Berkeley Radiological Air and Water Dose Calculation

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The Dose calculation for water and air intake was performed based upon the annual limit on intake (ALI) for effluent release in table 2 from the US Nuclear Regulatory Commission regulations(10 CFR) part 20 appendix B. The NRC numbers are based on the International Commission on Radiological Protection (ICRP) Publication 30.

This annual limit corresponds to the limit of radiation in water and air being released from a site handling nuclear materials (i.e., hospitals, nuclear reactors, research laboratories, etc.). The "reference man" is assumed to drink 730 liters of water per year or breathe 2.4 million (2.4E6) liters of air per year, and if the person drinks water or breathes air at the stated limit for one year the person would receive a total effective dose of 50 millirem. The total effective dose takes into consideration the method of intake (ingestion for water or inhalation for air) and the combined biological and radiological removal of the isotope from the human body.

These figures are conservative because any exposure to these radionuclides in California would be for a short time (days or weeks at most), while the NRC and ICRP numbers assume a yearlong constant exposure where the radionuclides reach equilibrium in the body.

Dose Conversion Factors used in our analysis

The dose conversion factor relates the activity of a radionuclide (in Becquerels (Bq) or microcuries (uCi)) to the total effective dose equivalent (TEDE) received by the person (in millirem or microSieverts (uSv)). See the examples after the table that explain how we arrived at these numbers and how they can be used to calculate dose from our measurements.

Dose Conversion Factors for WATER

Units I-131 I-132 Cs-134 Cs-137 Te-132 Be-7

millirem/uCi 6.849E+01 6.849E-01 7.610E+01 6.849E+01 7.610E+00 1.142E-01

uSv/uCi 6.849E+02 6.849E+00 7.610E+02 6.849E+02 7.610E+01 1.142E+00

millirem/Bq 1.851E-03 1.851E-05 2.057E-03 1.851E-03 2.057E-04 3.085E-06

uSv/Bq 1.851E-02 1.851E-04 2.057E-02 1.851E-02 2.057E-03 3.085E-05

Dose Conversion Factors for AIR

Units I-131 I-132 Cs-134 Cs-137 Te-132 Be-7

millirem/uCi 1.042E+02 1.042E+00 1.042E+02 1.042E+02 2.315E+01 6.944E-01

uSv/uCi 1.042E+03 1.042E+01 1.042E+03 1.042E+03 2.315E+02 6.944E+00

millirem/Bq 2.815E-03 2.815E-05 2.815E-03 2.815E-03 6.256E-04 1.877E-05

uSv/Bq 2.815E-02 2.815E-04 2.815E-02 2.815E-02 6.256E-03 1.877E-04

Dose Conversion Factor Calculation: I-131 in Water

First, to calculate the Dose Conversion Factor (DCF) for I-131 in water, we take the definition of the 50 millirem limit in 730 liters (h) of water consumed by the reference man in one year to calculate the dose per liter:

(50 millirem) / (730 L) = 0.06849 millirem/L

Next, we use the ALI-derived concentration limit for I-131 in water of 1E-6 uCi/milliliter given in table 2 to calculate the total DCF for I-131 in water:

(0.06849 millirem/L)/(1E-6 uCi/mL * (1000 mL/1 L)) = 68.49 millirem/uCi.

The activity we report for water is in Becquerel/liter (Bq/L). The conversion between Bq and uCi is 1 uCi = 37,000 Bq. So the DCF in units of millirem/Bq is:

(68.49 millirem/uCi) * (1 uCi/3.7E4 Bq) = 1.851E-3 millirem/Bq

If you are used to using Sieverts (Sv) instead of millirems, by using the conversion of 1 millirem = 10 microSieverts (uSv), we get the DCF in yet another set of units:

(68.49 millirem/uCi) * (10 uSv/1 millirem) = 684.9 uSv/uCi

(1.851E-3 millirem/Bq) * (10 uSv/1 millirem) = 1.851E-2 uSv/Bq

So depending on the dose units (uSv or millirems) and activity units (uCi or Becquerels) that you prefer, there are four ways of expressing the Dose Conversion Factor for I-131 in water:

Units DCF

millirem/uCi 68.49

uSv/uCi 684.9

millirem/Bq 1.851E-3

uSv/Bq 1.851E-2

Now let's calculate the dose for a specific case. For example, the first activity we measured for I-131 is 4.65 Bq/L. Using the DCF for millirem/Bq, we can easily calculate the total effective dose equivalent (TEDE) of I-131 per liter of water:

(4.65 Bq/L) * (1.851E-3 millirem/Bq) = 8.61E-3 millirem/L

The TEDE from a typical flight from San Francisco to Washington DC and back is approximately 5 millirem. In order to determine the number of liters one would have to drink to receive this same dose, the dose received for the roundtrip flight is divided by the TEDE per liter:

(5 millirem)/(8.61E-3 millirem/L) = 581 liters

Dose Conversion Factor Calculation: I-131 in Air

To calculate the Dose Conversion Factor (DCF) for I-131 in air, we take the definition of the 50 millirem limit in 2.4E6 liters (h) of air breathed by the reference man in one year to calculate the dose per liter of air breathed:

(50 millirem) / (2.4E6 L) = 2.083E-5 millirem/L

Next, we use the ALI-derived concentration for I-131 in air of 2E-10 uCi/milliliter given in table 2 to calculate the total DCF for I-131 in air:

(2.083E-5 millirem/L)/(2E-10 uCi/mL * (1000 mL/1 L)) = 104.2 millirem/uCi.

The activity we report for air is in Becquerel/liter (Bq/L). The conversion between Bq and uCi is 1 uCi = 37,000 Bq. So the DCF in units of millirem/Bq is:

(104.2 millirem/uCi) * (1 uCi/3.7E4 Bq) = 2.816E-3 millirem/Bq

If you are used to using Sieverts (Sv) instead of millirems, by using the conversion of 1 millirem = 10 microSieverts (uSv), we get the DCF in yet another set of units:

(104.2 millirem/uCi) * (10 uSv/1 millirem) = 1,042 uSv/uCi

(2.816E-3 millirem/Bq) * (10 uSv/1 millirem) = 2.816E-2 uSv/Bq

So depending on the dose units (uSv or millirems) and activity units (uCi or Becquerels) that you prefer, there are four ways of expressing the Dose Conversion Factor for I-131 in air:

Units DCF

millirem/uCi 104.2

uSv/uCi 1,042

millirem/Bq 2.816E-3

uSv/Bq 2.816E-2

Now let's calculate the dose for a specific case. For example, the first activity we measured for I-131 is 1.52E-6 Bq/L. Using the DCF for millirem/Bq, we can easily calculate the total effective dose equivalent (TEDE) of I-131 per liter of air breathed:

(1.52E-6 Bq/L) * (2.816E-3 millirem/Bq) = 4.28E-9 millirem/L

Then using the average figure of 2.4E6 liters of air breathed per year, the TEDE if breathed continually for one year is:

(4.28E-9 millirem/L) * (2.4E6 L/year) = 0.01027 millirem/year

The TEDE from a typical flight from San Francisco to Washington DC and back is approximately 5 millirem. In order to determine the number of years one would have to breathe to receive this same dose, the dose received for the roundtrip flight is divided by the average dose per year:

(5 millirem)/(0.01027 millirem/year) = 489 years

[4:19:22 PM] David: Then by your numbers current calculation is every 1 day or 24 hours of exposure is equal to 489 years of dosage for radiation worker as if the world works for the NRC and or should have ALARA base

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