KAHIBARO
Table of Contents
Long-lived natural decay families
Some radioactive nuclei found in nature are not isolated. They belong to long sequences of decays called natural radioactive series. A heavy unstable nucleus transforms into another nucleus, then another, and continues through many steps until a stable nucleus is reached. These families are called natural because their parent nuclei have half-lives long enough for measurable amounts to still exist on Earth today.
The most important natural radioactive series begin with very heavy nuclei, mainly uranium and thorium. As these nuclei decay, they produce chains of daughter nuclei through repeated alpha and beta decays. Each chain ends at a stable isotope of lead.
A natural radioactive series is a sequence of radioactive decays starting from a long-lived naturally occurring parent nucleus and ending at a stable nucleus.
In heavy natural series, the main decay modes are $\alpha$ decay and $\beta^-$ decay.
Why only a few natural series exist
Only a few decay families remain in nature because most possible parent nuclei would have decayed away long ago. The Earth is very old, so only nuclei with extremely long half-lives can still survive in significant amounts. These surviving parents feed the decay chains that we observe today.
A useful pattern comes from the mass number $A$. Alpha decay changes $A$ by 4, while beta decay leaves $A$ unchanged. Because of this, each decay chain stays within one residue class modulo 4. Historically, this led to the classification of decay families by forms like $4n$, $4n+1$, $4n+2$, and $4n+3$.
The main natural radioactive series
There are three principal natural radioactive series that are important in terrestrial radioactivity.
| Series name | Parent nucleus | Type by mass number | Stable end product |
|---|---|---|---|
| Thorium series | $^{232}\mathrm{Th}$ | $4n$ | $^{208}\mathrm{Pb}$ |
| Uranium series | $^{238}\mathrm{U}$ | $4n+2$ | $^{206}\mathrm{Pb}$ |
| Actinium series | $^{235}\mathrm{U}$ | $4n+3$ | $^{207}\mathrm{Pb}$ |
A fourth family, the neptunium series, has the form $4n+1$. Its original long-lived parent is not abundant in nature today, so it is not usually counted among the main natural series currently present on Earth.
In a decay chain, $\alpha$ decay changes the mass number and atomic number as
$$
A \to A - 4, \qquad Z \to Z - 2
$$
Beta-minus decay changes them as
$$
A \to A, \qquad Z \to Z + 1
$$
Therefore the value of $A \bmod 4$ stays constant throughout the whole series.
The thorium series
The thorium series begins with $^{232}\mathrm{Th}$, a very long-lived nucleus present in rocks and minerals. Through many intermediate daughters, it eventually ends as stable $^{208}\mathrm{Pb}$. This family is sometimes called the $4n$ series because all nuclei in it have mass numbers divisible by 4.
Some important members include radium, radon, and polonium isotopes. The gaseous radon isotope in this chain is $^{220}\mathrm{Rn}$, often called thoron. Because radon is a gas, it can escape from rocks and soils and enter the air.
A simplified path is
$$
^{232}\mathrm{Th} \to \cdots \to ^{228}\mathrm{Ra} \to \cdots \to ^{220}\mathrm{Rn} \to \cdots \to ^{208}\mathrm{Pb}
$$
The uranium series
The uranium series starts with $^{238}\mathrm{U}$ and ends with stable $^{206}\mathrm{Pb}$. It is the $4n+2$ family. This is one of the most important natural decay chains because $^{238}\mathrm{U}$ is widespread in the Earth's crust.
A famous member of this series is $^{222}\mathrm{Rn}$, the radon isotope most associated with indoor radon exposure. Since radon is chemically inert and gaseous, it can move through pores in soil and accumulate in enclosed spaces.
A simplified chain is
$$
^{238}\mathrm{U} \to \cdots \to ^{226}\mathrm{Ra} \to ^{222}\mathrm{Rn} \to \cdots \to ^{206}\mathrm{Pb}
$$
The actinium series
The actinium series begins with $^{235}\mathrm{U}$ and terminates at stable $^{207}\mathrm{Pb}$. It is the $4n+3$ family. Because $^{235}\mathrm{U}$ is less abundant than $^{238}\mathrm{U}$, this series contributes less to natural radioactivity in many ordinary materials.
This series contains several historically important isotopes, including actinium itself. A simplified form is
$$
^{235}\mathrm{U} \to \cdots \to ^{227}\mathrm{Ac} \to \cdots \to ^{207}\mathrm{Pb}
$$
A visual view of branching through alpha and beta decay
The decay path is not always a simple straight line. At some steps, a nucleus may have more than one possible decay mode, although one mode is often much more probable than the other. Still, the overall chain remains inside its modulo 4 family and eventually reaches the stable lead endpoint.
Why these series matter
Natural radioactive series are important because they are major sources of background radiation. Rocks, soil, groundwater, and building materials may contain uranium or thorium. Their daughters, especially radon and short-lived decay products, contribute significantly to natural radiation exposure.
These series also matter in geochronology. Because parent and daughter isotopes are linked by well-defined decay processes, they are used in radioactive dating. The full treatment of dating methods belongs elsewhere, but the natural series provide the physical basis for such techniques.
Secular equilibrium in natural series
If the parent nucleus has a much longer half-life than its daughters, the chain can approach secular equilibrium. In that case, the activity of each daughter becomes approximately equal to the activity of the parent, after enough time has passed and if none of the daughters escape from the material.
For natural series in rocks, this idea is often useful, but it can be broken when a daughter is chemically mobile or gaseous. Radon is the classic example. Once radon leaves the rock, the later part of the chain is no longer in equilibrium with the earlier part.
In secular equilibrium, for a long-lived parent and shorter-lived daughters,
$$
A_{\text{parent}} \approx A_{\text{daughter}}
$$
for each member of the chain after equilibrium is established.
This equality is about activity, not about equal numbers of atoms.
The special role of radon
Among all members of natural radioactive series, radon is especially important because it is a noble gas. It does not remain chemically bound in minerals the way many solid daughters do. It can diffuse through soil, enter houses, and then decay into solid radioactive daughters that may attach to dust and be inhaled.
The two most important naturally occurring radon isotopes from these series are shown below.
| Radon isotope | Series | Parent family |
|---|---|---|
| $^{222}\mathrm{Rn}$ | Uranium series | $^{238}\mathrm{U}$ chain |
| $^{220}\mathrm{Rn}$ | Thorium series | $^{232}\mathrm{Th}$ chain |
Because $^{222}\mathrm{Rn}$ has a longer half-life than $^{220}\mathrm{Rn}$, it is generally more important in environmental exposure.
Summary picture
The natural radioactive series are long decay families of heavy nuclei that still exist in nature because their parents are extremely long-lived. The three main natural series are the thorium series, uranium series, and actinium series. Each chain is built mainly from alpha and beta decays, stays within a fixed mass-number class modulo 4, and ends in a stable lead isotope. These series are central to natural background radiation and are especially important because of radon and its daughters.