Radioactive decay

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Radioactive decay is the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles (radiation). Decay is said to occur in the parent nucleus and produces a daughter nucleus. This is a random process, i.e. it is impossible to predict the decay of individual atoms.

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, one 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 involve changes in the arrangement of the outer electrons of atoms.

(Some nuclear reactions do involve external sources of energy, in the form of "collisions" with outside particles. However, these are not considered decay. Rather this is induced fission or fusion.)


Radioactivity was first discovered in 1896 by the French scientist Henri Becquerel while working on phosphorescent materials. These materials glow in the dark after exposure to light, and he thought that the glow produced in cathode ray tubes by X-rays might somehow be connected with phosphorescence. So he tried wrapping a photographic plate in black paper and placing various phosphorescent minerals on it. All results were negative until he tried using uranium salts. The result with these compounds was a deep blackening of the plate.

However, it soon became clear that the blackening of the plate had nothing to do with phosphorescence because the plate blackened when the mineral was kept in the dark. Also non-phosphorescent salts of uranium and even metallic uranium blackened the plate. Clearly there was some new form of radiation that could pass through paper that was causing the plate to blacken.

At first it seemed that the new radiation was similar to then recently discovered x-rays. However further research by Becquerel, Marie Curie, Pierre Curie, Ernest Rutherford and others discovered that radioactivity was significantly more complicated. Different types of decay can occur.

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.

Reaction Participating particles 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 an antineutrino 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 a neutrino 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 ? Decreases by one
Neutron emission A n ejected from nucleus ? No Change
Electron capture A p+ combines with an orbiting e-, emits a neutrino and becomes an n ? Decreases by one
Spontaneous fission Nucleus disintegrates into two or more random smaller nuclei and other particles ? ?
Cluster decay Nucleus emits a specific type of smaller nucleus (larger than an alpha particle) ? ?
Double beta decay Two ns emit two e-s and two antineutrinos and become two p+s ? Increases by two

Radioactive decay results in a loss of mass, which is converted to energy (the disintegration energy) according to the formula Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle E = mc^2} . 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.

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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \frac{dN}{dt} = -\lambda N}

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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle N(t) = N_0 e^{-\lambda t} \,\!}

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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle \tau = \frac{1}{\lambda}}

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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "":): {\displaystyle t_{1/2} = \frac{\ln 2}{\lambda}}

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 more than 1012 years for very nearly stable nuclides, to 10-6 seconds for highly unstable ones.

See also

External links

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