The purpose of this post is to give a brief overview of how the activity of radionuclides correspond to the concentration of radionuclides measured in environmental samples. There appears to be some confusion in the public and within the scientific community as to how units are used and the degree of their interchangeability. This post is somewhat technical but falls into the category of “In Case You’re Interested” (ICYI), an acronym I am shamelessly borrowing from a fine book (Everything and More: A Compact History of Infinity) by one of my favorite writers David F. Wallace.
As an example we will consider how activity in seawater relates to concentration of a radionuclide in seawater although what follows can be generalized to radionuclide activities and activity concentrations in marine biota and other substances as well.
As in previous posts it is useful to point out that scientists use a variety of units to measure radioactivity. A commonly used unit is the Becquerel (Bq for short) which represents an amount of radioactive material where one atom decays per second and has units of inverse time (per second). Another unit commonly used is disintegrations per minute (dpm) where the number of atoms undergoing radioactive decay in one minute are counted (so 1 Bq = 60 dpm).
Almost all the radioactivity in seawater is the result of primordial, naturally occurring radionuclides that have been transported or deposited in the oceans by natural processes like the erosion of the continental crust. There is spatial variability in the amount of radioactivity in the ocean that mostly relates to differences in salinity where the dilution of seawater with freshwater reduces the overall activity of the radioactive elements. The average radioactivity of seawater is about 14 Bq per Litre of seawater (Bq L-1) of which 88% is from naturally occurring potassium-40 (40-K, half life ). About 7% is from anthropogenic fallout from atmospheric nuclear weapons testing and nuclear accidents like Chernobyl (1986) and Fukushima Daiichi (2011). So there is about 13 Bq L-1 of natural radioactivity on average is the oceans. In high salinity areas (where conservative elements that scale with salinity like K and U have the highest concentration) activity can be as high as 22 Bq L-1 (Persian Gulf) and 15 Bq L-1 (eastern Mediterranean). When chemical oceanographers report activities they generally report them in terms of Bq per liter of seawater (Bq L-1) or in Bq per cubic meter of seawater (Bq m-3 where 1 m3 = 1000 L) when activities are very low.
For example, activities of the Fukushima sourced radionuclide Cesium-137 (137-Cs, half life ~30 years) that was released in great quantities to the North Pacific Ocean is currently present off the west coast of North America on the order of 0.005 Bq L-1 or 5 Bq m-3. The activity relates directly to the concentration of 137-Cs in seawater as follows:
relating activity to concentration where A is the activity of 137-Cs in a liter of seawater, M is the number of moles of 137-Cs per liter of seawater, N is Avogadros number (~6.02 x 1023 atoms per mole), ln(2) is the natural logarithm of 2 and t1/2 is the half life of 137-Cs in seconds (~9.5 x 108 sec; seconds corresponding to ~ 30 years).
Substituting in the the value of 0.005 Bq L-1 for 137-Cs activity and the other values allows us to calculate a concentration for 137-Cs of 1 x 10-17 mole L-1. This corresponds to roughly 1.5 x 10-16 grams of 137-Cs per liter of seawater and to roughly 6 million 137-Cs atoms per liter of seawater. These concentrations of 137-Cs are roughly 8-orders of magnitude (100 million times) lower than naturally occurring Uranium-238 in seawater. This is an incredibly small number to grasp.
To use an analogy, borrowed from Shawn Urban of the University of Alberta, the number of 137-Cs atoms compared to other atoms in a litre of water is roughly like, if we imagined a 137-Cs atom to be the size of a green pea, a single green pea compared to the number green peas required to blanket the area of the province of Alberta to a depth of ~1 meter (~3 ft).
The ability to measure activities of these radionuclides at these levels requires incredibly sensitive detectors, shielding from natural sources of radiation, and days to weeks of counting disintegrations to achieve statistically meaningful measurements.