorporated the effects of radioactive decay. As discussed in Section 3.4 of 

this paper, the Agency decided to evaluate decay only over the period of 

exposure (i.e., decay over the release period and decay over the time between 

release and the start of an individual's exposure was neglected). To 

incorporate decay over the exposure period, Equation (36) was modified to 

include an exponential decay term as shown below: 
-26-

(41) Direct Exposure = (6.41xl0-5) * (Dn) * (S2) 

Release Value 

(E ) * (u ) * (T) * (exp(-u S)) * (l-exp(-Xt)) 

l a a 

where t = Period of exposure in days; and 

\ = 0.693/T-1/2, where T-l/2 = radionuclide half-life in days. 

Substituting the values Dn = 0.025 rem, S = 30 meters, T = 24 hours, and t = 1 

day into Equation (41) as called for under Condition 4, the equation reduced 

to: 

(42) Direct Exposure = 1.26 

Release Value (E ) * (T-l/2 - T-l/2 exp(-.693/T-l/2)) 

1 

where T-l/2 = radionuclide half-life in days. 

Condition 5. This condition was exactly the same as Condition 4 except 

that it assumed a dose-equivalent limit of 0.1 rem rather than 0.025 rem. 

Plugging this revised value into Equation (41) but keeping all the other 

parameter values specified in Condition 4, the equation became: 

(43) Direct Exposure = 5.03 

Release Value (E ) * (T-l/2 - T-l/2 exp(-.693/T-1/2)) 

1 

where T-l/2 = radionuclide half-life in days. 

Condition 6. The only difference between this set of conditions and the 

one assumed in the NPRM is that it assumed the exposed individual was 1 meter 

rather than 30 meters from the point source. Therefore, using Equation (36) 

and all the values specified for it in accordance with the NPRM conditions 

except a revised value of 1 meter for S, the equation used in this case became: 

(44) Direct Exposure Release Value = 3.6 x 10-2/E 

1 

Condition 7. This condition was the same as Condition 4 above except that 

it considered a distance of 1 meter. Therefore, using Equation (41) and 

substituing the values Dn = 0.025 rem, S = 1 meter, T = 24 hours, and t = 1 

day, the equation for this condition became: 

(45) Direct Exposure = 1.25 x IO-3 

Release Value 

(E ) * (T-l/2 - T-l/2 exp(-.693/T-l/2)) 

1 

where T-l/2 = radionuclide half-life in days. 
P.29 

-27-

Condition 8. This set of conditions was the same as the one assumed in 

the NPRM except that it assumed an exposure period of 365 days. Therefore, 

using Equation. (36) and substituting the values Dn = 0.5 rem, S = 30 meters, 

and T = 24 hours * 365 days = 8760 hours, the equation used for this condition 

reduced to: 

(46) Direct Exposure Release Value = 0.1/E 

1 

Condition 9. Because this condition considered radioactive decay, the 

equation used here was derived from Equation (41) (see discussion for 

Condition 4 above). Plugging the values Dn = 0.5 rem, S = 30 meters, T = 24 

hours, and t = 365 days into Equation (41), the equation became: 

(47) Direct Exposure = __ 25 .1 

Release Value (E ). * (T-l/2 - T-l/2 exp(-253/T-l/2)) 

1 

where T-l/2 = radionuclide half-life in days. 

Condit ion 10. The equation used under this set of conditions was derived 

by using Equation (41) (see discussion for Condition 4 above) and plugging in 

the values Dn = 25 rem, S = 1 meter, T = 24 hours, and t = 1 day: 

(48) Direct Exposure = 1.25 

Release Value (E ) * (T-l/2 - T-l/2 exp(-.693/T-1/2)) 

1 

where T-l/2 = radionuclide half-life in days. 

Condition 11. The equation for this condition was derived in the same way 

as described for Condition 10 except that a value of Dn = 0.5 rem was used 

rather than 25 rem. This substitutional change yielded the following equation: 

(49) Direct Exposure = 2.5 x 10-2 

Release Value 

(E ) * (T-l/2 - T-l/2 exp(-.693/T-l/2)) 

1 

where T-l/2 = radionuclide half-life in days. 

Conditions 12-15. These conditions were concerned only with the ingestion 

and inhalation pathways. Therefore, no direct exposure calculations were 

performed under these conditions. 

Condition 16. This set of conditions was identical to the one assumed 

under Condition 4 except that it assumed a dose limit of 0.5 rem rather than 

0.025 rem. Accordingly, the equation used in this case was derived by using 

Equation (41) and plugging in the values Dn = 0.5 rem, S = 30 meters, T = 24 

hours, and t = 1 day. This process yielded the following equation: 
-28-

(50) Direct Exposure = 25.1 

Release Value (E ) * (T-l/2 - T-l/2 exp(-.693/T-1/2)) 

1 

where T-l/2 = radionuclide half-life in days. 

Condition 17. This set of conditions differed from the one assumed in the 

NPRM in two respects. First, it assumed an exposure period of 365 days rather 

than 1 day and, second, it assumed a dose-equivalent limit of 0.1 rem rather 

than 0.5 rem. Accordingly, the equation used in this case was derived by 

using Equation (36) and plugging in the values Dn = 0.1 rem, S = 30 meters, 

and T = 24 hours * 365 days = 8760 hours to yield: 

(51) Direct Exposure Release Value = 0.02/E 

1 

Condition 18. The equation for this condition was derived by using 

Equation (41) (see discussion for Condition 4 above) and plugging in the 

values Dn = 0.1 rem, S = 1 meter, T = 24 hours, and t = 1 day. This yielded 

the following equation: 

(52) Direct Exposure = 5 x 10-2 

Release Value 

(E ) * (T-l/2 - T-l/2 exp(-.693/T-l/2)) 

1 

where T-l/2 = radionuclide half-life in days. 

4.5 Equations for Direct Exposure by Submersion in a Cloud 

Equation Used in the NPRM. Section 4.2.3 of the TBD outlines the 

rationale for and provides a derivation of the basic equation used in the NPRM 

to evaluate submersion in a cloud of noble gas. This equation is reprinted 

below: 

(53) Submersion Release = (83) * (DAC) * (T) 

Value (in curies) (AF) * (X/Q) * (1x10s) 

where 

DAC = Derived Airborne Concentration for a particular radionuclide 

(microcuries/cm3); 

T = Duration of exposure (assumed to be 1 day in all cases because the 

maximum airborne release period applicable to RQs, and hence the 

maximum period that a person can be submersed in a cloud for the 

purpose of this analysis, is 1 day); 

X/Q = Atmospheric relative concentration value at 30 meters (8.4 x 

10-13 day/cm3); 
P.31 

-29-

AF =•Dose-equivalent limit adjustment factor to convert the doseequivalent built into the DAC, 5 rem, to a dose-equivalent limit 

of.interest; 

83 = Time period conversion factor to convert the exposure period 

considered in the DAC, 2000 hours, to a 24 hour exposure period 

(i.e., 2000 hours * 24 hours); and 

1x10s = Conversion factor between microcuries and curies. 

Under the set of conditions assumed in the NPRM, AF = 10 (i.e., the assumed 

dose-equivalent is 0.5 rem). Plugging this value into Equation (53) along 

with the other values spelled.out above, the equation simplified to: 

(54) Submersion Release Value = DAC/(1 x IO-7) 

Condition 1. Because this condition differed from that assumed in the 

NPRM only by assuming a different dose-equivalent limit (0.025 rem rather than 

0.5 rem), the equation for this condition was derived by using Equation (53) 

but with a value of 200 for AF. By making this substitutional change, the 

equation used for this condition became: 

(55) Submersion Release Value = DAC/(2 x 10-6) 

Condition 2. The. equation for this set of conditions was derived by using 

Equation (53) along with all the parameter values specified for that equation, 

except that a value of 50 was used for AF rather than 10. This change was 

needed to arrive at a different dose limit; 0.1 rem rather than 0.5 rem. By 

using this revised AF value in Equation (53), the equation became: 

(56) Submersion Release Value = DAC/(5.lxlO-7) 

Condition 4. This set of conditions differed from the one assumed in the 

NPRM in two respects. First, this condition assumed a dose-equivalent limit 

of 0.025 rem rather than 0.5 rem. To make this change, a dose-equivalent 

adjustment factor of 200 was used. Second, this condition incorporated the 

effects of radioactive decay. As described in Section 3.4 of this paper, 

however, the Agency decided not to consider radioactive decay in this exposure 

pathway model. Accordingly, the equation used here was derived by using 

Equation (53) and substituting AF = 200 along with the other input values 

specified above for that equation: 

(57) Submersion Release Value = DAC/(2xlO-6) 

Condition 5. Because the Agency decided to neglect the consideration of 

radioactive decay in this pathway model, this set of conditions for submersion 

in a cloud was the same as those assumed under Condition 2. Accordingly, 

Equation (56) derived above for Condition 2 was also used for this case. 
P.32 

-30-

Condition 8. As shown in Exhibit 1, the only difference between this 

condition and the set of conditions assumed in the NPRM was that a 365 day 

exposure period was assumed here. However, as described in Section 3.2 of 

this paper, the maximum period of time that a person can be submersed in an 

airborne cloud for the purpose of this analysis is 1 day. Recognizing this 

fact, there was no difference between this condition and the set of conditions 

used in the NPRM, and Equation (53) (derived above) also was used for 

Condition 8. 

Condition 9. The equation used under this set of conditions was also the 

same equation used in the NPRM (i.e., Equation (53)). This equation could be 

used again here because the two differences between the NPRM conditions and 

Condition 9 -- different exposure periods and different decay considerations 

-- were not taken into account in the submersion-in-a-cloud analysis. Refer 

to Sections 3.2 and 3.4 in this paper for an explanation of why the exposure 

period and the approach to modeling decay were not varied in the equations for 

modeling this exposure pathway. 

Conditions 12-15. These conditions were concerned only with the 

inhalation and ingestion exposure pathways and, therefore, direct exposure by 

submersion in an airborne cloud was not evaluated under these conditions. 

Condition 16. This set of conditions was the same as that assumed in the 

NPRM except that it incorporated radioactive decay. For the reasons given in 

Section 3.4 of this paper, however, the Agency decided to ignore radioactive 

decay in the analysis of direct exposure by submersion in a cloud. 

Accordingly, the same equation used for the NPRM conditions, Equation (53), 

was also used under this set of conditions. 

Condition 17. Because the maximum exposure period considered by the 

Agency in analyzing this exposure pathway was 1 day, the 365-day exposure 

period specified for Condition 17 was not considered in the submersion pathway 

model. The dose-equivalent limit of 0.1 rem was taken into account, however, 

by using a dose-equivalent adjustment' factor of 50 in Equation (53) along with 

the other input variables used for the NPRM. Using AF = 50 in Equation (53), 

the equation simplified to: 

(58) Submersion Release Value = DAC/(5.lxlO-7) 

4.6 Milk Ingestion Pathway Equations 

In the TBD supporting the NPRM on radionuclides, EPA did not perform a 

specific analysis of exposure through the ingestion of contaminated milk. 

This exposure pathway was analyzed as part of this analysis, however, to see 

how the proposed RQs would have varied if such exposures had been taken into 

account. 

Conceptually, the Agency assumed in this model that radionuclides are 

released to air over a period of one day. Twenty-four hours is the timeframe 

for which RQs are applicable. The released radionuclides were assumed to 
P.33 

-31-

be transported in an airborne plume to a pasture approximately 30 meters away, 

where they are deposited on soil and growing grass for the time that it took 

the plume to pass (i.e., one day). This grass was assumed to be the only food 

source for a grazing cow, which started eating the grass the day after it was 

contaminated and continued to eat it for a period of 60 days.5 It was finally 

assumed that an individual ingested the cow's contaminated milk, for a period 

of 60 days. The milk ingested by the person was assumed to be produced by the 

cow two days earlier.6 

The basic equation that EPA used to calculate release values assuming this 

cow-milk-man exposure scenario is presented below: 

(59) Milk Ingestion = ALI 

Release Value (AF)*(DF)*(MC)*(CT)*(R)*(lxlOs) 

(in curies) 

where 

ALI = Annual Limit of Intake for ingestion (microcuries); 

i 

AF = Dose-equivalent limit adjustment factor to convert the 

dose-equivalent built into the ALI, 5 rem, to a dose-equivalent 

limit of interest; 

DF = Dilution factor accounting for the transfer of radionuclides from 

air to grass and from grass to milk (curies/liter of milk at the 

point of exposure per curie released to the atmosphere); 

MC = Milk consumption rate of reference man (0.85 liter/day);. 

CT = Contact time, or the number of days over which contaminated milk 

is ingested; 

R = Airborne release fraction; and 

1x10s = Conversion factor between microcuries and curies. 

The values used for DF and CT in Equation (59), as well as the methods 

used to derive those values, warrant further explanation. The value for DF 

5This period of time was selected to be consistent with the vegetable 

ingestion pathway model. 

6Milk consumption delay time used in AIRDOS-EPA generic site 

assessments. See: U.S. Environmental Protection Agency, Radionuclides: 

Background Information Document for Final Rules, Volume II, Office of 

Radiation Programs, EPA 520/1-84-022-2, 1984. 
P.34 

-32-

was derived using the following equation used in AIRDOS-EPA, an EPA model used 

to calculate environmental concentrations resulting from radionuclide 

emissions into air:7 

(60) DF = Q F C 

f m v 

where DF = Dilution factor; that is, the concentration of radionuclide in 

milk per curie of radionuclide released to the atmosphere 

(Ci/liter per Ci; or liter-1); 

Q = Cow feed consumption rate (15.6 kg/day on a dry basis); 

f 

F -= Equilibrium transfer factor accounting for the transfer of 

m radionuclides ingested by a cow to the cowrs milk (day/liter); 

and 

C = Concentration of radionuclide in forage per curie released to 

v the atmosphere (Ci/kg per Ci; or kg-1). 

The value of F in Equation (60) is radionuclide-specific. Where 

m 

available, EPA used for this analysis the F values developed for the 

m 

AIRDOS-EPA computer code.8 F values were not available, however, in the 

m 

AIRDOS-EPA documentation for a majority of radionuclides. For those 

radionuclides, EPA used an F default value based on available F values 

m m 

for radionuclides from the same series in the periodic chart. 

The value for C in Equation (60) was derived basically from the same 

v 

equation used to calculate the concentration of radionuclides in vegetables in 

the vegetable ingestion pathway model (see Equation (26) described in Section 

4.3 of this paper). This equation, adapted from an equation presented by the 

NCRP in NCRP Commentary No. 3 (see footnote 4 of this paper), is shown below: 

r[l - exp(-X t )] B [1 - exp(-X t )]' 

Ei e iv i b 

(26). C = V C + 

v d air Y PX 

v i 

exp(-X t ) 

i h 

rU.S. Environmental Protection Agency, Radionuclides: Background 

Information Document for Final Rules, Volume I, Office of Radiation Programs, 

EPA 520/1-84-022-1, 1984. 

"Baes III, CF. and R.D. Sharp, A Directory of Parameters Used in a 

Series of Assessment Applications of the AIRDOS-EPA and DARTAB Computer Codes, 

eftNL for the U.S. Environmental Protection Agency, ORNL-5710, 1981. 
P.35 

-33-

where 

C = Concentration of radionuclide in forage per curie of radionuclide 

v released to the atmosphere (kg-1); 

V = Deposition velocity for wet and dry deposition (1000 meters/day); 

d 

C = Concentration of radionuclide in air at the location of growing 

air vegetables 

= (Radionuclide release rate)*(X/Q at 30 meters) 

= (Ci/day)*(8.4 x IO-7 day/m3) 

= 8.4 x IO-7 Ci/m3; 

r = Fraction of deposited activity retained on crops (0.25, 

dimensionless); 

Y = Pasture productivity (0.280 kg/m2, on a dry basis); 

v 

X = Effective removal rate constant for radionuclide i from grass 

Ei (in day-1 ), where X = X + X ; 

Ei i w 

X = 0.693/T-1/2, where T-l/2 = half-life in days; 

i 

X = Removal rate constant for physical loss by weathering, calculated 

w on the basis of a weathering half-life of 14 days, such that 

X = 0.693/14 days = 0.0495/days; 

w 

t = Time period that the grass; is exposed to contamination during the 

e growing season (assigned a value of 1 day because the maximum period 

of release, and hence the maximum period of airborne deposition, 

applicable to RQs is 1 day); 

B = Concentration factor for uptake of radionuclide i from soil by 

iv vegetation; 

P = Effective surface density for soil (240 kg/m2, dry weight); 

t = Time period over which the soil is exposed to contamination 

b (assigned a value of 1 day following the same reasoning given above 

for t ); and 

e 

t = Time interval between the time that the milk is produced by the cow 

h to the time that the exposed individual consumes the milk (2 days). 
P.36 

-34-

Assuming no radioactive decay between the point of release and contact 

with the grass (i.e., X =0 ) and plugging all of the 

i 

above-specified values into Equation (61), the expression for C becomes: 

v 

(62) C = (7.3 x 10-* + 3.5 x IO-6 B )kg-J 

v iv 

Inputting this equation for C into Equation (60) along with the value of 

v 

Q =15.6 kg/day, the equation for DF becomes: 

f 

(63) DF = (F ) * (1.1 x IO-2 + 5.5 x IO-5 B ) 

m iv 

The value for the contact time, CT, used in Equation (59) varied, 

depending on whether radioactive decay was taken into account. As stated 

above, the exposed individual was assumed to ingest milk over a 60 day period 

following the airborne deposition of radionuclides after 1 day. To account 

for radionuclide loss from the grass due to weathering and/or radioactive 

decay over the 60-day ingestion period, an "equivalent" contact time was 

derived using the following equation: 

(64) CT = 1 - exp(-X t) 

Ei 

X 

Ei 

where t = 60 days; 

X = \ + X = (0.693/T-1/2) + (0.693/14 days) = (0.693/T-1/2) + 

Ei i w 

(0.0495 day-1), where T-l/2 = radionuclide half-life in days. 

For those sets of assumptions in which radioactive decay was neglected (i.e., 

X =0) , the contact time was derived in the following way: 

i 

(65) CT = 1 - exp(-(0.0495/day) * (60 days)) = 19 days 

0.0495/day 

For those sets of assumptions in which radioactive decay was incorporated into 

the model, the contact time was derived in the following manner: 

(66) CT = 1 - exp(-((0.693/T-l/2) + (0.0495)) * (60)) 

(0.693/T-1/2) + (0.0495) 

= 1 - exp - ((41.6/T-1/2) + (3)) 

(0.693/T-1/2) + (0.0495) 

where T-l/2 = radionuclide half-life in days. 
-35-

In summary, therefore, milk ingestion release values were calculated using 

the following expression derived by plugging Equation (63) for DF into 

Equation (59):-

(67) Milk Ingestion = ALI 

Release Value (AF)*(F )*(9.69xl03 + 4.59xlOxB )*(CT)*(R) 

m iv 

where CT was either 19 days, under conditions where radioactive decay was 

neglected, or calculated using Equation (66) where radioactive decay was taken 

into account. 

Equation Based on Conditions Assumed in the NPRM. As shown in Exhibit 1, 

the set of assumptions used in the NPRM included a dose-equivalent limit of 

0.5 rem and no consideration of radioactive decay. Accordingly, the 

dose-equivalent adjustment factor (AF) under these assumptions was 10 (to 

adjust the 5 rem dose-equivalent considered in the ALI to a dose-equivalent of 

0.5 rem) and the contact time (CT) was 19 days as derived in Equation (65). 

Plugging these values into Equation (67), the equation simplified to: 

(68) Milk Ingestion = ALI 

Release Value (F )*(R)*(1.8x10s + 8.72xl03B ) 

m iv 

Condition 1. Under this set of assumptions, a dose-equivalent adjustment 

factor of 200 was used to go from the 5 rem on which the ALI is based to 0.025 

rem. Also, because radioactive decay was neglected in this case, CT = 19 days 

as shown in Equation (65). Plugging these values into Equation (67), the 

equation used here became: 

(69) Milk Ingestion = ALI 

Release Value (F )*(R)*(3.68xl07 + 1.74xl05B ) 

m iv 

Condition 2. The only difference between this set of assumptions and the 

one used in the NPRM is that a dose-equivalent limit of 0.1 rem was used 

rather than a 0.5 rem limit. To accommodate this difference, the appropriate 

value for AF under Condition 2 was 50 (5 rem/50 =0. 1 rem). Plugging this 

value into Equation (67) along with a contact time of 19 days (decay also was 

neglected here), the equation reduced to: 

(70) Milk Ingestion = ALI 

Release Value (F )*(R)*(9.2x10s + 4.36xl0*B ) 

m iv 

Condition 4. Unlike the preceeding sets of conditions, the effects of 

radioactive decay were taken into account under Condition 4. Therefore, the 

value for CT in this case was calculated using Equation (66). Using that 

equation along with an AF value of 200 (to arrive at a dose-equivalent limit 

of 0.025 rem, i.e., 5 rem/200 = 0.025 rem) in Equation (67), the equation used 

to calculate release values under the set of conditions assumed here became: 
-36-

(71) Milk Ingestion = ALI 

Release Value (CT)*(F )*(R)*(1.93x10* + 9.2xl03B ) 

m iv 

where CT was calculated using Equation (66). 

Condition 5. To calculate release values under this set of assumptions, 

the value of CT was calculated using Equation (66) (because radioactive decay 

was incorporated) and the value for AF was 50 (to adjust the 5 rem on which 

the ALI is based to 0.1 rem). The equation used in this case, shown below, 

was derived by inputting these values into Equation (67): 

(72) Milk Ingestion = ALI 

Release Value (CT)*(F )*(R)*(4.84x10s + 2.29xl03B ) 

m iv 

where CT was calculated using Equation (66). 

Condition 8. The only difference from the conditions assumed in this case 

and those assumed in the NPRM was that a 365-day exposure period was used 

under Condition 8 in the evaluation of direct exposure to a point source. 

However, because a 365-day exposure period was not used in the milk ingestion 

pathway model (see Section 3.2 of this paper), the same equation used under 

the NPRM conditions (i.e., Equation 68)) also was used here. 

Condition 9. As described in Section 3.2 of this paper, the Agency 

assumed a 365-day exposure period only in the evaluation of direct exposure to 

a point source. The exposure period, or contact time, in the milk ingestion 

pathway model was determined using either Equation (65) or (66) depending on 

whether radioactive decay was taken into account. Because the effects of 

decay were considered under this set of assumptions, the contact time in this 

case was determined using Equation (66). Using this expression for CT, a 

value of AF = 10 as used under the NPRM conditions, and Equation (67), the 

equation used for Condition 9 reduced to: 

(73) Milk Ingestion = ALI 

Release Value (CT)*(F )*(R)*(4.84xl05 + 2.29xl03B ) 

m iv 

where CT was calculated using Equation (66). 

Conditions 12-15. Because the ingestion ALIs are applicable regardless of 

whether radionuclides are ingested in water, vegetables, or milk, the same 

equations used in the ground-water ingestion and vegetable ingestion models 

under these sets of assumptions also are applicable here. These equations 

were derived in exactly the same way as the inhalation equations for 

Conditions 12-15. The only difference between the two sets of equations is 

that the ALI for ingestion was used here rather than the inhalation ALI as 

used in the inhalation pathway equations. Refer to the derivation of these 

individual equations given in Section 4.1 of this paper. 
-37-

Condition 16. For the milk ingestion pathway, there was no difference 

between the set of conditions assumed here and that assumed under Condition 9. 

Therefore, the same equation derived for Condition 9 (i.e., Equation (73)) 

also was used for Condition 16. 

Condition 17. As discussed in Section 3.2 of this paper, EPA did not 

consider a 365-day exposure period in the evaluation of contaminated milk. 

Accordingly, there was no difference between Condition 17 and Condition 2 for 

the milk ingestion pathway model, and the same equation used under that set of 

assumptions -- Equation (70) -- also was used here. 

4.7 Analysis of the Ingestion of Vegetables Contaminated By Irrigation 

As part of this analysis, EPA considered potential exposures through the 

ingestion of vegetables contaminated by irrigation. Equations for the 

calculation of release values for this exposure pathway were developed but, 

based on the range of values to be used in this equation, it was determined 

that release values for the irrigation-vegetable pathway would be higher for 

all radionuclides than the release values for the ground-water ingestion 

pathway. That is, the irrigation-vegetable pathway is always less critical 

than the ground-water ingestion pathway. The Agency recognizes that the 

ingestion of vegetables contaminated by irrigation water actually could be 

more critical than the ingestion of ground water under certain scenarios 

(e.g., under scenarios where ground water is not used for drinking); the 

Agency's conclusion about the relative significance of these exposure pathways 

is based only on the release and exposure scenarios considered in this 

analysis. Based on this conclusion, EPA decided that it was not necessary to 

develop separate equations and to calculate release values for the 

irrigation-vegetable ingestion pathway under each set of assumptions shown in 

Exhibit 1. The specific rationale supporting this approach is outlined below. 

Conceptually, the release and environmental transport characteristics 

assumed in the irrigation pathway model were identical to those assumed in the 

ground-water ingestion model (see Section F.l.l of the TBD). Specifically, it 

was assumed that radionuclides are instantaneously released to ground water, 

they then migrate 30 meters downgradient, and contaminate an irrigation well. 

Contaminated water was assumed to be extracted from the well and applied to 

vegetables for the period of time that it takes the contaminant plume to pass 

the well. As described in Section 4.2 of this paper and in Section F.l.l of 

the TBD, EPA estimated that this period of time varied from 9 days to up to 

365 days, depending on the retardation factor for the radionuclide in 

question. Regardless of the period of time over which the crop was irrigated 

with contaminated water, it was assumed that an individual eats vegetables 

from the crop for 60 days, the entire length of the vegetable growing season. 

Finally, it was assumed that the vegetables are eaten immediately after they 

are harvested; that is, the vegetables are not stored between the time they 

are harvested and the time they are eaten. 

The following equation was developed to calculate release values based on 

the exposure scenario outlined above: 
P.40 

-38-

(74) Irrigation Release = ALI 

Value (in curies) (AF)*(DF)*(FC)*(CT)*(lxlOs) 

where 

ALI = Annual limit of intake for ingestion for a particular radionuclide; 

DF = Dilution factor, the concentration of a radionuclide in and on 

vegetables per curie released to ground water (Ci/kg per Ci; or 

kg-1); 

FC = Food (i.e., leafy vegetable) consumption rate of reference man 

(0.175 kg/day); 

CT = Contact time, or the number of days over which contaminated 

vegetables are ingested; and 

1x10s = Conversion factor between microcuries and curies. 

To determine the value for the dilution factor, DF, in Equation (74), EPA 

adapted an equation from the Nuclear Regulatory Commission's Regulatory Guide 

1.109. This equation is shown below: 

r[l-exp(-X t )] f B [l-exp(-X t )] 

Ei e i iv i b 

+ 

Y X PX 

v Ei i 

(75) DF = C I 

w 

exp(-X t ) 

i h 

where 

DF = Dilution factor, that is, the concentration of radionuclide in and 

on edible portion of vegetation per curie of radionuclide released 

to ground water (Ci/kg per-Ci; or kg-1); 

C = Concentration of radionuclide in irrigation water per curie of 

w radionuclide released to ground water (Ci/liter per Ci; or 

liter-1); 

I = Average irrigation rate (2.5 l/m2-day); 

f = Fraction of year crops are irrigated with contaminated water; and 

i 

all the other parameters and values are as defined for Equation (26) in 

Section 4.3 of this paper. 

The value for C used in Equation (75) was the same concentration 

w 

calculated for the ground-water ingestion pathway model, (7.6xl0-8/Rd) 

liter-1 (see Section F.l.l of the TBD for the derivation of this value). 
P.41 

-39-

To determine the value of the contact time, CT, in Equation (74), it was 

recognized that weathering and/or radioactive decay over the period of 

ingestion would result in some radionuclide loss. An "equivalent" contact 

time, therefore, was calculated using the following equation: 

(76) CT = l-exp(-X t) 

Ei 

X 

Ei 

where t = exposure period (60 days); and 

X = X + X = (0.693/T-1/2) + (0.693/14 days) = (0.693/T-1/2) + 

Ei i w 

(0.0495 day-1), where T-l/2 = radionuclide half-life in 

days. 

Under conditions involving no radionuclide retardation during ground-water 

transport (i.e., Rd = 1) and no radioactive decay (i.e., X = 0 ), the 

i 

expression for DF reduced to: 

(77) DF = (1.7 x 10-7 + 1.9 x lO-^B )kg-x 

iv 

and the value for CT, using Equation (76), was calculated to be 19 days. If 

the second term in the expression for DF is dropped for the sake of simplicity 

(it is approximately four orders of magnitude lower than the first term and 

therefore does not significantly affect the release value results), plugging a 

value of DF = 1.7xl0-7 into Equation (74) along with the values AF = 10 (for 

example), FC = 0.175 kg/day, and CT = 19 days, the equation for irrigation 

release values reduced to: 

(78) Irrigation Release Value (in curies) = ALI (in microcuries)/5.6 

Equation (78) can be compared to Equation (12), which represents the 

release value for the ingestion of ground water under the same set of 

assumptions used to derive Equation (78): 

(12) Ground-water Ingestion Release Value = ALI/14 

Based on this comparison, it is evident that the ground-water release value 

will be lower than the irrigation release value when Rd = 1 and radioactive 

decay is neglected. As the value for Rd is increased (i.e., when 

radionuclides with high sorption coefficients are considered), the 

ground-water release value becomes even smaller when compared to the 

irrigation release value. This change is the result of the change in the 

exposure period in the two models. In the ground-water ingestion model, the 

exposure period increases to 365 days when Rd is greater than one, such that 

the equation became (see derivation of Equation (13)): 
P.42 

-40-

(79) Ground-water Ingestion Release Value = ((ALI)*(Rd))/(550) 

In the irrigation pathway model, however, the exposure period remains 60 days 

regardless of the value for Rd. Equation (78) also remains applicable when RD 

-t 1 except that a value for Rd needs to be included in the numerator as 

follows: 

(80) Irrigation Release Value = ((ALI)*(Rd))/5.6 

Consequently, comparing Equations (79) and (80) shows that the ground-water 

ingestion release value also will be smaller than the irrigation release value 

when Rd > 1. 

For both the ground-water ingestion and irrigation models, the calculated 

release values are very large in comparison to the other exposure pathway 

models when radioactive decay is considered. Results from these two models, 

therefore, did not have to be evaluated and compared for situations in which 

decay is incorporated. 

5. SUMMARY OF RESULTS 

This section summarizes the RQ results calculated for each set of 

conditions considered in this analysis. Refer to the Superfund docket 

supporting the radionuclide rule (Superfund Docket No. 102RQ-RN) for the raw 

results obtained from-each calculation, including a list of pathway-specific 

release values and RQs calculated for the 757 radionuclides identified in the 

NPRM. 

Exhibit 2 summarizes for each set of conditions the number of 

radionuclides calculated to have an RQ of a given size. The first row in this 

exhibit identifies the set of modeling conditions assumed in the NPRM (52 FR 

8172, March 16, 1987) and presents the distribution of RQs proposed in the 

NPRM. The distribution of RQs presented in the second row of Exhibit 2 is 

based on the same set of conditions assumed in the NPRM; however, the RQs were 

calculated using a revised vegetable ingestion pathway model. Specifically, 

the vegetable ingestion model used to calculate the RQs shown in the second 

row in Exhibit 2 relied on a revised deposition velocity accounting for the 

transfer of radionuclides from air to vegetation (see the detailed discussion 

of this modeling change in Section 4.3 of this paper). Comparing the first 

and second rows in this exhibit shows that the change in deposition velocity 

did not have a significant effect on the overall distribution of RQs, although 

(as demonstrated by data in the docket) the specific RQs calculated for 

several radionuclides did change as a result of the revised vegetable 

ingestion model. In general, the change in the vegetable ingestion model 

resulted in a slight lowering of the RQs; fewer radionuclides were calculated 

to have RQs of 100 Ci and 1000 Ci when compared to the distribution proposed 

in the NPRM, while more radionuclides were calculated to have an RQ of 10 Ci 

or less. All the RQs for Conditions 1 through 18 were calculated using the 

revised vegetable ingestion model. 

Exhibit 2 also serves to demonstrate the relative effects of certain 

variable changes on the overall distribution of RQs. For example, as would be 
EXHIBIT 2 

DISTRIBUTIONS OF RQs FOR THE SETS OF CONDITIONS CONSIDERED IN THIS ANALYSIS 

Condi t ion 

Number 

NPRM (52 f_R 8172) 

NPRM (revised) 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

1*4 

15 

16 

17 

18 

b/ 

Di stance 

Exposure 

Point 

(meters) 

a/ 30 

30 

30 

30 

1 

30 

30 

1 

1 

30 

30 

1 

1 

£/ 

£/ 

£/ 

£/ 

30 

30 

1 

Assumed Cond 

to Period of 

Di rect 

Exposure 

(days) 

1 

1 

1 

1 

1 

1 

1 

1 

1 

365 

365 

1 

1 

£/ 

£/ 

£/ 

£/ 

1 

365 

1 

i t ions 

Dose 

Limit 

( rem) 

0.5 

0.5 

0.025 

0.1 

0.1 

0.025 

0. 1 

0.5 

0.025 

0.5 

0.5 

25 

0.5 

5 

5000 

25 

500 

0.5 

0.1 

0.1 

Rad ioactive 

Decay 

Cons idered? 

No 

No 

No 

No 

No 

Yes 

Yes 

No 

Yes 

No 

Yes 

Yes 

Yes 

No 

No 

No 

No 

Yes 

No 

Yes 

-7 

<10 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

56 

2 

41 

24 

0 

0 

0 

Number of 

-6 -4 

10 -10 

0 

0 

15 

7 

0 

12 

5 

0 

21 

1 

1 

0 

0 

209 

54 

104 

56 

1 

7 

0 

Rad ionucI ides 

-3 -2 

10 10 

6 25 

7 31 

36 68 

29 32 

206 246 

37 43 

28 25 

2 295 

196 208 

10 183 

9 46 

0 0 

0 149 

237 217 

24 46 

166 229 

46 139 

9 29 

74 342 

85 213 

Havinq 

-1 

10 

24 

28 

162 

86 

102 

94 

64 

192 

110 

295 

68 

23 

214 

35 

139 

188 

237 

38 

168 

175 

an RQ 

1 

35 

45 

353 

287 

26 

230 

143 

79 

36 

132 

100 

191 

150 

2 

237 

29 

217 

63 

75 

78 

(in curies) of 

10 

342 

413 

96 

245 

11 

194 

231 

14 

26 

59 

152 

210 

47 

1 

217 

0 

35 

208 

40 

10 

100 

236 

179 

24 

57 

19 

98 

162 

16 

14 

33 

174 

111 

31 

0 

35 

1 

2 

215 

17 

23 

1000 

89 

54 

3 

14 

8 

49 

99 

20 

7 

44 

207 

83 

27 

0 

3 

0 

1 

194 

34 

13 

a/ This is the assumed set of conditions and proposed distribution of RQs in the NPRM published on March 16, 1987 (52 £R 8172). 

b/ The distribution of RQs in this row was calculated using the same set of conditions assumed in the NPRM; however, the model 

for calculating release values for the vegetable ingestion pathway was revised to incorporate a different airborne deposition 

velocity than that assumed in the NPRM (see Section 4.3 of this paper). 

c/ In Conditions 12 through 15, RQs were calculated simply by taking multiples of the inhalation and ingestion Annual Limits 

of Intake. Neither distance nor time, therefore, were considered in these calculations. 
p 

» 

-42-

expected, the exhibit shows that lowering the dose-equivalent limit while 

keeping all other variables constant resulted in a general lowering of RQs 

(e.g., compare the distribution of RQs for Conditions 1 and 2, and the 

distribution for Conditions 4 and 5). Similarly, keeping all other variables 

constant but incorporating radioactive decay into the pathway models resulted 

in higher RQs (e.g., compare the distribution of RQs for Conditions 1 and 4, 

and for Conditions 8 and 9). 

Trends associated with changes in the exposure period and the distance 

from the release point are more difficult to identify because: (1) these 

variables were changed only for the pathway model considering direct exposure 

to a point source; and (2) only direct exposure to a point source and gamma 

emitting radionuclides were considered for those sets of conditions assuming a 

distance of 1 meter (note there are RQs for 618, not 757, radionuclides for 

Conditions 3, 6, 7, 10, 11, and 18 because 139 of the radionuclides never emit 

gamma rays). Nevertheless, Exhibit 2 does illustrate the lowering of RQs that 

would result if a direct exposure period of 365 days rather than 1 day were 

assumed (compare the results for Condition 8 and those in the revised NPRM). 

Additionally, it is important to clarify that the results for Conditions 3, 6, 

7, 10, 11, and 18 are only release values for the direct exposure pathway; 

these values were not compared with release values for other exposure pathways 

to determine RQs. It is possible that the release values for the exposure 

pathways other than direct exposure would be lower than those shown in Exhibit 

2, resulting in lower RQs than are presented in Conditions 3, 6, 7, 10, 11, 

and 18. 

Finally, Exhibit 2 shows that the lowest RQs, as a group, were calculated 

for Conditions 12 through 15, with Condition 12 yielding the lowest RQs. As 

described in Section 4 of this paper, RQs were calculated under these sets of 

conditions simply by taking multiples of the radionuclide ALIs, which in 

effect, does not account for any dispersion or dilution that would occur 

between the point of release and the point of exposure. When all exposure 

pathways considered in this analysis were taken into account (i.e., when a 

distance of 30 meters was assumed), the highest group of RQs was calculated 

under Conditions 9 and 16. 

Exhibit 3 summarizes the number of radionuclides whose calculated RQs are 

based on the different exposure pathways considered in this analysis. As in 

Exhibit 2, the first row in Exhibit 3 presents the conditions and limiting 

exposure pathways published in the NPRM, while the results in the second row 

are for the same set of conditions but are based on a revised vegetable 

ingestion model. As discussed in Section 4.3 of this paper, the revised 

vegetable ingestion model considered a greater transfer of radionuclides from 

air to vegetation when compared to the model used in the NPRM and, 

accordingly, Exhibit 3 shows that this revision resulted in a significantly 

larger number of RQs being based on the vegetable ingestion pathway. 

Exhibit 3 demonstrates several useful points about the way the limiting 

pathways generally shifted when different sets of conditions were assumed. 

First, regardless of the combination of distance, exposure period, dose limit, 

and modeling approach for radioactive decay, the direct exposure pathway model 

used in this analysis yielded the lowest release values for the majority of 
EXHIBIT 3 

NUMBER OF PROPOSED RQs BASED ON PARTICULAR EXPOSURE PATHWAYS 

Cond ition 

Number 

NPRM (52 FR 

NPRM ( rev i si 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

8172) 

2d) £/ 

Assumed Cond 

Distance to 

Exposure 

Point 

(meters) 

b/ 30 

30 

30 

30 

1 

30 

30 

1 

1 

30 

30 

1 

1 

e/ 

§/ 

£/ 

£/ 

30 

••• 3 0 

1 

Pei 

D 

~iod of 

rect 

Exposure 

(c lays) 

1 

1 

1 

1 

1 

1 

1 

1 

1 

365 

365 

1 

1 

§/ 

e/ 

£/ 

e/ 

1 

365 

1 

t ions 

Dose 

Limit 

( rem) 

0.5 

0.5 

0.025 

0.1 

0. 1 

0.025 

0.1 

0.5 

0.025 

0.5 

0.5 

25 

0.5 

5 

5000 

25 

500 

0.5 

0.1 

0.1 

Rad ioactive 

Decay 

Cons idered? 

No 

No 

No 

No 

No 

Yes 

Yes 

No 

Yes 

No 

Yes 

Yes 

Yes 

No 

No 

No 

No 

Yes 

No 

Yes 

Mi Ik 

Ingestion 

207 

207 

130 

130 

70 

95 

130 

70 

Number 

Vegeta 

of RQs 

ble 

Ingestion 

4 

266 

143 

143 

81 

81 

38 

. 44 

81 

38 

Based on 

GroundWater 

Ingestion 

113 

31 

25 

25 

1 

1 

14 

0 

475 

475 

475 

475 

1 

14 

£/ 

1/ 

£/ 

£/ 

an Expo; sure 

1nhalat ion 

184 

104 

94 

94 

157 

157 

72 

143 

330 

330 

330 

330 

157 

72 

fl/ 

9/ 

fl/ 

fl/ 

Pa thway 

Di rect 

Exposure a./ 

456 

356 

288 

288 

618 

388 

388 

618 

618 

563 

475 

618 

618 

388 

563 

618 

d/ 

fl7 

d/ 

d/ 

d/ 

d/ 

a/ Includes direct exposure to a point source and submersion in an airborne cloud. 

b/ This is the assumed set of conditions and proposed distribution of RQs in the NPRM published on March 16, 1987 (52 £R 8172). 

c/ The distribution of RQs in this row was calculated using the same set of conditions assumed in the NPRM; however, the model 

for calculating release values for the vegetable ingestion pathway was revised to incorporate a different airborne deposition 

velocity than that assumed in the NPRM (see Section 4.3 of this paper). 

d/ This total is 618 rather than 757 because: (1) a distance of 1 meter between the point of release and the point of 

exposure was assumed only in the direct exposure pathway model; and (2) 139 of the radionuclides of interest to this analysis do 

not emit gamma rays (exposures to beta particles 1 meter away from the point of release were not considered in this analysis). 

These values are release values for the direct exposure to a point source pathway; they were not compared to the release values 

for other exposure pathways under these conditions for the determination of RQs. If such a comparison had been made, however, 

other exposure pathways may have been found to be more limiting than the direct exposure to a point source. 

e/ In Conditions 12 through 15, RQs were calculated simply by taking multiples of the inhalation and ingestion Annual Limits 

of Intake. Neither distance nor time, therefore, were considered in these calculations. 

£/ This is the number of radionuclides whose RQs are based on the ALIs for ingestion, which are the same regardless of whether 

the radionuclides are ingested in ground water, vegetables, or milk. Therefore, while this number is displayed above in the 

ground-water ingestion pathway column, ground-water ingestion was not determined to be necessarily more critical than milk or 

vegetable ingestion under Conditions 12 through 15. 

g/ Under Conditions 12 through 15, the release values 

and inhalation (i.e., for those radionuclides, the lowest 

inhalation nor ingestion could be counted as the limiting 

of this exhibit, are stated to be based on both ingestion 

for 48 radionuclides were calculated to be the same for both ingestion 

ingestion ALI equals the lowest inhalation ALI). Accordingly, neither 

exposure pathway for these radionuclides and their RQs, for the purpose 

and inhalation. This results in a "double counting" of RQs for 48 

radionuclides such that the total number of radionuclides accounted for in Conditions 12 through 15 is 805, rather than 757. 
P.46_ 

-44-

radionuclides when compared to the release values calculated by the other 

exposure pathway models. It is important to clarify, however, that only 

direct exposure to a point source was considered when a distance of 1 meter 

was assumed and, thus, the results shown for Conditions 3, 6, 7, 10, 11, and 

18 are direct exposure release values rather than RQs. Had release values for 

the other exposure pathways under these sets of conditions been compared to 

those for direct exposure, other exposure pathways may have been found to be 

more limiting. In addition, as mentioned previously, the total number of 

release values for Conditions 3, 6, 7, 10, 11, and 18 equal 618 rather than 

757 because 139 of the radionuclides of interest do not emit gamma rays and 

were excluded from the direct exposure pathway analysis. 

Second, Exhibit 3 demonstrates how the relative significance of the 

ground-water ingestion pathway decreased when radioactive decay was taken into 

account. For example, note how the number of RQs based on the ground-water 

ingestion pathway decreased in going from the original NPRM results to the 

results for Condition 16, and in going from the results for Condition 1 to 

those for Condition 4. This shift was the result of radionuclide loss due to 

decay during the slow migration of radionuclides to a well located 30 meters 

downgradient from the point of release. 

Finally, Exhibit 3 illustrates that, with one exception, changes only in 

the dose-equivalent limit did not change the relative significance of the 

various exposure pathways. That is, while changes in the dose-equivalent 

limit resulted in a shift in the magnitude of RQs (see Exhibit 2), the 

exposure pathways that were limiting under the assumption of one doseequivalent level were the same as the limiting pathways under another level. 

This is evident, for example, when the results for Conditions 1 and 2, and the 

results for Conditions 4, 5, and 16 are compared. The one exception to this 

finding is that, based on the pathway models used in this analysis, the milk 

ingestion pathway was not limiting when a dose-equivalent of 0.5 rem or higher 

was assumed.