Radioactive decay

Radioactive decay

Overview
Radioactive decay is the process by which an atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 of an unstable atom loses energy by emitting ionizing particles (ionizing radiation
Ionizing radiation
Ionizing radiation is radiation composed of particles that individually have sufficient energy to remove an electron from an atom or molecule. This ionization produces free radicals, which are atoms or molecules containing unpaired electrons...

). The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom. Usually, radioactive decay happens due to a process confined to the nucleus of the unstable atom, but, on occasion (as with the different processes of electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

 and internal conversion
Internal conversion
Internal conversion is a radioactive decay process where an excited nucleus interacts with an electron in one of the lower atomic orbitals, causing the electron to be emitted from the atom. Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but...

), an inner electron of the radioactive atom is also necessary to the process.

Radioactive decay is a stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...

 (i.e., random) process at the level of single atoms, in that, according to quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, it is impossible to predict when a given atom will decay.
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Encyclopedia
Radioactive decay is the process by which an atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 of an unstable atom loses energy by emitting ionizing particles (ionizing radiation
Ionizing radiation
Ionizing radiation is radiation composed of particles that individually have sufficient energy to remove an electron from an atom or molecule. This ionization produces free radicals, which are atoms or molecules containing unpaired electrons...

). The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom. Usually, radioactive decay happens due to a process confined to the nucleus of the unstable atom, but, on occasion (as with the different processes of electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

 and internal conversion
Internal conversion
Internal conversion is a radioactive decay process where an excited nucleus interacts with an electron in one of the lower atomic orbitals, causing the electron to be emitted from the atom. Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but...

), an inner electron of the radioactive atom is also necessary to the process.

Radioactive decay is a stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...

 (i.e., random) process at the level of single atoms, in that, according to quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, it is impossible to predict when a given atom will decay. However, the chance that a given atom will decay is constant over time. For a large number of identical atoms (of the same nuclide
Nuclide
A nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....

), the decay rate for the collection is predictable to the extent allowed by the law of large numbers
Law of large numbers
In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times...

, and is easily calculated from the measured decay constant of the nuclide (or equivalently from the half-life
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

).

The decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide
Radionuclide
A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or to an atomic electron. The radionuclide, in this process, undergoes radioactive decay, and emits gamma...

, transforms to an atom with a nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide. Often the parent and daughter are different chemical element
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

s, and in such cases the decay process results in nuclear transmutation
Nuclear transmutation
Nuclear transmutation is the conversion of one chemical element or isotope into another. In other words, atoms of one element can be changed into atoms of other element by 'transmutation'...

. In an example of this, a carbon-14
Carbon-14
Carbon-14, 14C, or radiocarbon, is a radioactive isotope of carbon with a nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues , to date archaeological, geological, and hydrogeological...

 atom (the "parent") emits radiation (a beta particle
Beta particle
Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles emitted are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay...

, antineutrino, and a gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

) and transforms to a nitrogen-14 atom (the "daughter"). By contrast, there exist two types of radioactive decay processes (gamma decay and internal conversion
Internal conversion
Internal conversion is a radioactive decay process where an excited nucleus interacts with an electron in one of the lower atomic orbitals, causing the electron to be emitted from the atom. Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but...

 decay) that do not result in transmutation, but only decrease the energy of an excited nucleus. This results in an atom of the same element as before but with a nucleus in a lower energy state. An example is the nuclear isomer
Nuclear isomer
A nuclear isomer is a metastable state of an atomic nucleus caused by the excitation of one or more of its nucleons . "Metastable" refers to the fact that these excited states have half-lives more than 100 to 1000 times the half-lives of the other possible excited nuclear states...

 technetium-99m
Technetium-99m
Technetium-99m is a metastable nuclear isomer of technetium-99, symbolized as 99mTc. The "m" indicates that this is a metastable nuclear isomer, i.e., that its half-life of 6 hours is considerably longer than most nuclear isomers that undergo gamma decay...

 decaying, by the emission of a gamma ray, to an atom of technetium-99
Technetium-99
Technetium-99 is an isotope of technetium which decays with a half-life of 211,000 years to stable ruthenium-99, emitting soft beta rays, but no gamma rays....

.

Nuclides produced by radioactive decay are called radiogenic nuclide
Radiogenic nuclide
A radiogenic nuclide is a nuclide that is produced by a process of radioactive decay. It may itself be radioactive, or stable.Radiogenic nuclides form some of the most important tools in geology...

s, whether they themselves are stable
Stable isotope
Stable isotopes are chemical isotopes that may or may not be radioactive, but if radioactive, have half-lives too long to be measured.Only 90 nuclides from the first 40 elements are energetically stable to any kind of decay save proton decay, in theory...

 or not. There exist stable radiogenic nuclides that were formed from short-lived extinct radionuclide
Extinct radionuclide
An extinct radionuclide is one that scientists believe was formed by primordial processes, such as stellar nucleogenesis in the supernova that contributed radioisotopes to the early solar system, about 4.6 billion years ago...

s in the early solar system. The extra presence of stable radiogenic nuclides against the background of primordial stable nuclides can be inferred by various means. Presently-radioactive nuclides are from three sources: many naturally-occurring radionuclide
Radionuclide
A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or to an atomic electron. The radionuclide, in this process, undergoes radioactive decay, and emits gamma...

s are short-lived radiogenic nuclides that are the daughters of ongoing radioactive primordial nuclide
Primordial nuclide
In geochemistry and geonuclear physics, primordial nuclides or primordial isotopes are nuclides found on the earth that have existed in their current form since before Earth was formed. Only 288 such nuclides are known...

s (types of radioactive atoms that have been present since the beginning of the Earth and solar system). Other naturally-occurring radioactive nuclides are cosmogenic nuclide
Cosmogenic nuclide
See also Environmental radioactivity#NaturalCosmogenic nuclides are rare isotopes created when a high-energy cosmic ray interacts with the nucleus of an in situ solar system atom, causing cosmic ray spallation...

s, formed by cosmic ray bombardment of material in the Earth's atmosphere or crust. Finally, some primordial nuclides are radioactive, but are so long-lived that they remain present from the primordial solar nebula. For a summary table showing the number of stable nuclides and of radioactive nuclides in each category, see radionuclide
Radionuclide
A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or to an atomic electron. The radionuclide, in this process, undergoes radioactive decay, and emits gamma...

.

The SI
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

 unit of activity is the becquerel
Becquerel
The becquerel is the SI-derived unit of radioactivity. One Bq is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. The Bq unit is therefore equivalent to an inverse second, s−1...

 (Bq). One Bq is defined as one transformation (or decay) per second. Since any reasonably-sized sample of radioactive material contains many atoms, a Bq is a tiny measure of activity; amounts on the order of GBq (gigabecquerel, 1 x 109 decays per second) or TBq (terabecquerel, 1 x 1012 decays per second) are commonly used. Another unit of radioactivity is the curie
Curie
The curie is a unit of radioactivity, defined asThis is roughly the activity of 1 gram of the radium isotope 226Ra, a substance studied by the pioneers of radiology, Marie and Pierre Curie, for whom the unit was named. In addition to the curie, activity can be measured using an SI derived unit,...

, Ci, which was originally defined as the amount of radium emanation (radon-222) in equilibrium with one gram of pure radium
Radium
Radium is a chemical element with atomic number 88, represented by the symbol Ra. Radium is an almost pure-white alkaline earth metal, but it readily oxidizes on exposure to air, becoming black in color. All isotopes of radium are highly radioactive, with the most stable isotope being radium-226,...

, isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 Ra-226. At present it is equal, by definition, to the activity of any radionuclide decaying with a disintegration rate of 3.7 × 1010 Bq. The use of Ci is currently discouraged by the SI.

Explanation


The neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s and proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s that constitute nuclei, as well as other particles that approach close enough to them, are governed by several interactions. The strong nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...

, not observed at the familiar macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...

 scale, is the most powerful force over subatomic distances. The electrostatic force
Coulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

 is almost always significant, and, in the case of beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

, the weak nuclear force
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

 is also involved.

The interplay of these forces produces a number of different phenomena in which energy may be released by rearrangement of particles in the nucleus or the change of one particle into others. The rearrangement is hindered energetically, so that it does not occur immediately. Random quantum vacuum fluctuations are theorized to promote relaxation to a lower energy state (the "decay") in a phenomenon known as quantum tunneling.

One might draw an analogy with a snowfield on a mountain: While friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 between the ice crystals may be supporting the snow's weight, the system is inherently unstable with regard to a state of lower potential energy. A disturbance would thus facilitate the path to a state of greater entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

: The system will move towards the ground state, producing heat, and the total energy will be distributable over a larger number of quantum states. Thus, an avalanche
Avalanche
An avalanche is a sudden rapid flow of snow down a slope, occurring when either natural triggers or human activity causes a critical escalating transition from the slow equilibrium evolution of the snow pack. Typically occurring in mountainous terrain, an avalanche can mix air and water with the...

 results. The total energy does not change in this process, but, because of the law of entropy
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

, avalanches happen only in one direction and that is toward the "ground state
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...

" — the state with the largest number of ways in which the available energy could be distributed.

Such a collapse (a decay event) requires a specific activation energy
Activation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...

. For a snow avalanche, this energy comes as a disturbance from outside the system, although such disturbances can be arbitrarily small. In the case of an excited atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

, the arbitrarily small disturbance comes from quantum vacuum fluctuations. A radioactive nucleus (or any excited system in quantum mechanics) is unstable, and can, thus, spontaneously stabilize to a less-excited system. The resulting transformation alters the structure of the nucleus and results in the emission of either a photon or a high-velocity particle that has mass (such as an electron, alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...

, or other type).

Discovery


Radioactivity was first discovered during 1896 by the French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 scientist Henri Becquerel
Henri Becquerel
Antoine Henri Becquerel was a French physicist, Nobel laureate, and the discoverer of radioactivity along with Marie Curie and Pierre Curie, for which all three won the 1903 Nobel Prize in Physics.-Early life:...

, while working on phosphorescent
Phosphorescence
Phosphorescence is a specific type of photoluminescence related to fluorescence. Unlike fluorescence, a phosphorescent material does not immediately re-emit the radiation it absorbs. The slower time scales of the re-emission are associated with "forbidden" energy state transitions in quantum...

 materials. These materials glow in the dark after exposure to light, and he suspected that the glow produced in cathode ray tube
Cathode ray tube
The cathode ray tube is a vacuum tube containing an electron gun and a fluorescent screen used to view images. It has a means to accelerate and deflect the electron beam onto the fluorescent screen to create the images. The image may represent electrical waveforms , pictures , radar targets and...

s by X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s might be associated with phosphorescence. He wrapped a photographic plate in black paper and placed various phosphorescent salts on it. All results were negative until he used uranium salts
Uranium
Uranium is a silvery-white metallic chemical element in the actinide series of the periodic table, with atomic number 92. It is assigned the chemical symbol U. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons...

. The result with these compounds was a blackening of the plate. These radiations were called Becquerel Rays.

It soon became clear that the blackening of the plate did not have anything to do with phosphorescence, because the plate blackened when the mineral was in the dark. Non-phosphorescent salts of uranium and metallic uranium also blackened the plate. It was clear that there is a form of radiation that could pass through paper that was causing the plate to become black.

At first it seemed that the new radiation was similar to the then recently-discovered X-rays. Further research by Becquerel, Ernest Rutherford
Ernest Rutherford
Ernest Rutherford, 1st Baron Rutherford of Nelson OM, FRS was a New Zealand-born British chemist and physicist who became known as the father of nuclear physics...

, Paul Villard, Pierre Curie
Pierre Curie
Pierre Curie was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity and radioactivity, and Nobel laureate. He was the son of Dr. Eugène Curie and Sophie-Claire Depouilly Curie ...

, Marie Curie
Marie Curie
Marie Skłodowska-Curie was a physicist and chemist famous for her pioneering research on radioactivity. She was the first person honored with two Nobel Prizes—in physics and chemistry...

, and others discovered that this form of radioactivity was significantly more complicated. Different types of decay can occur, producing very different types of radiation. Rutherford was the first to realize that they all occur with the same mathematical exponential formula (see below), and to realize that many decay processes resulted in the transmutation
Nuclear transmutation
Nuclear transmutation is the conversion of one chemical element or isotope into another. In other words, atoms of one element can be changed into atoms of other element by 'transmutation'...

 of one element to another.

The early researchers also discovered that many other chemical element
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

s besides uranium have radioactive isotope
Radionuclide
A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or to an atomic electron. The radionuclide, in this process, undergoes radioactive decay, and emits gamma...

s.
A systematic search for the total radioactivity in uranium ores also guided Marie Curie
Marie Curie
Marie Skłodowska-Curie was a physicist and chemist famous for her pioneering research on radioactivity. She was the first person honored with two Nobel Prizes—in physics and chemistry...

 to isolate a new element polonium
Polonium
Polonium is a chemical element with the symbol Po and atomic number 84, discovered in 1898 by Marie Skłodowska-Curie and Pierre Curie. A rare and highly radioactive element, polonium is chemically similar to bismuth and tellurium, and it occurs in uranium ores. Polonium has been studied for...

 and to separate a new element radium
Radium
Radium is a chemical element with atomic number 88, represented by the symbol Ra. Radium is an almost pure-white alkaline earth metal, but it readily oxidizes on exposure to air, becoming black in color. All isotopes of radium are highly radioactive, with the most stable isotope being radium-226,...

 from barium
Barium
Barium is a chemical element with the symbol Ba and atomic number 56. It is the fifth element in Group 2, a soft silvery metallic alkaline earth metal. Barium is never found in nature in its pure form due to its reactivity with air. Its oxide is historically known as baryta but it reacts with...

. The two elements' chemical similarity would otherwise have made them difficult to distinguish.

Danger of radioactive substances





The dangers of radioactivity and radiation were not immediately recognized. Acute effects of radiation were first observed in the use of X-rays when electrical engineer and physicist Nikola Tesla
Nikola Tesla
Nikola Tesla was a Serbian-American inventor, mechanical engineer, and electrical engineer...

 intentionally subjected his fingers to X-rays during 1896. He published his observations concerning the burns that developed, though he attributed them to ozone rather than to X-rays. His injuries healed later.

The genetic effects of radiation, including the effect on cancer risk, were recognized much later. During 1927, Hermann Joseph Muller
Hermann Joseph Muller
Hermann Joseph Muller was an American geneticist, educator, and Nobel laureate best known for his work on the physiological and genetic effects of radiation as well as his outspoken political beliefs...

 published research showing genetic effects, and in 1946 was awarded the Nobel prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

 for his findings.

Before the biological effects of radiation were known, many physicians and corporations had begun marketing radioactive substances as patent medicine
Patent medicine
Patent medicine refers to medical compounds of questionable effectiveness sold under a variety of names and labels. The term "patent medicine" is somewhat of a misnomer because, in most cases, although many of the products were trademarked, they were never patented...

, glow-in-the-dark pigments, and radioactive quackery
Radioactive quackery
Radioactive quackery refers to various products sold during the early 20th century, after the discovery of radioactivity, which promised radioactivity as a cure for various illnesses...

. Examples were radium enema
Enema
An enema is the procedure of introducing liquids into the rectum and colon via the anus. The increasing volume of the liquid causes rapid expansion of the lower intestinal tract, often resulting in very uncomfortable bloating, cramping, powerful peristalsis, a feeling of extreme urgency and...

 treatments, and radium-containing waters to be drunk as tonics. Marie Curie
Marie Curie
Marie Skłodowska-Curie was a physicist and chemist famous for her pioneering research on radioactivity. She was the first person honored with two Nobel Prizes—in physics and chemistry...

 protested this sort of treatment, warning that the effects of radiation on the human body were not well understood (Curie later died from aplastic anemia
Aplastic anemia
Aplastic anemia is a condition where bone marrow does not produce sufficient new cells to replenish blood cells. The condition, per its name, involves both aplasia and anemia...

, which was likely caused by exposure to ionizing radiation). By the 1930s, after a number of cases of bone necrosis and death in enthusiasts, radium-containing medical products had been largely removed from the market.

Types of decay


As for types of radioactive radiation, it was found that an electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

 or magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 could split such emissions into three types of beams. For lack of better terms, the rays were given the alphabetic
Greek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

 names alpha
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...

, beta
Beta particle
Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles emitted are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay...

, and gamma
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

, still in use today. While alpha decay was seen only in heavier elements (atomic number 52, tellurium, and greater), the other two types of decay were seen in all of the elements.

In analyzing the nature of the decay products, it was obvious from the direction of electromagnetic forces produced upon the radiations by external magnetic and electric fields that alpha rays
Alpha decay
Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle and thereby transforms into an atom with a mass number 4 less and atomic number 2 less...

 carried a positive charge, beta rays
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

 carried a negative charge, and gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

s were neutral. From the magnitude of deflection, it was clear that alpha particles were much more massive than beta particles. Passing alpha particles through a very thin glass window and trapping them in a discharge tube
Neon lamp
A neon lamp is a miniature gas discharge lamp that typically contains neon gas at a low pressure in a glass capsule. Only a thin region adjacent to the electrodes glows in these lamps, which distinguishes them from the much longer and brighter neon tubes used for signage...

 allowed researchers to study the emission spectrum
Emission spectrum
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....

 of the resulting gas, and ultimately prove that alpha particles are helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 nuclei. Other experiments showed the similarity between classical beta radiation and cathode ray
Cathode ray
Cathode rays are streams of electrons observed in vacuum tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, the glass opposite of the negative electrode is observed to glow, due to electrons emitted from and travelling perpendicular to the cathode Cathode...

s: They are both streams of electrons. Likewise gamma radiation and X-rays were found to be similar high-energy electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

.

The relationship between types of decays also began to be examined: For example, gamma decay was almost always found associated with other types of decay, occurring at about the same time, or afterward. Gamma decay as a separate phenomenon (with its own half-life, now termed isomeric transition
Isomeric transition
An isomeric transition is a radioactive decay process that involves emission of a gamma ray from an atom where the nucleus is in an excited metastable state, referred to in its excited state, as a nuclear isomer....

), was found in natural radioactivity to be a result of the gamma decay of excited metastable nuclear isomer
Nuclear isomer
A nuclear isomer is a metastable state of an atomic nucleus caused by the excitation of one or more of its nucleons . "Metastable" refers to the fact that these excited states have half-lives more than 100 to 1000 times the half-lives of the other possible excited nuclear states...

s, in turn created from other types of decay.

Although alpha, beta, and gamma were found most commonly, other types of decay were eventually discovered. Shortly after the discovery of the positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

 in cosmic ray products, it was realized that the same process that operates in classical beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

 can also produce positrons (positron emission
Positron emission
Positron emission or beta plus decay is a type of beta decay in which a proton is converted, via the weak force, to a neutron, releasing a positron and a neutrino....

). In an analogous process, instead of emitting positrons and neutrinos, some proton-rich nuclides were found to capture their own atomic electrons (electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

), and emit only a neutrino (and usually also a gamma ray). Each of these types of decay involves the capture or emission of nuclear electrons or positrons, and acts to move a nucleus toward the ratio of neutrons to protons that has the least energy for a given total number of nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

s (neutrons plus protons).

Shortly after discovery of the neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 in 1932, it was discovered by Enrico Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...

 that certain rare decay reactions yield neutrons as a decay particle (neutron emission
Neutron emission
Neutron emission is a type of radioactive decay of atoms containing excess neutrons, in which a neutron is simply ejected from the nucleus. Two examples of isotopes which emit neutrons are helium-5 and beryllium-13...

). Isolated proton emission
Proton emission
Proton emission is a type of radioactive decay in which a proton is ejected from a nucleus. Proton emission can occur from high-lying excited states in a nucleus following a beta decay, in which case the process is known as beta-delayed proton emission, or can occur from the ground state of very...

 was eventually observed in some elements. It was also found that some heavy elements may undergo spontaneous fission
Spontaneous fission
Spontaneous fission is a form of radioactive decay characteristic of very heavy isotopes. Because the nuclear binding energy reaches a maximum at a nuclear mass greater than about 60 atomic mass units , spontaneous breakdown into smaller nuclei and single particles becomes possible at heavier masses...

 into products that vary in composition. In a phenomenon called cluster decay
Cluster decay
Cluster decay is a type of nuclear decay in which a parent atomic nucleus with A nucleons and Z protons emits a cluster of Ne neutrons and Ze protons heavier than an alpha particle but lighter than a typical binary fission fragment Cluster decay (also named heavy particle radioactivity or heavy...

, specific combinations of neutrons and protons (atomic nuclei) other than alpha particles (helium nuclei) were found to be spontaneously emitted from atoms, on occasion.

Other types of radioactive decay that emit previously seen particles were found, but by different mechanisms. An example is internal conversion
Internal conversion
Internal conversion is a radioactive decay process where an excited nucleus interacts with an electron in one of the lower atomic orbitals, causing the electron to be emitted from the atom. Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but...

, which results in electron and sometimes high-energy photon emission, even though it involves neither beta nor gamma decay. This type of decay (like isomeric transition
Isomeric transition
An isomeric transition is a radioactive decay process that involves emission of a gamma ray from an atom where the nucleus is in an excited metastable state, referred to in its excited state, as a nuclear isomer....

 gamma decay) did not transmute one element to another.

Rare events that involve a combination of two beta-decay type events happening simultaneously (see below) are known. Any decay process that does not violate conservation of energy or momentum laws (and perhaps other particle conservation laws) is permitted to happen, although not all have been detected. An interesting example (discussed in a final section) is bound state beta decay of rhenium-187. In this process, an inverse of electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

, beta electron-decay of the parent nuclide is not accompanied by beta electron emission, because the beta particle has been captured into the K-shell of the emitting atom. An antineutrino, however, is emitted.

Decay modes in table form


Radionuclides can undergo a number of different reactions. These are summarized in the following table. A nucleus with mass number
Mass number
The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...

 A and atomic number
Atomic number
In chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...

 Z is represented as (A, Z). The column "Daughter nucleus" indicates the difference between the new nucleus and the original nucleus. Thus, (A − 1, Z) means that the mass number is one less than before, but the atomic number is the same as before.
Mode of decay Participating particlesDaughter nucleus
Decays with emission of nucleons:
Alpha decay
Alpha decay
Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle and thereby transforms into an atom with a mass number 4 less and atomic number 2 less...

 
An alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...

 (A = 4, Z = 2) emitted from nucleus
(A − 4, Z − 2)
Proton emission
Proton emission
Proton emission is a type of radioactive decay in which a proton is ejected from a nucleus. Proton emission can occur from high-lying excited states in a nucleus following a beta decay, in which case the process is known as beta-delayed proton emission, or can occur from the ground state of very...

 
A proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 ejected from nucleus
(A − 1, Z − 1)
Neutron emission
Neutron emission
Neutron emission is a type of radioactive decay of atoms containing excess neutrons, in which a neutron is simply ejected from the nucleus. Two examples of isotopes which emit neutrons are helium-5 and beryllium-13...

 
A neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 ejected from nucleus
(A − 1, Z)
Double proton emission
Proton emission
Proton emission is a type of radioactive decay in which a proton is ejected from a nucleus. Proton emission can occur from high-lying excited states in a nucleus following a beta decay, in which case the process is known as beta-delayed proton emission, or can occur from the ground state of very...

 
Two protons ejected from nucleus simultaneously (A − 2, Z − 2)
Spontaneous fission
Spontaneous fission
Spontaneous fission is a form of radioactive decay characteristic of very heavy isotopes. Because the nuclear binding energy reaches a maximum at a nuclear mass greater than about 60 atomic mass units , spontaneous breakdown into smaller nuclei and single particles becomes possible at heavier masses...

 
Nucleus disintegrates into two or more smaller nuclei and other particles
Cluster decay
Cluster decay
Cluster decay is a type of nuclear decay in which a parent atomic nucleus with A nucleons and Z protons emits a cluster of Ne neutrons and Ze protons heavier than an alpha particle but lighter than a typical binary fission fragment Cluster decay (also named heavy particle radioactivity or heavy...

 
Nucleus emits a specific type of smaller nucleus (A1, Z1) smaller than, or larger than, an alpha particle (A − A1, Z − Z1) + (A1, Z1)
Different modes of beta decay:
β decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

 
A nucleus emits an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

 and an electron antineutrino 
(A, Z + 1)
Positron emission
Positron emission
Positron emission or beta plus decay is a type of beta decay in which a proton is converted, via the weak force, to a neutron, releasing a positron and a neutrino....

 (β+ decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

)
A nucleus emits a positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

 and an electron neutrino
Electron neutrino
The electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...

 
(A, Z − 1)
Electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

 
A nucleus captures an orbiting electron and emits a neutrino the daughter nucleus is left in an excited unstable state (A, Z − 1)
Bound state beta decay  A nucleus beta decays to electron and antineutrino, but the electron is not emitted, as it is captured into an empty K-shell;the daughter nucleus is left in an excited and unstable state. This process is suppressed except in ionized atoms that have K-shell vacancies. (A, Z + 1)
Double beta decay
Double beta decay
Double beta decay is a radioactive decay process where a nucleus releases two beta rays as a single process.In double-beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted...

 
A nucleus emits two electrons and two antineutrinos (A, Z + 2)
Double electron capture
Double electron capture
Double electron capture is a decay mode of atomic nucleus. For a nuclide with number of nucleons A and atomic number Z, double electron capture is only possible if the mass of the nuclide of is lower....

 
A nucleus absorbs two orbital electrons and emits two neutrinos – the daughter nucleus is left in an excited and unstable state (A, Z − 2)
Electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

 with positron emission
Positron emission
Positron emission or beta plus decay is a type of beta decay in which a proton is converted, via the weak force, to a neutron, releasing a positron and a neutrino....

 
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:
Isomeric transition
Isomeric transition
An isomeric transition is a radioactive decay process that involves emission of a gamma ray from an atom where the nucleus is in an excited metastable state, referred to in its excited state, as a nuclear isomer....

 
Excited nucleus releases a high-energy photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

 (gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

)
(A, Z)
Internal conversion
Internal conversion
Internal conversion is a radioactive decay process where an excited nucleus interacts with an electron in one of the lower atomic orbitals, causing the electron to be emitted from the atom. Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but...

 
Excited nucleus transfers energy to an orbital electron and it is ejected from the atom (A, Z)


Radioactive decay results in a reduction of summed rest mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

, once the released energy (the disintegration energy) has escaped in some way (for example, the products might be captured and cooled, and the heat allowed to escape). Although decay energy is sometimes defined as associated with the difference between the mass of the parent nuclide products and the mass of the decay products, this is true only of rest mass measurements, where some energy has been removed from the product system. This is true because the decay energy must always carry mass with it, wherever it appears (see mass in special relativity
Mass in special relativity
Mass in special relativity incorporates the general understandings from the concept of mass-energy equivalence. Added to this concept is an additional complication resulting from the fact that "mass" is defined in two different ways in special relativity: one way defines mass as an invariant...

) according to the formula E = mc2. The decay energy is initially released as the energy of emitted photons plus the kinetic energy of massive emitted particles (that is, particles that have rest mass). If these particles come to thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

 with their surroundings and photons are absorbed, then the decay energy is transformed to thermal energy, which retains its mass.

Decay energy therefore remains associated with a certain measure of mass of the decay system invariant mass
Invariant mass
The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

. The energy of photons, kinetic energy of emitted particles, and, later, the thermal energy of the surrounding matter, all contribute to calculations of invariant mass
Invariant mass
The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

 of systems. Thus, while the sum of rest masses of particles is not conserved in radioactive decay, the system mass and system invariant mass
Invariant mass
The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

 (and also the system total energy) is conserved throughout any decay process.

Decay chains and multiple modes


The daughter nuclide of a decay event may also be unstable (radioactive). In this case, it will also decay, producing radiation. The resulting second daughter nuclide may also be radioactive. This can lead to a sequence of several decay events. Eventually, a stable nuclide is produced. This is called a decay chain
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...

(see this article for specific details of important natural decay chains).
An example is the natural decay chain of 238U, which is as follows:
  • decays, through alpha-emission, with a half-life
    Half-life
    Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

     of 4.5 billion years to thorium-234
  • which decays, through beta-emission, with a half-life of 24 days to protactinium-234
  • which decays, through beta-emission, with a half-life of 1.2 minutes to uranium-234
  • which decays, through alpha-emission, with a half-life of 240 thousand years to thorium-230
  • which decays, through alpha-emission, with a half-life of 77 thousand years to radium-226
  • which decays, through alpha-emission, with a half-life of 1.6 thousand years to radon-222
  • which decays, through alpha-emission, with a half-life of 3.8 days to polonium-218
  • which decays, through alpha-emission, with a half-life of 3.1 minutes to lead-214
  • which decays, through beta-emission, with a half-life of 27 minutes to bismuth-214
  • which decays, through beta-emission, with a half-life of 20 minutes to polonium-214
  • which decays, through alpha-emission, with a half-life of 160 microseconds to lead-210
  • which decays, through beta-emission, with a half-life of 22 years to bismuth-210
  • which decays, through beta-emission, with a half-life of 5 days to polonium-210
  • which decays, through alpha-emission, with a half-life of 140 days to lead-206, which is a stable nuclide.


Some radionuclides may have several different paths of decay. For example, approximately 36% of bismuth-212 decays, through alpha-emission, to thallium-208 while approximately 64% of bismuth-212 decays, through beta-emission, to polonium-212. Both the thallium-208 and the polonium-212 are radioactive daughter products of bismuth-212, and both decay directly to stable lead-208.

Occurrence and applications


According to the Big Bang theory, stable isotopes of the lightest five elements (H
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

, He
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

, and traces of Li
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

, Be
Beryllium
Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...

, and B
Boron
Boron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...

) were produced very shortly after the emergence of the universe, in a process called Big Bang nucleosynthesis
Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 during the early phases of the universe...

. These lightest stable nuclides (including deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

) survive to today, but any radioactive isotopes of the light elements produced in the Big Bang (such as tritium
Tritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...

) have long since decayed. Isotopes of elements heavier than boron were not produced at all in the Big Bang, and these first five elements do not have any long-lived radioisotopes. Thus, all radioactive nuclei are, therefore, relatively young with respect to the birth of the universe, having formed later in various other types of nucleosynthesis
Nucleosynthesis
Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...

 in star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s (in particular, supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...

e), and also during ongoing interactions between stable isotopes and energetic particles. For example, carbon-14
Carbon-14
Carbon-14, 14C, or radiocarbon, is a radioactive isotope of carbon with a nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues , to date archaeological, geological, and hydrogeological...

, a radioactive nuclide with a half-life of only 5730 years, is constantly produced in Earth's upper atmosphere due to interactions between cosmic rays and nitrogen.

Radioactive decay has been put to use in the technique of radioisotopic labeling, which is used to track the passage of a chemical substance through a complex system (such as a living organism
Organism
In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...

). 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
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

), it has been used in hardware random-number generators. Because the process is not thought to vary significantly in mechanism over time, it is also a valuable tool in estimating the absolute ages of certain materials. For geological materials, the radioisotopes and some of their decay products become trapped when a rock solidifies, and can then later be used (subject to many well-known qualifications) to estimate the date of the solidification. These include checking the results of several simultaneous processes and their products against each other, within the same sample. In a similar fashion, and also subject to qualification, the rate of formation of carbon-14 in various eras, the date of formation of organic matter within a certain period related to the isotope's half-life may be estimated, because the carbon-14 becomes trapped when the organic matter grows and incorporates the new carbon-14 from the air. Thereafter, the amount of carbon-14 in organic matter decreases according to decay processes that may also be independently cross-checked by other means (such as checking the carbon-14 in individual tree rings, for example).

Radioactive decay rates



The decay rate, or activity, of a radioactive substance are characterized by:

Constant quantities:
  • half-life
    Half-life
    Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

     — symbol t1/2 — the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value.
  • mean lifetime — symbol τ — the average lifetime of a radioactive particle before decay.
  • decay constant — symbol λ — the inverse of the mean lifetime.


Although these are constants, they are associated with statistically random behavior of populations of atoms. In consequence predictions using these constants are less accurate for small number of atoms.

In principle a third-life, tenth-life, or even (1/√2)-life (the reciprocal of any real number greater than and not equal to 1) etc can of course be used in exactly the same way as half-life. The half-life is adopted as the standard time associated with exponential decay.

Time-variable quantities:
  • Total activity — symbol A — number of decays per unit time of a radioactive sample.
  • Number of particles — symbol N — the total number of particles in the sample.
  • Specific activity — symbol SA — number of decays per unit time per amount of substance of the sample at time set to zero (t = 0). "Amount of substance" can be the mass, volume or moles of the initial sample.


These are related as follows:
where a0 is the initial amount of active substance — substance that has the same percentage of unstable particles as when the substance was formed.

Activity measurements


The units in which activities are measured are: becquerel
Becquerel
The becquerel is the SI-derived unit of radioactivity. One Bq is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. The Bq unit is therefore equivalent to an inverse second, s−1...

 (symbol Bq) = one disintegration per second; curie
Curie
The curie is a unit of radioactivity, defined asThis is roughly the activity of 1 gram of the radium isotope 226Ra, a substance studied by the pioneers of radiology, Marie and Pierre Curie, for whom the unit was named. In addition to the curie, activity can be measured using an SI derived unit,...

 (Ci) = 3.7 × 1010 Bq. Low activities are also measured in disintegrations per minute (dpm).

Mathematics of radioactive decay


Universal law of radioactive decay


Radioactivity is one very frequent example of exponential decay. The law however is only statistical - not exact. In the following formalism, the number of nuclides or nuclide population N, is of course a descrete variable (a natural number) - but for any physical sample N is so large (amounts of L = 1023, avagadro's constant) that it can be treated as a continuous variable. Differential calculus to set up differential equations for modelling the behaviour of the nuclear decay.

One-decay process


Consider the case of a nuclide A decaying into another B by some process, i.e. A → B (emission of other particles, like electron neutrino
Electron neutrino
The electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...

s and electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s e in beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

, are irrelevant in what follows). The decay of an unstable nucleus 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 N, that is


Particular radionuclides decay at different rates, so each has its own decay constant λ (lower Greek lambda
Lambda
Lambda is the 11th letter of the Greek alphabet. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed . Letters in other alphabets that stemmed from lambda include the Roman L and the Cyrillic letter El...

). The probability of decay (−dN/N) is proportional to an increment of time, dt:


The negative sign indicates that N decreases as time increases, as each decay event follows one after another. The solution to this first-order differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

 is the function:


where N0 is the value of N at the time set to zero (t = 0).

This equation is of particular interest; the behaviour of numerous important quantities can be found from it (see below). Although the parent decay distribution follows an exponential, observations of decay times will be limited by a finite integer number of N atoms and follow Poisson statistics as a consequence of the random nature of the process.

We have for all time t:


where Ntotal is the constant number of particles throughout the decay process, clearly equal to the initial number of A nuclides since this is the initial substance.

If the number of non-decayed A nuclei is:


then the number of nuclei of B, i.e. number of decayed A nuclei, is

Chain-decay processes


Chain of two decays

Now consider the case of a chain of two decays: one nuclide A decaying into another B by one process, then B decaying into another C by a second process, i.e. A → B → C. The previous equation cannot be applied to a decay chain, but can be generalized as follows. The decay rate of B is proportional to the number of nuclides of B present, so again we have :


but care must be taken. Since A decays into B, then B decays into C, the activity of A adds to the total number of B nuclides in the present sample, before those B nuclides decay and reduce the number of nuclides leading to the later sample. In other words, the number of 2nd generation nuclei B increases as a result of the 1st generation nuclei decay of A, and decreases as a result of its own decay into the 3rd generation nuclei C. The proportionality becomes an equation:


adding the increasing (and correcting) term obtains the law for a decay chain for two nuclides:


The equation is not


since this implies the number of atoms of B is only decreasing as time increases, which is not the case. The rate of change of NB, that is dNB/dt, is related to the changes in the amounts of A and B, NB can increase as B is produced from A and decrease as B produces C.

Re-writing using the previous results:


The subscripts simply refer to the respective nuclides, i.e. NA is the number of nuclides of type A, NA0 is the initial number of nuclides of type A, λA is the decay constant for A - and similarly for nuclide B. Solving this equation for NB gives:


Naturally this equation reduces to the previous solution, in the case B is a stable nuclide (λB = 0):


as shown above for one decay. The solution can be found by the integration factor
Integrating factor
In mathematics, an integrating factor is a function that is chosen to facilitate the solving of a given equation involving differentials. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus, in this case often multiplying through by an...

 method, where the integrating factor is . This case is perhaps the most useful, since it can derive both the one-decay equation (above) and the equation for multi-decay chains (below) more directly.

Chain of any number of decays

For the general case of any number of consecutive decays in a decay chain, i.e. A1 → A2 ... → Ai ... → AD, where D is the number of decays and i is a dummy index (i = 1,2,3...D), each nuclide population can be found in terms of the previous population, using the above result in a recursive form:


The general solution to the recursive problem are given by Bateman's equations:



Alternative decay modes


In all of the above examples, the initial nuclide decays into only one product. Consider the case of one initial nuclide which can decay into two products, that is A → B + C. We have for all time t:



in which,


so the relations follow in parallel:


indicating that the total decay constant is that of A, given by:



Solving this equation for NA:


When measuring the production of one nuclide, one can only observe the total decay constant λA. The decay constants λB and λC determine the probability for the decay to result in products B or C as follows:



These perhaps seemingly disjionted results are consistent:


Corollaries of the decay laws


The solutions to the above differential equations are sometimes written using quantities related to the number of nuclides, such as:
  • the activity A of a sample relates to N by:
  • the number of moles (aka amount of substance
    Amount of substance
    Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units defines the amount of substance to be...

    ) n of sample relates to N via L = 6.023 × 1023 (Avagadro's constant) by:
  • the mass
    Mass
    Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

     M of the sample relates to N via relative atomic mass number Ar (or Ar) by:
  • collecting these results together for conveinence:


Equivalant ways to write the decay solutions are as follows:

One-decay processes

The solution


can be written:


Notice how we can simply replace each quantity (on both sides of the equation), since they are directly proportional to N and so the constants cancel (constant at least for a particular nuclide).

Chain-decay processes

For the two-decay chain,


its almost as simple:

Time constant and mean-life


For the one-decay solution (A → B):


the equation indicates that the decay constant λ has units of 1/time, and can thus also be represented as 1/τ, where τ is a characteristic time for the process: called the time constant
Time constant
In physics and engineering, the time constant, usually denoted by the Greek letter \tau , is the risetime characterizing the response to a time-varying input of a first-order, linear time-invariant system.Concretely, a first-order LTI system is a system that can be modeled by a single first order...

 of the process.

In radioactive decay, this process time constant is also the mean lifetime for decaying atoms. Each atom "lives" for a finite amount of time before it decays, and it may be shown that this mean lifetime is the arithmetic mean
Arithmetic mean
In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...

 of all the atoms' lifetimes, and that it is τ, which again is related to the decay constant as follows:


This form is also true for two-decay processes simaltaneously (A → B + C), inserting the equivalent values of decay constants (as given above)


into the decay solution leads to:

Half-life


A more commonly used parameter is the half-life
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

. Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions:


the half-life is related to the decay constant as follows: set N = N0/2 and t = T1/2 to obtain


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 1019 years (such as for very nearly stable nuclides, e.g., 209Bi), to 10−23 seconds for highly unstable ones.

The factor of ln2 in the above relations results from the fact that concept of "half-life" is merely a way of selecting a different base other than the natural base e for the lifetime expression. The time constant τ is the "1/e" life (time till only 1/e = about 36.8% remains) rather than the "1/2" life of a radionuclide where 50% remains (thus, τ is longer than t½). Thus, the following equation can be shown to be equaly valid:


Since radioactive decay is exponential with a constant probability, each process could as easily be described with a different constant time period that (for example) gave its "1/3-life" (how long until only 1/3 is left) or "1/10-life" (a time period till only 10% is left), and so on. Thus, the choice of τ and t½ for marker-times, are only for convenience, and from convention. They reflect a fundamental principle only in so much as they show that the same proportion of a given radioactive substance will decay, during any time-period that one chooses.

Mathematically, the n-th life for the above situation would be found in the same way as above - by setting N = N0/n, t = T1/n and substituing into the deacy solution to obtain

Example


A sample of 14C, whose half-life is 5730 years, has a decay rate of 14 disintegration per minute (dpm) per gram of natural carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

. An artefact is found to have radioactivity of 4 dpm per gram of its present C, how old is the artefact?

Using the above equation, we have:
where: years, years.

Changing decay rates


The radioactive decay modes of electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

 and internal conversion
Internal conversion
Internal conversion is a radioactive decay process where an excited nucleus interacts with an electron in one of the lower atomic orbitals, causing the electron to be emitted from the atom. Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but...

 are known to be slightly sensitive to chemical and environmental effects which change the electronic structure of the atom, which in turn affects the presence of 1s and 2s electrons that participate in the decay process. A small number of mostly light nuclides are affected. For example, chemical bonds can affect the rate of electron capture to a small degree (in general, less than 1%) depending on the proximity of electrons to the nucleus in beryllium. In 7Be, a difference of 0.9% has been observed between half-lives in metallic and insulating environments. This relatively large effect is because beryllium is a small atom whose valence electrons are in 2s atomic orbital
Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

s, which are subject to electron capture in 7Be because (like all s atomic orbitals in all atoms) they naturally penetrate into the nucleus.

Rhenium-187 is a more spectacular example. 187Re normally beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

s to 187Os with a half-life
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

 of 41.6 × 109 y, but studies using fully ionised 187Re
Rhenium
Rhenium is a chemical element with the symbol Re and atomic number 75. It is a silvery-white, heavy, third-row transition metal in group 7 of the periodic table. With an average concentration of 1 part per billion , rhenium is one of the rarest elements in the Earth's crust. The free element has...

 atoms (bare nuclei) have found that this can decrease to only 33 y. This is attributed to "bound-state β- decay" of the fully ionised atom — the electron is emitted into the "K-shell" (1s atomic orbital), which cannot occur for neutral atoms in which all low-lying bound states are occupied.

A number of experiments have found that decay rates of other modes of artificial and naturally-occurring radioisotopes are, to a high degree of precision, unaffected by external conditions such as temperature, pressure, the chemical environment, and electric, magnetic, or gravitational fields. Comparison of laboratory experiments over the last century, studies of the Oklo natural nuclear reactor
Natural nuclear fission reactor
A natural nuclear fission reactor is a uranium deposit where analysis of isotope ratios has shown that self-sustaining nuclear chain reactions have occurred. The existence of this phenomenon was discovered in 1972 at Oklo in Gabon, Africa, by French physicist Francis Perrin. The conditions under...

 (which exemplified the effects of thermal neutrons on nuclear decay), and astrophysical observations of the luminosity decays of distant supernovae (which occurred far away so the light has taken a great deal of time to reach us), for example, strongly indicate that decay rates have been constant (at least to within the limitations of small experimental errors) as a function of time as well.

Recent results suggest the possibility that decay rates might have a weak dependence (0.5% or less) on environmental factors. It has been suggested that measurements of decay rates of silicon-32, manganese-54, and radium-226 exhibit small seasonal variations (of the order of 0.1%), proposed to be related to either solar flare activity or distance from the sun. However, such measurements are highly susceptible to systematic errors, and a subsequent paper has found no evidence for such correlations in six other isotopes, and sets upper limits on the size of any such effects.

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