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Answer to Question #1048 Submitted to "Ask the Experts"Category: Doses and Dose Calculations — Internal dose calculations The following question was answered by an expert in the appropriate field: Q
How can one estimate the dose from drinking water, given the specific activity in curies per gram for a given radionuclide such as 241Am, 129I, 3H, depleted uranium, and 137Cs?
A
I assume that when it is stated in the question that the specific activity is in curies per gram (Ci g-1) that the meaning is that this is the water concentration of the radionuclide in Ci g-1 of water.
The International Commission on Radiological Protection (ICRP) has published Annual Limits on Intake of Radionuclides by Workers Based on the 1990 Recommendations (Publication 60) of the ICRP for limiting dose. The annual limit on intake (ALI) is the maximum intake in becquerel (1 Bq = 1 disintegration per second) that a worker may ingest orally and not exceed his/her annual average dose limit as per the 1990 recommendations. This average annual limit was 20 mSv. The ALIs themselves are published in ICRP Publication 61.
Therefore a dose conversion factor (DCF) can be derived from the ALI by dividing 20 mSv by the ALI, i.e.:
DCF = 20/ALI. (Sv/Bq) [eq. 1]
The ALIs for oral ingestion as listed in ICRP-61 are:
241Am: 30,000 Bq
129I: 200,000 Bq
3H: 1 billion Bq (1,000,000,000 Bq)
137Cs: 1 million Bq (1,000,000 Bq)
Depleted uranium (DU) is a little more complicated because it consists of 238U, 234Th, 234Pa, and 234U all in secular equilibrium. This means that there is the same activity amount present for each of the progeny as there is for the 238U parent. I assume here that the activity quoted for DU is the actual activity of the parent 238U. If so, the ALI for DU (ALI-DU) is given by:
1/ALI-DU = (1/ALI 238U) + (1/ALI 234Th) + (1/ALI 234Pr) + (1/ALI 234U) [eq. 2]
Where ALI 238U, ALI 234Th, ALI 234Pr, and ALI 234U are the ALIs for 238U, 234Th, 234Pr, and 234U respectively. These are:
238U: 8.0×105 (most conservative, Class D Compounds)
234Th: 4.0×106
234Pr: 4.0×107
234U: 7.0×105
Applying Eq. 2 we get 1/(ALI-DU) = 1.25×10-6 + 2.5×10-7 + 2.5×10-8 + 1.4×10-6 = 2.95×10-6
Which gives 3.4×105 Bq of 238U as the ALI for DU.
Water consumption for humans is usually quoted in litres. However your water concentrations, C, are quoted in Ci g-1 of water. Each litre of water is about 1000 g. Also 1 Ci = 3.7×1010 Bq
Therefore the intake, I, of the radionuclide (in Bq) is the quantity, Q (in L), consumed times C (in Ci g-1) times 1000 times 3.7×1010 or
I = 3.7×1013 QC Bq [Eq. 3]
Dose = (DCF)×I
=(20/ALI)×(3.7×1013 QC)
So Dose is given by:
Dose = 7.4×1014 QC/ALI (mSv) QED
Where:
Q = water consumption in L
C = radionuclide concentration in curies
ALI= annual limit on intake in Bq.
Note: If the activity of DU is quoted as the total activity of the parent and the three progeny, then the ALI is four times the value calculated above.
John Barnard, PhD
Answer posted on 19 July 2001. The information and material posted on this Web site is intended as general reference information only. Specific facts and circumstances may alter the concepts and applications of materials and information described herein. The information provided is not a substitute for professional advice and should not be relied upon in the absence of such professional advice specific to whatever facts and circumstances are presented in any given situation. Answers are correct at the time they are posted on the Web site. Be advised that over time, some requirements could change, new data could be made available, or Internet links could change. For answers that have been posted for several months or longer, please check the current status of the posted information prior to using the responses for specific applications.
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