Radioactive decay

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 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.

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) requires 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 and it is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any time. Therefore, given a sample of a particular radioisotope, the number of decay events expected to occur in a small interval of time dt is proportional to the number of atoms present. If N is the number of atoms, the following first-order differential equation can be written:

<math>\frac{dN}{dt} = -\lambda N<math>

Particular radionuclides decay at different rates, each having its own decay constant (λ). The negative sign indicates that N decreases with each decay event. The solution to this equation is the following function:

<math>N(t) = N_0 e^{-\lambda t} \,\!<math>

This function represents exponential decay. It is only an approximate solution, for two reasons. Firstly, the exponential function is continuous, but the physical quantity N can only take positive integer values. Secondly, because it describes a random process, it is only statistically true. However, in most common cases, N is a very large number and the function is a good approximation.

In addition to the decay constant, radioactive decay is sometimes characterized by the mean lifetime. Each atom "lives" for a finite amount of time before it decays, and the mean lifetime is the arithmetic mean of all the atoms' lifetimes. It is represented by the symbol τ, and is related to the decay constant as follows:

<math>\tau = \frac{1}{\lambda}<math>

A more commonly used parameter is the half-life. Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. The half life is related to the decay constant as follows:

<math>t_{1/2} = \frac{\ln 2}{\lambda}<math>

This relationship between the half-life and the decay constant shows that highly radioactive substances are quickly spent, while those that radiate weakly endure longer. Half-lives of known radionuclides vary widely, from 10⁹ years for very nearly stable nuclides, 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.

Radioactive decay results in a loss of mass, which is converted to energy (the disintegration energy) according to the formula <math>E = mc^2<math>. 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

• Nuclear physics
• Poisson process
• Radiation
• Radioactive contamination

External links

• 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)
• List of decay modes (http://www.nuclides.net/Applets/about_radioactive_decay.htm)
• More examples (http://www.public.iastate.edu/~chemistry/Courses/chem178/apr23.html) - does not work...
• Uranium-232 decay chain, Bismuth-212 decay modes (http://www.nuclides.net/Nuclides_2000/U-232.htm)
• Nomenclature of Radiochemistry (http://www.radiochemistry.org/nomenclature/i.htm)
• Radiochemistry Primer (http://cadfael.cmc.sandia.gov/Central/public-docs/APrimeronRadiochemistry1.htm) - does not work...
• Nuclear stability (http://www2.slac.stanford.edu/vvc/theory/nuclearstability.html)
• A page explaining nuclear decay (http://207.10.97.102/chemzone/lessons/11nuclear/nuclear.htm)
• Table of Nuclides (http://atom.kaeri.re.kr/ton/nuc2.html)be:Радыеактыўнасьць

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