2.3 Radioactive Tracers

A radioactive tracer is any of several species of the same chemical element with different masses that have an unstable nucleus that dissipates excess energy by spontaneously emitting radiation in the form of alpha, beta, and/or gamma rays. If radioactive decay is the dominant process causing changes in the concentration of a tracer, then these changes can be used to infer timescales of groundwater movement. If the concentration of the radioactive element that serves as the tracer in groundwater recharge has been relatively constant, then its concentration will decrease exponentially over time (Figure 3). Assuming no other process is reducing the concentration of the element, the age of a groundwater sample is given by Equation 1.

\displaystyle t=-\lambda^{-1}\ln \left(\frac{c}{c_0}\right) (1)

where:

c = measured concentration of radioactive tracer
c0 = initial concentration of radioactive tracer (same dimension as c)
λ = decay constant (T-1)

The decay constant and half-life are related by Equation 2.

\displaystyle \lambda=\frac{-\ln (0.5)}{t_{1/2}} (2)

where:

t1/2 = half-life of radioactive tracer (T)

A number of different radioactive isotopes have been used to estimate the age of groundwater in this way, including 14C (t1/2 = 5,730 years), 32Si (t1/2 = 140 years), 35S (t1/2 = 88 days), 36Cl (t1/2 = 301,000 years), 39Ar (t1/2 = 269 years) and 81Kr (t1/2  = 229,000 years), with 14C the most commonly used. These isotopes are produced by cosmic ray interactions with various elements in the atmosphere and dissolve in rain and enter the hydrologic cycle.

Graph showing radioactive decay
Figure 3  – In the radioactive decay process, the concentration of the radioactive element will be reduced to half of its initial value after one half life, and the concentration will continue to halve after every subsequent half life until it is no longer measurable. The equation in the Figure is a re arrangement of Equation 1 in the text (Cook, 2020).

If the input concentration of a radioactive tracer is variable or not well known, it is sometimes possible to measure the concentrations of both the radioactive parent (the radioactive element that originally entered the groundwater) and the daughter product (the element that is produced by the radioactive decay), and to sum these to determine the initial concentration of the parent. This is generally only possible when the daughter product is not itself radioactive. This is the basis of the 3H/3He method of groundwater dating (the parent 3H decays to the stable daughter 3He; Figure 4), but it cannot be used for some of the other radioactive tracers (e.g., 14C, 35S, 36Cl, 39Ar) as their decay products are difficult to measure, in some cases due to high background concentrations (elemental symbols are defined in the caption of Table 1). A background concentration is the concentration of a substance unrelated to that input by the source of the tracer (e.g., 14C decays to stable nitrogen, which is widespread in the environment).

Where both parent and daughter concentrations are measured, the daughter is stable, and background concentrations are low, then the age of a groundwater sample is given by Equation 3.

\displaystyle t=-\lambda^{-1}\ln \left(\frac{c_p}{c_p+c_d}\right) (3)

where:

cp = parent concentration
cd = daughter concentration (same dimension as cp)
λ = decay constant of the parent (T-1)
Schematic illustration of the decay of 3H and growth of 3He over time
Figure 4 – Schematic illustration of the decay of 3H and growth of 3He over time. The ratio of 3He to 3H increases with time and can be used to estimate the groundwater age. After 12.3 years, the half-life of 3H, exactly half of the 3H has decayed to 3He (Cook, 2020).

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