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Radioactive decay

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Radioactive redirects here, for other uses, see Radioactive (disambiguation).

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.

1 General introduction
2 Discovery
3 Modes of decay
4 Decay chains and multiple modes
5 Occurrence and applications
6 Decay timing
7 See also
8 External links

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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 is the weak nuclear force. The gravitational force has no influence on nuclear processes.

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.)

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Discovery

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 the 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.

For instance, it was found that an electric or magnetic field could split such emissions into three beams. For want of better terms, the rays were given the alphabetic names alpha, beta, and gamma, names they still hold today. It was immediately obvious from the direction of electromagnetic forces that alpha rays carried a positive charge, beta rays carried a negative charge, and gamma rays were neutral. From the magnitude of deflection, it was also clear that alpha particles were much more massive than beta particles. Passing alpha rays through a thin glass membrane and trapping them in a discharge tube allowed researchers to study the emission spectrum of the resulting gas, and ultimately prove that alpha particles are in fact helium nuclei. Other experiments showed the similarity between beta radiation and cathode rays, and between gamma radiation and X-rays.

These researchers also discovered that many other chemical elements have radioactive isotopes. Radioactivity also guided Marie Curie to isolate radium from barium; the two elements' chemical similarity would otherwise have made them difficult to distinguish.

The dangers of radioactivity and of radiation were not immediately recognized. Acute radiation poisoning was observed early on, but it was initially assumed that, like fire, if no immediate effect was observed there was no danger. Moreover, it was not realized that if radioactive material was taken into the body, it would continue to radiate while inside, often causing cancer or other severe problems. Many physicians and corporations began marketing radioactive substances as patent medicine; one particularly alarming example was radium enema treatments. Marie Curie, before her death, spoke out against this sort of treatment, warning that the effects of radiation on the human body were not well understood.

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Modes of decay

Radionuclides can undergo a number of different reactions. These are summarized in the following table. A nucleus with charge (atomic number) Z and atomic weight A is represented as (A, Z).

Mode of decay	Participating particles	Daughter nucleus
Decays with emission of nucleons:
Alpha decay	An alpha particle (A=4, Z=2) emitted from nucleus	(A-4, Z-2)
Proton emission	A proton ejected from nucleus	(A-1, Z-1)
Neutron emission	A neutron ejected from nucleus	(A-1, Z)
Spontaneous fission	Nucleus disintegrates into two or more random smaller nuclei and other particles	-
Cluster decay	Nucleus emits a specific type of smaller nucleus (A₁, Z₁) larger than an alpha particle	(A-A₁, Z-Z₁) + (A₁,Z₁)
Different modes of beta decay:
Beta decay	A nucleus emits an electron and an antineutrino	(A, Z+1)
Positron emission	A nucleus emits a positron and a neutrino	(A, Z-1)
Electron capture	A nucleus captures an orbiting electron and emits a neutrino	(A, Z-1)
Double beta decay	A nucleus emits two electrons and two antineutrinos	(A, Z+2)
Double electron capture	A nucleus absorbes two orbital electrons and emits two neutrinos	(A, Z-2)
Electron capture with positron emission	A nucleus absorbs one orbital electron, emits one positron and two neutrinos	(A, Z-2)
Double positron emission	A nucleus emits two positrons and two neutrinos	(A, Z-2)
Transitions between states of the same nucleus:
Gamma decay	Excited nucleus releases a high-energy photon (gamma ray)	(A, Z)
Internal conversion	Excited nucleus transfers energy to an orbital electron and ejects it	(A, Z)

Radioactive decay results in a loss of mass, which is converted to energy (the disintegration energy) according to the formula $E = m c 2$ . This energy is released as kinetic energy of the emitted particles.

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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.

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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.

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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 –dN 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, then the probability of decay (– dN/N) is proportional to dt:

$\left(-\frac{dN}{N} \right) = \lambda \cdot dt$

Rearranging, we obtain the following first-order differential equation:

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

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:

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

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:

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

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:

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

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 10²⁴ years for very nearly stable nuclides, to 10^-6 seconds for highly unstable ones.

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