# Calculating equivalent dose from exposure to radium

My mother was unknowingly exposed to radiation from some radium needles (Ra-226). The exposure was at waist height, from a distance of about 25cm, for a total duration of about 1.25 hours. This happened some years ago and she was not wearing any protective clothing.

I'm assuming that the exposure was only to gamma radiation, since the radium was inside a patient being treated for cervical cancer, and so the alpha and beta radiation would have been absorbed.

I've been trying to work out how much radiation she was exposed to, but I've got stuck. I've discovered from this page that radium needles typically contained between 1mg and 10mg of radium each. I'm assuming there were three needles that each contained 5mg.

I've seen this page and I've tried to calculate it using the exposure rate constant for Ra-226, but I think I went wrong. I don't know whether this is the correct way to calculate the exposure anyway. Ideally I would like to know the equivalent dose.

The WP page you linked to gives an exposure rate constant, which from context seems to refer only to the gamma radiation. (Radium is an alpha emitter, but the later decay chain involves the emission of gammas.) 15 mg of radium is 15 mCi, because the Curie was originally defined in terms of radium. Plugging in the data you estimated gives an exposure of about 0.3 roentgen, which is equivalent to about $$3\times10^{-3}$$ Gy. Because the weighting factor for gammas is 1, this is a biological dose of $$3\times10^{-3}$$ Sv, or 3000 $$\mu$$Sv.
Because she was at some distance from the source, this is, roughly speaking, a whole-body dose. This is in the same ballpark as one year's worth of natural background radiation (2000-7000 $$\mu$$Sv), or maybe equivalent to spending a year in someplace like Denver that has a higher natural background. Although this was a dose delivered rapidly rather than spread out over a longer time, like natural background, I don't think that matters here, because she evidently didn't suffer any acute effect. If, for example, she is still alive and worried that she might have gotten cancer from this, then under the linear no-threshold (LNT) hypothesis, her added cancer risk really is on the same order of magnitude as going to Denver for a year.