Decay chain

In nuclear science, the decay chain refers to the radioactive decay of different discrete radioactive decay products as a chained series of transformations. Most radioactive elements do not decay directly to a stable state, but rather undergo a series of decays until eventually a stable isotope is reached.

Decay stages are referred to by their relationship to previous or subsequent stages. A parent isotope is one that undergoes decay to form a daughter isotope. The daughter isotope may be stable or it may decay to form a daughter isotope of its own. The daughter of a daughter isotope is sometimes called a granddaughter isotope.

The time it takes for a single parent atom to decay to an atom of its daughter isotope can vary widely, not only for different parent-daughter chains, but also for identical pairings of parent and daughter isotopes. While the decay of a single atom occurs spontaneously, the decay of an initial population of identical atoms over time, t, follows a decaying exponential distribution, e^-λt, where λ is called a decay constant. Because of this exponential nature, one of the properties of an isotope is its half-life, the time by which half of an initial number of identical parent radioisotopes have decayed to their daughters. Half-lives have been determined in laboratories for thousands of radioisotopes (or, radionuclides). These can range from nearly instantaneous to as much as 10¹⁹ years or more.

The intermediate stages often emit more radioactivity than the original radioisotope. For example, natural uranium is not significantly radioactive, but samples of pitchblende, a uranium ore, are radioactive because of the radium and other daughter isotopes they contain. Not only are unstable radium isotopes significant radioactive emitters, but they also generate gaseous radon as the next stage in the decay chain. Thus, radon is a naturally occurring radioactive gas, which is the leading cause of lung cancer in non-smokers[1].

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Types

  The four most common modes of radioactive decay are: alpha decay, beta minus decay, beta plus decay (considered as both positron emission and electron capture) and isomeric transition. Of these decay processes, alpha decay changes the atomic mass number of the nucleus, and always decreases it by four. Because of this, almost any decay will result in a nucleus whose atomic mass number has the same residue mod 4, dividing all nuclides into four classes. The members of any possible decay chain must be drawn entirely from one of these classes.

Three main decay chains (or families) are observed in nature, commonly called the thorium series, the radium series (not uranium series), and the actinium series, representing three of these four classes, and ending in three different, stable isotopes of lead. The mass number of every isotope in these chains can be represented as A=4n, A=4n+2 and A=4n+3, respectively. The starting isotopes of these three have existed since the formation of the earth. The fourth chain, the neptunium series with A=4n+1, due to quite short half life time of its starting isotope ²³⁷Np, is already extinct, except for the final rate-limiting step. The ending isotope of this chain is ²⁰⁵Tl. Some older sources give the final isotope as ²⁰⁹Bi, but it was recently discovered that ²⁰⁹Bi is radioactive with half-life of 1.9×10¹⁹ years.

There are also many shorter chains, for example carbon-14. On the earth, most of the starting isotopes of these chains are generated by cosmic radiation.

In the tables below, the minor branches of decay (with the branching ratio of less than 0.0001%) are omitted. The energy release includes the total kinetic energy of all the emitted particles (electrons, alpha particles, gamma quanta, neutrinos, Auger electrons and X-rays) and the recoil nucleus.

Thorium series

The 4n chain of Th-232 is commonly called the "thorium series". In this chart, the letter 'a' represents a Julian year (365.25 days).

Radium series

The 4n+2 chain of U-238 is commonly called the "radium series".

Actinium series

The 4n+3 chain of U-235 is commonly called the "actinium series".

Neptunium series

4n + 1 chain: