Calculating Total Extra Exposure from Multiple Radiation Sources

[Von Neumann]

Question:

I'm looking to estimate my total extra exposure (dose above background) by taking into account account roughly how long I was near each source, the strength of the source, and its approximate distance from me. I believe it's useful to use the following equation,

$\frac{dD}{dt}=\frac{dD_{0}}{dt}e^{-cx}$

where $\frac{dD_{0}}{dt}$ is the dose rate at x=0 and c is the absorption coefficient.

The dose rates measured at x=0 for the 3 sources, as well as the calculated absorption coefficients are

Ba-133: 277 μR/h , c=0.303/in.
Cs-137: 107 μR/h , c=0.375/in.
Co-60: 117 μR/h , c=0.360/in.

*note that the background radiation has been subtracted from the dose rates shown.

So if I take the time t spend near each source as 10 minutes, and the distance from each source as x=0 in. (as I was holding the sources as we varied the distance in the first part of the experiment) I can approximate the exposure as


$\frac{dD_{0}}{dt}\cdot$$t$

and then sum these for from each source. So therefore I get,

Ba-133: 277 μR/h * (10 min) * (1 h/ 60 min) = 0.0462 mR
Co-60: 107 μR/h * (10 min) * (1 h/ 60 min) = 0.0195 mR
Cs-137: 117 μR/h * (10 min) * (1 h/ 60 min) = .0178 mR

Thus as my total extra exposure I get,

0.0462 mR + 0.0195 mR + 0.0178 mR = 0.0835 mR

Is this reasoning correct? Thank you in advance for any input.

 

[mfb]

Neither the dose measurement nor you received all radioactive decays, as just some fraction of them went in the direction where they got detected / absorbed in your body. In general, this fraction will be different, and depend on the setup.

as I was holding the sources

I would expect that you were holding something which was holding the sources. Even without absorber, distance to the source is crucial in the analysis.