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.
For didactic purposes we will consider how activity in seawater relates to concentration of a radionuclide in seawater.
As in previous diaries 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/L of which 88% is from naturally occurring potassium-40 (K-40). 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 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 (Persian Gulf) and 15 Bq/L (eastern Mediterranean). When chemical oceanographers report activities they generally report them in terms of Bq per liter of seawater (Bq/L) or in Bq per cubic meter of seawater (Bq/m^3 where 1 m^3 = 1000 L) when activities are very low.
For example activities of the Fukushima sourced radionuclide 137-Cs that was released in great quantities to the North Pacific Ocean currently present off the west coast of North America are on the order of 0.001 Bq/L or 1 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 (~6.02E23 per mole), ln(2) is the natural logarithm of 2 and t 1/2 is the half life of 137-Cs in seconds (~9.5E8 seconds). Numbers separated by "E" are to be read as the first number multiplied by 10 raised to the power of the second number and is short form for scientific notation.
Substituting in the the value of 0.001 Bq/L for 137-Cs activity and the other values allows us to calculate a concentration for 137-Cs of 2E-18 mole/L. This corresponds to roughly 3E-16 grams per liter of seawater and to roughly 1.2 million 137-Cs atoms per liter of seawater. These concentrations of 137-Cs are roughly 9-orders of magnitude lower than naturally occurring 238-U in seawater. The ability to detect radiation 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.
4:53 PM PT: These results can be generalized to any other radioisotope by looking up current activity levels and isotope half life.