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Radioactive decay is the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles. Decay is said to occur in the parent nucleus and produce a daughter nucleus.

The trefoil symbol is used to indicate radioactive material. The Unicode encoding of this symbol is U+2622 (☢).

The SI unit for measuring radioactive decay is the becquerel (Bq). If a quantity of radioactive material produces one decay event per second, it has an activity of one Bq. Since any reasonably-sized sample of radioactive material contains very many atoms, a becquerel is a tiny level of activity; numbers on the order of gigabecquerels are seen more commonly.

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## General introduction

The neutrons and protons that constitute nuclei, as well as other particles that may approach them, are governed by several interactions. The strong nuclear force, not observed at the familiar macroscopic scale, is the most powerful force over subatomic distances. The electrostatic force is also significant. Of lesser importance are the weak nuclear force and the gravitational force.

The interplay of these forces is very complex. Some configurations of the particles in a nucleus have the property that, should they shift ever so slightly, the particles could fall into a lower-energy arrangement. One might draw an analogy with a tower of sand: while friction between the sand grains can support the tower's weight, a disturbance will unleash the force of gravity and the tower will collapse.

Such a collapse (a decay event) requres a certain activation energy. In the case of the tower of sand, this energy must come from outside the system, in the form of a gentle prod or swift kick. In the case of an atomic nucleus, it is already present. Quantum-mechanical particles are never at rest; they are in continuous random motion. Thus, if its constituent particles move in concert, the nucleus can spontaneously destabilize. The resulting transformation changes the structure of the nucleus; thus it is a nuclear reaction, in contrast to chemical reactions, which concern interactions of electrons with nuclei.

(Some nuclear reactions do involve external sources of energy, in the form of "collisions" with outside particles. However, these are not considered decay.)

## Decay timing

As discussed above, the decay of an unstable nucleus (radionuclide) is entirely random. Thus, it is impossible to predict when the radionuclide will decay. However, it is equally likely to decay at any time. Thus, given a sample of many radionuclides of the same type, the number of decay events that we expect to occur in any small interval of time dt is proportional to the number of radionuclides present. If this number is represented by the symbol N, we have the following differential equation (said to be first-order ):

$\frac{dN}{dt} = -\lambda N.$

In fact, the expected number of decays depends also on the type of the radionuclides, since some types decay more quckly than others. The decay constant λ accounts for this variation. The negative sign indicates that N decreases with each decay event. It can be shown that the solution to this equation is the following function:

$N(t) = N_0 e^{-\lambda t}. \,$

This function represents exponential decay (see that article for a derivation). It is in fact only approximate, for two reasons. First, the exponential function is continuous, but the physical quantity N can only take positive integer values. Second, because it describes a random process, it is only statistically true. However, for realistically encountered values of N, it is a very good approximation.

A parameter sometimes used to characterize exponential decay is the mean lifetime. If the lifetime of a radionuclide is the time that elapses between some initial reference time and the radionuclide's decay, the mean lifetime is the arithmetic mean of these. Mean lifetime is often represented by the symbol τ, and related to the decay constant in the following way:

$\tau = \frac{1}{\lambda}$

A more commonly used parameter is the half-life. Given a sample of radionuclides of the same type, the half-life is defined as the time expected to elapse before half of the radionuclides decay. The half-life is related to the decay constant as follows:

$t_{1/2} = \frac{\ln 2}{\lambda}$

This relationship between half-life and decay constant expresses the fact that highly radioactive substances are quickly spent, while those that radiate only weakly can endure very long. Half-lives of known radioisotopes vary widely, from 109 years for very nearly stable isotopes, to 10-6 seconds for highly unstable ones.

## Modes of decay

Radionuclides can undergo a number of different reactions. These are summarized in the following table, in rough order of increasing rarity. For brevity, neutrons, protons and electrons are represented by the symbols n, p+, and e- respectively.

Name of reaction Participating particles Excitation of nucleus Change in atomic number
Alpha decay Two n and two p+ emitted from nucleus Increases Decreases by two
Beta decay A n emits an e- and becomes a p+ Increases Increases by one
Gamma decay Excited nucleus releases a high-energy photon (gamma ray) Decreases No change
Positron emission A p+ emits a positron and becomes an n Increases Decreases by one
Internal conversion Excited nucleus transfers energy to an orbiting e- and ejects it Decreases No change
Proton emission A p+ ejected from nucleus  ?  ?
Neutron emission A n ejected from nucleus  ?  ?
Electron capture A p+ combines with an orbiting e- and becomes an n  ?  ?
Spontaneous fission Nucleus disintegrates into two or more smaller nuclei and other particles  ?  ?

Radioactive decay results in a loss of mass, which is converted to energy (the disintegration energy) according to the formula E = mc2. This energy is commonly released as photons (gamma radiation).

## Decay chains and multiple modes

Many radionuclides have several different observed modes of decay. Bismuth-212, for example, has three.

The daughter nuclide of a decay event is usually also unstable, sometimes even more unstable than the parent. If this is the case, it will proceed to decay again. A sequence of several decay events, producing in the end a stable nuclide, is a decay chain.

Of the commonly occurring forms of radioactive decay, the only one that changes the number of aggregate protons and neutrons (nucleons) contained in the nuclide is alpha emission, which reduces it by four. Thus, the number of nucleons modulo 4 is preserved across any decay chain.

## Occurrence and applications

According to the Big Bang theory, radioactive isotopes of the lightest elements H, He, and traces of Li) were produced very shortly after the emergence of the universe. However, these structures are so highly unstable that virtually none of these original nuclides remain today. With this exception, all unstable nuclides were formed in stars (particularly supernovae).

Radioactive decay has been put to use in the technique of radioisotopic labelling, used to track the passage of a chemical substance through a complex system (such as a living organism). A sample of the substance is synthesized with a high concentration of unstable atoms. The presence of the substance in one or another part of the system is determined by detecting the locations of decay events.

On the premise that radioactive decay is truly random (rather than merely chaotic), it has been used in hardware random-number generators.

## Related topics

• Decay chains http://www.epa.gov/radiation/understand/chain.htm
• Uranium-238 decay chain http://www.atral.com/U2381.html
• Sulfur-38 decay chain http://www.ag.ohio-state.edu/~rer/rerhtml/rer_20.html