Radioactive decay

"Radioactive" and "Radioactivity" redirect here. For other uses see Radioactive (disambiguation).

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

Radioactive decay is the process in which an unstable electromagnetic waves. 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, called 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 random process on the atomic level, in that it is impossible to predict when a particular atom will decay, but given a large number of similar atoms, the decay rate, on average, is predictable.

The 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 SI.

Explanation

The beta decay.
The interplay of these forces is simple. Some configurations of the particles in a nucleus have the property that, should they shift ever so slightly, the particles could fall into a lower-energy arrangement (with the extra energy moving elsewhere). One might draw an analogy with a snowfield on a mountain: while friction between the snow crystals can support the snow's weight, the system is inherently unstable with regard to a lower-potential-energy state, and a disturbance may facilitate the path to a greater entropy state (i.e., towards the ground state where heat will be produced, and thus total energy is distributed over a larger number of quantum states). Thus, an avalanche results. The total energy does not change in this process, but because of entropy effects, avalanches only happen in one direction, and the end of this direction, which is dictated by the largest number of chance-mediated ways to distribute available energy, is what we commonly refer to as the "ground state."
Such a collapse (a decay event) requires a specific electrons of atoms, rather than their nuclei.
Some nuclear reactions do involve external sources of energy, in the form of collisions with outside particles. However, these are not considered decay. Rather, they are examples of induced nuclear reactions. Nuclear fusion are common types of induced nuclear reactions.

Discovery

Radioactivity was first discovered in 1896 by the French scientist uranium salts. The result with these compounds was a deep blackening of the plate.
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 blacken.

At first it seemed that the new radiation was similar to the then recently discovered X-rays. Further research by Becquerel, 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).
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 electromagnetic radiation.
Although alpha, beta, and gamma are most common, other types of decay were eventually discovered. Shortly after discovery of the 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.
The early researchers also discovered that many other barium. The two elements' chemical similarity would otherwise have made them difficult to distinguish.
The dangers of radioactivity and of radiation were not immediately recognized. Acute effects of radiation were first observed in the use of X-rays when the Serbo-Croatian-American electric engineer 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 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.

Modes of decay

Radionuclides can undergo a number of different reactions. These are summarized in the following table. A nucleus with mass number A 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 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:

antineutrino (A, Z+1)

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:

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, which is converted to energy (the disintegration energy) according to the formula $E = m c 2$ . This energy is released as kinetic energy of the emitted particles. The energy remains associated with a measure of mass of the decay system invariant mass, inasmuch the kinetic energy of emitted particles 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 is usually also unstable, sometimes even more unstable than the parent. If this is the case, it will proceed to decay again. A sequence of several decay events, producing in the end a stable nuclide, is a decay chain.
Many radionuclides have several different observed modes of decay. Bismuth-212, for example, has three. Thus a given nuclide may lead to several different decay chains.

Occurrence and applications

According to the Big Bang theory, radioactive isotopes of the lightest elements (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, 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 for half of a substance to decay.
mean lifetime — symbol $τ$ — the average lifetime of any given particle.
decay constant — symbol $λ$ — the inverse of the mean lifetime.

(Note that although these are constants, they are associated with statistically random behavior of substances, and 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
$a_0 \$ 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

As discussed above, 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:

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

This function represents exponential decay. It is only an approximate solution, for two reasons. Firstly, the exponential function is continuous, but the physical quantity N can only take non-negative integer values. Secondly, because it describes a random process, it is only statistically true. However, in most common cases, N is a very large number and the function is a good approximation.
In addition to the decay constant, radioactive decay is sometimes characterized by the mean lifetime. Each atom "lives" for a finite amount of time before it decays, and the mean lifetime is the arithmetic mean of all the atoms' lifetimes. It is represented by the symbol $τ$ , and is related to the decay constant as follows:

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

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

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

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.

References

"Radioactivity", Encyclopædia Britannica. 2006. Encyclopædia Britannica Online. 18 Dec. 2006

See also

Nuclear pharmacy
Nuclear physics
Radioactivity in biology
Poisson process
Radiation
Radiation therapy
Radioactive contamination
Radiometric dating
Actinides in the environment
Half-life
Fallout shelter
Particle decay

v • d • e
Nuclear processes
Radioactive decay S-process · P-process · Rp-process
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Radioactivity

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Radioactive_decay". A list of authors is available in Wikipedia.