this is not a problem. The gas rises and is released to the atmosphere, where it is dispersed and diluted to very low levels. But if radon gas is released into a confined space such as a home, especially one that is well insulated and not well ventilated, radon gas concentrations can reach hazardous levels. Most radon gas enters the home through cracks in the walls and foundations, either as gas or in water from which the gas is released. Most of the remainder is released when water from radon‐contaminated wells is used, again releasing radon into the home atmosphere. The problem is especially bad in winter and spring months when homes are heated, basements flooded, and ventilation poor. As warm air in the home rises, air is drawn from the soil into the home, increasing radon concentrations. The insulation that increases heat efficiency also increases radon concentrations. What can be done to reduce the risk? Making sure that basements and foundation walls are well sealed and improving ventilation can reduce radon concentrations to acceptable levels, even in homes built on soils with high concentrations of uranium. Radon test kits can be purchased from hardware stores. If indoor radon levels exceed 4 pCi/l, remediation is recommended by the installation of indoor air pumps and ventilation pipes to remove gases from beneath basement floors. Radon remediation typically costs $1500 and is highly recommended as a health measure.
In the following sections we have chosen a few examples, among the many that exist, to illustrate the importance of radioactive isotopes and decay series in the study of Earth materials.
Age determinations using radioactive decay series
Table 3.3 lists several radioactive parent to stable daughter transformations that can be used to determine the formation ages of Earth materials. All these are based on the principle that after the radioactive isotope is incorporated into Earth materials, the ratio of radioactive parent isotopes to stable daughter isotopes decreases through time by radioactive decay. The rate at which such parent: daughter ratios decrease depends on the rate of decay, which is given by the decay constant (λ) , the proportion of the remaining radioactive atoms that will decay per unit of time. One useful formula that governs decay series states that the number of radioactive atoms remaining at any given time (N) is equal to the number of radioactive atoms originally present in the sample (N0) multiplied by a negative exponential factor (e–λt) that increases with the rate of decay ( λ ) and the time since the sample formed (t), that is, its age. These relationships are given by:
Table 3.3 Systematics of radioactive isotopes important in age determinations in Earth materials.
| Decay series | Decay process | Decay constant (λ) | Half‐life | Applicable dating range |
|---|---|---|---|---|
| 14C → 14N | Beta decay | 1.29 × 10−4/year | 5.37 Ka | <60 Ka |
| 40K → 40Ar | Electron capture | 4.69 × 10−10/year | 1.25 Ga | 25 Ka to >4.5 Ga |
| 87Rb → 87Sr | Beta decay | 1.42 × 10−11/year | 48.8 Ga | 10 Ma to >4.5 Ga |
| 147Sm → 143Nd | Alpha decay | 6.54 × 10−12/year | 106 Ga | 200 Ma to >4.15 Ga |
| 232Th → 208Pb | Beta and alpha decays | 4.95 × 10−11/year | 14.0 Ga | 10 Ma to >4.5 Ga |
| 235U → 207Pb | Beta and alpha decays | 9.85 × 10−10/year | 704 Ma | 10 Ma to >4.5 Ga |
| 238U → 206Pb | Beta and alpha decays | 1.55 × 10−10/year | 4.47 Ga | 10 Ma to >4.5 Ga |
It should be clear from the formula that when t = 0, N = N0, and that N becomes smaller through time as a function of the rate of decay given by the decay constant; rapidly for a large decay constant, more slowly for a small one. Figure 3.13 illustrates a typical decay curve, showing how the abundance of the radioactive parent isotope decreases exponentially over time while the abundance of the daughter isotope increases in a reciprocal manner. The two curves cross where the number of radioactive parent and stable daughter atoms is equal. The time required for this to occur is called the half‐life of the decay series and is the time required for one half of the radioactive isotopes to decay into stable daughter isotopes.
Figure 3.13 Progressive change in the proportions of radioactive parent (N) and daughter (D) isotopes over time, in terms of number of half‐lives.
More generally, the age of any sample may be calculated from the following equation:
where t = age, λ = the decay constant, d = number of stable daughter atoms and p = number of radioactive parent atoms. Where stable daughter atoms were present in the original sample, a correction must be made to account for them, as explained below.
Many radioactive to stable isotope decay series, each with a unique decay constant, can be used, often together, to determine robust formation ages for Earth materials, especially for older materials. Table 3.3 summarizes some common examples. Three of these are discussed in more detail in the sections that follow.
Uranium–lead systematics
Uranium (U) occurs in two radioactive isotopes, both of which decay in steps to different stable isotopes of lead (Pb). The closely related actinide element thorium (Th) decays in a similar fashion to yet another stable isotope of lead. The essential information on the radioactive and stable isotopes involved for these three decay series (238U →206Pb,235U →207Pb, and232Th → 208Pb) is summarized in
