Answer to Question #7283 Submitted to "Ask the Experts"

Category: Radiation Basics

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


I'm a geologist and author, currently writing a book in which I need to convert an old measure of radioactivity to some measure that modern readers can understand. The background is that, in 1926, an analysis of the radioactivity of Radium Hot Springs, British Columbia, was published (Elworthy RT, "Hot Springs in Western Canada—Their Radioactivity and Chemical Properties," in Canada Mines Branch Report 669, pp. 1–33). Radium was indeed found to be dissolved in the water: 96 units per litre, where one unit was 10-12 grams of, presumably, radium. The gases emitted from the water were apparently quite radioactive as hot springs go. Elworthy measured up to 45,750 "units per litre," presumably of gas at STP, but I'm not sure. The report stated that Radium Hot Springs were the most radioactive springs known in North America at that time. It still may be true today but, incredibly, no more up-to-date measurements have been taken. My question concerns that figure of "45,750 units per litre." Can it be converted to more common activity units, such as becquerels? What dose, in some common unit such as gray, would result from exposure to this concentration?


As you are well aware, it is often difficult to interpret technical results from years past when terminology has changed and authors are no longer available. To the extent that I am able, I will attempt to provide an answer to your questions.

At the time of the article that you note, the unit of radioactivity recommended was the "curie," which was defined in relationship to radium as a reference material. By inference it represented the amount of radioactivity associated with one gram of radium—more specifically, in 1910 a Standards Committee chaired by Ernest Rutherford suggested that "the Curie be used as a new unit to express the quantity or mass of radium emanation in equilibrium with one gram of radium (element)." (Please see discussion in "WHY DID THEY CALL IT THAT? The Origin of Selected Radiological and Nuclear Terms" by Paul Frame of Oak Ridge Associated Universities.)

When the radium emanation (222Rn) is in secular equilibrium with one gram of the 226Ra precursor, it will have a total activity equal to that of the one gram of the radium, such activity being 3.7 x 1010 Bq (1 Bq = 1 becquerel = 1 disintegration per second). One picogram of radium (the 10-12 g of radium that you define as one unit) then represents 0.037 Bq.

As to the 45,750 units per liter that the author measured, I believe you should interpret the "unit" here as 0.037 Bq of 222Rn; I do not believe the number refers to air as the measurement medium, however, as this value would be greatly in excess of a likely air concentration that would derive from release from the water to the air and dilution in the air, considering the measured water concentration of 226Ra. I rather believe that the 45,750 units per liter (1,693 Bq L-1) refers to the 222Rn concentration in the water.

One might initially question how the 222Rn concentration could be so much greater than the 226Ra concentration in the water. This is not uncommon and originates from the fact that most of the radon in the water is coming from undissolved radium in the material that forms the walls and floor of the basin in which the water is contained, especially given the fact that these were hot springs in which rock cracks and fissures may provide paths for hot water to carry radon into the basin. Thus 226Ra, present possibly at quite high concentrations in the stone, decays to 222Rn, some of which enters the water pushing the concentration well beyond what one might expect from equilibrium considerations that apply to the dissolved radium in the water.

The dose question is not so straightforward. Most of the external dose (i.e., dose from radioactivity outside of the body) received from radioactivity in the water when an individual is bathing comes from the beta radiation and gamma radiation produced by the decay of the radioactive progeny of radon, although some dose also comes from gamma radiation being emitted from radionuclides in the rock. The alpha radiation does not contribute to external dose because the alpha particles are easily stopped and do not penetrate the dead layer of skin on the body.

If we considered the maximum possible dose from the radon decay products we could assume that all of the short-lived radioactive progeny were in equilibrium with the radon (which means that each of these progeny would be present in the same activity concentration as the radon); we could then do an estimation based on a further assumed condition of energy spatial equilibrium, which implies that the energy emitted per unit mass of water is equal to the energy absorbed per unit mass.

Without going through all the details, I have done this for the case here and estimated the dose rate in gray per hour to be 2.5 x 10-6 Gy h-1 (2.5 µGy h-1), which would represent the dose rate near the surface of the body of an individual immersed in the pool. For beta and gamma radiation this dose would represent a biological dose rate of 2.5 microsievert per hour (2.5 µSv h-1).

For a half-hour exposure period the integral dose would then be about 1.3 µSv, an inconsequential number. This is essentially a skin dose; about 70 percent of the dose is due to gamma radiation and 30 percent to beta radiation. The gamma dose component of 0.9 µSv could be interpreted as an estimate of external whole-body effective dose from immersion in the pool. This compares to about 1,000 µSv per year that we all get from cosmic plus terrestrial radiation (excluding breathing of radon, which probably accounts for about another 2,000 µSv).

There may also be some dose from inhalation of the radon and daughter products in the air. From a few numbers I have seen elsewhere that relate water concentration to air concentration of radon, the air activity concentration may be on the order of 5 x 10-4 of the pool activity concentration of radon, although this would have to be measured to get a reasonable estimate, especially for the breathing zone close to the pool surface. At any rate, if we used such a value, we would estimate the air concentration of radon to be about 850 Bq m-3 (note that 1 cubic meter = 1,000 liters). Such a concentration, together with equilibrium concentrations of radon progeny, breathed for 0.5 hours would result in an effective whole-body dose of about 7 µSv, also an inconsequential number from a dose impact perspective.

I hope this is helpful to you.

George Chabot, PhD, CHP

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