Radioactive decay

For decay rate in a more general context, see Particle decay.

This article is about radioactivity in nuclear physics. For Radioactive (disambiguation), see Radioactive decay (disambiguation).

Radioactive decay is the process by which an unstable atomic nucleus spontaneously loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, named the daughter nuclide. For example: a carbon-14 atom (the "parent") emits radiation and transforms to a nitrogen-14 atom (the "daughter"). This is a stochastic process on the atomic level, in that it is impossible to predict when a given atom will decay, but given a large number of similar atoms the decay rate, on average, is predictable.

The SI unit of activity is the becquerel (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, Ci, which was originally defined as the amount of radium emanation (radon-222) in equilibrium with of one gram of pure radium, isotope 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 presently discouraged by the SI.

Explanation

The trefoil symbol is used to indicate radioactive material.

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 almost always significant, and in the case of beta decay, the weak nuclear force is also involved.

The interplay of these forces produces a number of different phenomena in which energy may be released by rearrangement of particles. Some configurations of the particles in a nucleus have the property that, should they shift ever so slightly, the particles could rearrange into a lower-energy arrangement and release some energy. One might draw an analogy with a snowfield on a mountain: while 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: 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 results. The total energy does not change in this process, but because of the law of entropy, avalanches only happen in one direction and that is towards 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. 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, 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 which has mass (such as an electron, alpha particle, or other type).

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

It soon became clear that the blackening of the plate had nothing 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. Clearly there was 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, Marie Curie, Pierre Curie, Ernest Rutherford and others discovered that radioactivity was significantly more complicated. Different types of decay can occur, but Rutherford was the first to realize that they all occur with the same mathematical approximately exponential formula (see below).

The early researchers also discovered that many other chemical elements besides uranium have radioactive isotopes. A systematic search for the total radioactivity in uranium ores also guided Marie Curie to isolate a new element polonium and to separate a new element radium from barium. The two elements' chemical similarity would otherwise have made them difficult to distinguish.

Danger of radioactive substances

The danger classification sign of radioactive materials

File:New radiation symbol ISO 21482.svg

Ionizing radiation hazard symbol (recently introduced).

Alpha particles may be completely stopped by a sheet of paper, beta particles by aluminum shielding. Gamma rays can only be reduced by much more substantial barriers, such as a very thick layer of lead.

Different types of decay of a radionuclide. Vertical: atomic number Z, Horizontal: neutron number N

The dangers of radioactivity and of 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 intentionally subjected his fingers to X-rays in 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 effects on cancer risk, were recognized much later. In 1927 Hermann Joseph Muller published research showing genetic effects, and in 1946 was awarded the Nobel prize for his findings.

Before the biological effects of radiation were known, many physicians and corporations had begun marketing radioactive substances as patent medicine and radioactive quackery. Examples were radium enema treatments, and radium-containing waters to be drunk as tonics. Marie Curie spoke out against this sort of treatment, warning that the effects of radiation on the human body were not well understood (Curie later died from aplastic anemia assumed due to her work with radium, but later examination of her bones showed that she had been a careful laboratory worker and had a low burden of radium. A more likely cause was her exposure to unshielded X-ray tubes while a volunteer medical worker in WWI). By the 1930s, after a number of cases of bone necrosis and death in enthusiasts, radium-containing medical products had nearly vanished from the market.

Types of decay

As for types of radioactive radiation, it was found that an electric or magnetic field could split such emissions into three types of beams. For lack of better terms, the rays were given the alphabetic names alpha, beta and gamma, 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 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 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 allowed researchers to study the emission spectrum of the resulting gas, and ultimately prove that alpha particles are helium nuclei. Other experiments showed the similarity between beta radiation and cathode rays; they are both streams of electrons, and between gamma radiation and X-rays, which are both high energy electromagnetic radiation.

Although alpha, beta, and gamma are most common, other types of decay were eventually discovered. Shortly after discovery of the neutron in 1932, it was discovered by Enrico Fermi that certain rare decay reactions yield neutrons as a decay particle. Isolated proton emission was eventually observed in some elements. Shortly after the discovery of the positron in cosmic ray products, it was realized that the same process that operates in classical beta decay can also produce positrons (positron emission), analogously to negative electrons. Each of the two types of beta decay acts to move a nucleus toward a ratio of neutrons and protons which has the least energy for the combination. Finally, in a phenomenon called cluster decay, specific combinations of neutrons and protons other than alpha particles were spontaneously emitted from atoms on occasion.

Still other types of radioactive decay were found which emit previously seen particles, but by different mechanisms. An example is internal conversion, which results in electron and sometimes high energy photon emission, even though it involves neither beta nor gamma decay.

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 A and atomic number 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 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)
Double proton emission	Two protons ejected from nucleus simultaneously	(A–2, Z–2)
Spontaneous fission	Nucleus disintegrates into two or more smaller nuclei and other particles	-
Cluster decay	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:
Beta-Negative decay	A nucleus emits an electron and an antineutrino	(A, Z+1)
Positron emission, also Beta-Positive decay	A nucleus emits a positron and a neutrino	(A, Z–1)
Electron capture	A nucleus captures an orbiting electron and emits a neutrino — The daughter nucleus is left in an excited and unstable state	(A, Z–1)
Double beta decay	A nucleus emits two electrons and two antineutrinos	(A, Z+2)
Double electron capture	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 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:
Isomeric transition	Excited nucleus releases a high-energy photon (gamma ray)	(A, Z)
Internal conversion	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, once the released energy (the disintegration energy) has escaped. The energy carries mass with it (see mass in special relativity) according to the formula $E=mc^{2}$. The decay energy is initially released as kinetic energy of the emitted particles. Later these particles come to thermal equilibrium with their surroundings. The energy remains associated with a measure of mass of the decay system invariant mass, in as much as the kinetic energy of emitted particles, and, later, the thermal energy of the surrounding matter, contributes also to the total invariant mass of systems. Thus, the sum of rest masses of particles is not conserved in decay, but the system mass or system invariant mass (as also system total energy) is conserved.

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.

Gamma-ray energy spectrum of ²³⁸U (inset). Gamma-rays are emitted by decaying nuclides, and the gamma-ray energy can be used to characterize the decay (which nuclide is decaying to which). Here, using the gamma-ray spectrum, several nuclides which are typical of the decay chain have been identified: ²²⁶Ra, ²¹⁴Pb, ²¹⁴Bi.

An example is the natural decay chain of ²³⁸U which is as follows:

• decays, through alpha-emission, with a half-life 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, He, and traces of Li, Be, and B) were produced very shortly after the emergence of the universe, in a process called Big Bang nucleosynthesis. These lightest stable nuclides (including deuterium) survive to today, but any radioactive isotopes of the light elements produced in the Big Bang (such as tritium) 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 in stars (particularly supernovae), and also during ongoing interactions between stable isotopes and energetic particles. For example, carbon-14, 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). 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. 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-live 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 which 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 — symbol t_1/2 — 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.
• 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.

Time-variable quantities:

• Total activity — symbol A — number of decays an object undergoes per second.
• Number of particles — symbol N — the total number of particles in the sample.
• Specific activity — symbol S_A — number of decays per second per amount of substance. (The "amount of substance" can be the unit of either mass or volume.)

These are related as follows:

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

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

$S_{A}a_{0}=-{\frac {dN}{dt}}{\bigg |}_{t=0}=\lambda N_{0}$

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 (symbol Bq) = number of disintegrations per second; curie (Ci) = 3.7 × 10¹⁰ disintegrations per second. Low activities are also measured in disintegrations per minute (dpm).

Decay timing

See also: exponential decay

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. If N is the number of atoms, then the probability of decay (−dN/N) is proportional to dt:

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

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 first-order differential equation is the following function:

$N(t)=N_{0}\,e^{-{\lambda }t}=N_{0}\,e^{-t/\tau }.\,\!$

Where N₀ is the value of N at time zero (t = 0). The second equation recognizes that the differential 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. This characteristic time is called the time constant 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 of all the atoms' lifetimes, and that it is τ, which again is related to the decay constant as follows:

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

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms (left) or 400 (right). The number at the top indicates how many half-lives have elapsed. Note the law of large numbers: With more atoms, the overall decay is less random.

The previous exponential function generally represents the result of 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 non-negative integer values. Secondly, because it describes a random process, it is only statistically true. However, in most common cases, N is an extremely large number (comparable to Avogadro's number) and the function is a good approximation.

Half life

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:

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

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 life time 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 t_½). Thus, the following equation can easily be shown to be valid.

$N(t)=N_{0}\,e^{-t/\tau }=N_{0}\,2^{-t/t_{1/2}}.\,\!$

Since radioactive decay is exponential with a constant probability, each process could as easily be described with a different constant time period which (for example) gave its "1/3 life" (how long until only 1/3rd is left) or "1/10 life" (a time period till only 10% is left) and so on. Thus the choice of τ and t_½ 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.

Changing decay rates?

A number of experiments have shown that decay rates of naturally-occurring radioisotopes (for decay modes other than electron capture) 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, and astrophysical observations of the luminosity decays of distant supernovae (which occurred long ago 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.

On the other hand, some recent results suggest the possibility that decay rates might have a very weak dependence (0.1% 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 (about 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 a half-dozen isotopes, and sets upper limits on the size of any such effects.

An exception is the decay mode known as electron capture exhibited by a small number of nuclides. Chemical bonds can affect the rate of electron capture to a small degree (generally less than 1%) depending on the proximity of electrons to the nucleus. For example in ⁷Be, a difference of 0.9% has been observed between half-lives in metallic and insulating environments. This relatively large effect is due to the fact that beryllium is a small atom whose valence electrons are in 2s atomic orbitals which have a large degree of penetration very close to the nucleus, and thus are subject to electron capture.

See also

• Actinides in the environment
• Background radiation
• Fallout shelter
• Half-life
• Lists of nuclear disasters and radioactive incidents
• National Council on Radiation Protection and Measurements
• Nuclear medicine
• Nuclear pharmacy
• Nuclear physics
• Particle decay
• Poisson process
• Radiation
• Radiation therapy
• Radioactive contamination
• Radioactivity in biology
• Radiometric dating
• Radionuclide a.k.a. "radio-isotope"
• Secular equilibrium

References

• "Radioactivity", Encyclopædia Britannica. 2006. Encyclopædia Britannica Online. December 18, 2006
• Radio-activity by Ernest Rutherford Phd, Encyclopædia Britannica Eleventh Edition

External links

• NUCLEONICA Nuclear Science Portal
• NUCLEONICA wiki: Decay Engine
• General information
• Nomenclature of nuclear chemistry
• Some theoretical questions of nuclear stability
• Decay heat rate|quantity calculation
• Specific activity and related topics.
• The Lund/LBNL Nuclear Data Search - Contains tabulated information on radioactive decay types and energies.
• The Karlsruhe Nuclide Chart
• Monte Carlo Simulation of Radioactive Decay
• The Live Chart of Nuclides - IAEA in Java or HTML
• Health Physics Society Public Education Website