# Answer to Question #11545 Submitted to "Ask the Experts"

*Category: Radiation Basics — Photons*

The following question was answered by an expert in the appropriate field:

Rad Pro Calculator results of exposure rate for a given activity of cesium-137 (^{137}Cs) in units of milliroentgen per hour (mR h^{-1}) and microsievert per hour (µSv h^{-1}) are not a simple factor of 100. For example the dose rate at 50 centimeters (cm) due to 50 millicurie (mCi) of ^{137}Cs is 182.8 mR h^{-1}. But the output in µSv h^{-1} is 129.8 µSv h^{-1} and not the expected 1828 µSv h^{-1}. Why is this so?

I must first note that the numbers you cite for the Rad Pro Calculator results do not seem to agree with those I obtain when I use the Rad Pro Calculator "Gamma-Emitter Point Source Dose Rate" at this link. For the assumed 50 mCi point source at 50 cm from the dose point I obtain a result of 564.9 µSv h^{-1}, substantially different from your value of 129.8 µSv h^{-1}. When I specify units of mR h^{-1} I obtain 64.4 mR h^{-1}, appreciably different from your value of 182.8 mR h^{-1}. I cannot further address the values that you generated, although I suspect you might have inadvertently used different input value(s) from those that you cite.

At any rate, in order to convert dose equivalent rate units of µSv h^{-1} (which apply to tissue) to exposure rate units of mR h^{-1} (which apply to air), the multiplying factor is not 100 (or 10 as you seemed to use to get the 1828 µSv h^{-1} value from the 182.8 mR h^{-1}). First, if we multiply the µSv h^{-1} value by 100 microrem (µrem) µSv^{-1} we should obtain units of µrem h^{-1}; these units represent the quantity of equivalent dose rate to a small volume of tissue at the dose point. Keeping in mind that the equivalent dose rate is obtained by multiplying the absorbed dose rate in tissue by the appropriate radiation-weighting factor (1.0 for gamma radiation), we can assume that the equivalent dose rate in this case is equal in magnitude to the absorbed dose rate in soft tissue at the same point. Assuming that secondary charged-particle equilibrium exists at the dose point, which is an implicit assumption in the generation of gamma dose-conversion factors, the absorbed dose rate in tissue can be converted to absorbed dose rate in air by multiplying the tissue dose rate by the ratio of the mass energy absorption coefficient in air to soft tissue, (µ/ρ)_{en,air}/(µ/ρ)_{en,tissue} (for ^{137}Cs photons this ratio is equal to about 0.91); the exposure rate may then be obtained by using an exposure-to-dose conversion factor of 8.76 mGy R^{-1} (or 0.876 rad R^{-1} in non-SI units).

If we then take the value that I obtained from the Rad Pro Calculator of 564.9 µSv h^{-1} we can convert it to units of mR h^{-1} as follows:

(564.9 µSv h^{-1})(100 µrem µSv^{-1}) (1 µrad µrem^{-1})(1 rad/1,000,000 µrads)(0.91)(1 R/0.876 rad)(1,000 mR R^{-1}) = 58.7 mR h^{-1}

The value of 64.4 mR h^{-1} that Rad Pro Calculator yielded I believe results from the likelihood that the programmer assumed that the ratio of mass energy absorption coefficients (air to tissue) was 1.0, a simplification that is often suitable for reasonable approximations, although it can lead to more significant distortions, especially for low-energy photons.

George Chabot, PhD