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Encyclopedia > Decay rate

Radioactive decay is the set of various processes by which unstable atomic nuclei emit subatomic particles (radiation). Decay is said to occur in the parent nucleus and produces a daughter nucleus. This is a random process, i.e. it is impossible to predict the decay of individual atoms. A semi-accurate depiction of the helium atom. ... A subatomic particle is a particle smaller than an atom: it may be elementary or composite. ... Particle radiation is the radiation of energy by means of small fast-moving particles that have energy and mass. ... // About Bees This article is about completely random and illogical things. ...

The trefoil symbol is used to indicate radioactive material. The Unicode encoding of this symbol is U+2622 (☢).
The trefoil symbol is used to indicate radioactive material. The Unicode encoding of this symbol is U+2622 (☢).

The SI unit for measuring radioactivity is the becquerel (Bq). If a quantity of radioactive material produces one decay event per second, it has an activity of one Bq. Since any reasonably-sized sample of radioactive material contains many atoms, one becquerel is a tiny level of activity; numbers on the order of gigabecquerels are seen commonly. For example the curie, which was originally defined as the radioactivity of one gram of pure radium, is 37 gigabecquerels (GBq). Image File history File links Radioactive. ... Image File history File links Radioactive. ... Architecture Architectural Trefoil (also a Christian symbol) Trefoil (from Latin trifolium, three-leaved plant, French trèfle, German Dreiblatt and Dreiblattbogen) is a term in Gothic architecture given to the ornamental foliation or cusping introduced in the heads of window-lights, tracery, panellings, etc. ... Because of technical limitations, some web browsers may not display some special characters in this article. ... Cover of brochure The International System of Units. ... Radioactivity may mean: Look up radioactivity in Wiktionary, the free dictionary. ... The becquerel (symbol Bq) is the SI derived unit of radioactivity, defined as the activity of a quantity of radioactive material in which one nucleus decays per second. ... The curie (symbol Ci) is a former unit of radioactivity, defined as 3. ... General Name, Symbol, Number radium, Ra, 88 Chemical series alkaline earth metals Group, Period, Block 2, 7, s Appearance silvery white metallic Atomic mass (226) g/mol Electron configuration [Rn] 7s2 Electrons per shell 2, 8, 18, 32, 18, 8, 2 Physical properties Phase solid Density (near r. ...

Contents

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Explanation

The neutrons and protons that constitute nuclei, as well as other particles that may approach them, are governed by several interactions. The strong nuclear force, not observed at the familiar macroscopic scale, is the most powerful force over subatomic distances. The electrostatic force is also significant. Of lesser importance is the weak nuclear force. The gravitational force has no influence on nuclear processes. This article or section does not cite its references or sources. ... Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... The nuclear force (or nucleon-nucleon interaction or residual strong force) is the force between two or more nucleons. ... Macroscopic is commonly used to describe physical objects that are measurable and observable by the naked eye. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... Gravitation or gravity is a property of all objects with mass that causes them to attract each other. ...


The interplay of these forces is very complex. Some configurations of the particles in a nucleus have the property that, should they shift ever so slightly, the particles could fall into a lower-energy arrangement. One might draw an analogy with a tower of sand: while friction between the sand grains can support the tower's weight, a disturbance will unleash the force of gravity and the tower will collapse. Patterns in the sand Sand is an example of a class of materials called granular matter. ... It has been suggested that Coefficient of friction be merged into this article or section. ... Gravity is a force of attraction that acts between bodies that have mass. ...


Such a collapse (a decay event) requires a specific activation energy. In the case of the tower of sand, this energy must come from outside the system, in the form of a gentle prod or swift kick. In the case of an atomic nucleus, it is already present. Quantum-mechanical particles are never at rest; they are in continuous random motion. Thus, if its constituent particles move in concert, the nucleus can spontaneously destabilize. The resulting transformation alters the structure of the nucleus; thus it is a nuclear reaction, in contrast to chemical reactions, which involve changes in the arrangement of the outer electrons of atoms. The sparks generated by striking steel against a flint provide the activation energy to initiate combustion in this Bunsen burner. ... A semi-accurate depiction of the helium atom. ... Fig. ... In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce different products than the initial products. ... A chemical reaction is a process that results in the interconversion of chemical substances [1]. The substance or substances initially involved in a chemical reaction are called reactants. ... Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ...


(Some nuclear reactions do involve external sources of energy, in the form of "collisions" with outside particles. However, these are not considered decay. Rather this is induced fission/fusion or nuclear reaction.) In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce different products than the initial products. ... An induced nuclear fission event. ... The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing fusion power. ... In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce different products than the initial products. ...

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Discovery

Radioactivity was first discovered in 1896 by the French scientist Henri Becquerel while working on phosphorescent materials. These materials glow in the dark after exposure to light, and he thought that the glow produced in cathode ray tubes by X-rays might somehow be connected with phosphorescence. So he tried wrapping a photographic plate in black paper and placing various phosphorescent minerals on it. All results were negative until he tried using uranium salts. The result with these compounds was a deep blackening of the plate. Antoine Henri Becquerel (December 15, 1852 – August 25, 1908) was a French physicist, Nobel laureate, and one of the discoverers of radioactivity. ... Phosphorescent powder under visible light, ultraviolet light, and total darkness. ... Cathode ray tube employing electromagnetic focus and deflection Cutaway rendering of a color CRT Electron guns Electron beams Focusing coils Deflection coils Anode connection Mask for separating beams for red, green, and blue part of displayed image Phosphor layer with red, green, and blue zones Close-up of the phosphor... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... Minerals are natural compounds formed through geological processes. ... General Name, Symbol, Number uranium, U, 92 Chemical series actinides Group, Period, Block n/a, 7, f Appearance silvery gray metallic; corrodes to a spalling black oxide coat in air Atomic mass 238. ...


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

Alpha particles are completely stopped by a sheet of paper, beta particles by an aluminum plate. Gamma rays however, can only be reduced by much more substantial obstacles, such as a very thick piece of lead.
Alpha particles are completely stopped by a sheet of paper, beta particles by an aluminum plate. Gamma rays however, can only be reduced by much more substantial obstacles, such as a very thick piece of lead.

At first it seemed that the new radiation was similar to the then recently discovered X-rays. However further research by Becquerel, Marie Curie, Pierre Curie, Ernest Rutherford and others discovered that radioactivity was significantly more complicated. Different types of decay can occur. Download high resolution version (665x822, 24 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (665x822, 24 KB) Wikipedia does not have an article with this exact name. ... This article or section does not cite its references or sources. ... Pierre Curie (May 15, 1859, Paris – April 19, 1906, Paris) was a French physicist and a pioneer in the study of crystallography, magnetism, piezoelectricity and radioactivity. ... Ernest Rutherford Ernest Rutherford, 1st Baron Rutherford of Nelson, OM, PC, FRS (30 August 1871 – 19 October 1937), was a nuclear physicist from New Zealand. ...


For instance, it was found that an electric or magnetic field could split such emissions into three beams. For lack of better terms, the rays were given the alphabetic names alpha, beta, and gamma, names they still hold today. It was immediately obvious from the direction of electromagnetic forces that alpha rays carried a positive charge, beta rays carried a negative charge, and gamma rays were neutral. From the magnitude of deflection, it was also clear that alpha particles were much more massive than beta particles. Passing alpha rays through a thin glass membrane and trapping them in a discharge tube allowed researchers to study the emission spectrum of the resulting gas, and ultimately prove that alpha particles are in fact helium nuclei. Other experiments showed the similarity between beta radiation and cathode rays; they are both streams of electrons, and between gamma radiation and X-rays. In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ... Current (I) flowing through a wire produces a magnetic field (B) around the wire. ... Due to technical limitations, some web browsers may not display some special characters in this article. ... An alpha particle is deflected by a magnetic field Alpha particles (named after the first letter in the Greek alphabet, α) are a highly ionizing form of particle radiation which have low penetration. ... Alpha radiation consists of helium nuclei and is readily stopped by a sheet of paper. ... This article is about electromagnetic radiation. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Alpha decay is a form of radioactive decay in which an atomic nucleus ejects an alpha particle through the electromagnetic force and transforms into a nucleus with mass number 4 less and atomic number 2 less. ... In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ... This article is about electromagnetic radiation. ... An alpha particle is deflected by a magnetic field Alpha particles or alpha rays are a form of particle radiation which are highly ionizing and have low penetration. ... Beta particles are high-energy electrons emitted by certain types of radioactive nuclei such as potassium-40. ... Lighting neon lamp, two 220/230 volt and 110 V neon lamps and a screwdriver with neon lamp inside A neon lamp is a gas discharge lamp containing neon gas (or in types with different colors also other noble gas) at low pressure. ... A materials emission spectrum is the amount of electromagnetic radiation of each frequency it emits when it is heated (or more generally when it is excited). ... General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Atomic mass 4. ... A schematic diagram of a Crookes tube apparatus. ... Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ...


These researchers also discovered that many other chemical elements have radioactive isotopes. Radioactivity also guided Marie Curie to isolate radium from barium; the two elements' chemical similarity would otherwise have made them difficult to distinguish. The periodic table of the chemical elements A chemical element, often called simply an element, is a substance that cannot be decomposed or transformed into other chemical substances by ordinary chemical processes. ... Atoms of chemical elements may have many isotopes (different forms) with the same atomic numbers but different atomic weights / atomic mass numbers. ... General Name, Symbol, Number radium, Ra, 88 Chemical series alkaline earth metals Group, Period, Block 2, 7, s Appearance silvery white metallic Atomic mass (226) g/mol Electron configuration [Rn] 7s2 Electrons per shell 2, 8, 18, 32, 18, 8, 2 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number barium, Ba, 56 Chemical series alkaline earth metals Group, Period, Block 2, 6, s Appearance silvery white Atomic mass 137. ...


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 an 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 the X-rays. Fortunately his injuries healed later. Nikola Tesla (1856-1943)[1] was a world-renowned Serbian inventor, physicist, mechanical engineer and electrical engineer. ...


The genetic effects of radiation, including the effects on cancer risk, were recognized much later. It was only in 1927 that Hermann Joseph Muller published his research that showed the genetic effects. In 1947 he was awarded the Nobel prize for his findings. Hermann Joseph Muller (December 21, 1890 – April 5, 1967) was an American geneticist and educator. ... Nobel Prize medal. ...


Before the biological effects of radiation were known, many physicians and corporations had begun marketing radioactive substances as patent medicine and Radioactive quackery; particularly alarming 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 own 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 better candidate for her disease was her long exposure to unshielded X-ray tubes while a volunteer medical worker in WW I). By the 1930's, after a number of cases of bone-necrosis and death in enthusiasts, radium-containing medical products had all but vanished from the market. Patent medicine is the term given to various medical compounds sold under a variety of names and labels, though they were for the most part actually trademarked medicines, not patented. ... 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 ills. ... This 2qt (about 2 liters) enema bag, or fountain syringe, equipped with a rectal nozzle, is to be filled with water or a solution, then suspended near the patient using the hook. ... This article or section does not cite its references or sources. ... Aplastic anemia is a condition where the bone marrow does not produce enough, or any, new cells to replenish the blood cells. ...

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Modes of decay

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

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

Radioactive decay results in a loss of mass, which is converted to energy (the disintegration energy) according to the formula E = mc2. This energy is released as kinetic energy of the emitted particles. Alpha decay is a form of radioactive decay in which an atomic nucleus ejects an alpha particle through the electromagnetic force and transforms into a nucleus with mass number 4 less and atomic number 2 less. ... An alpha particle is deflected by a magnetic field Alpha particles (named after the first letter in the Greek alphabet, α) are a highly ionizing form of particle radiation which have low penetration. ... Proton emission (also known as proton radioactivity) is a type of radioactive decay in which a proton is ejected from a nucleus. ... Neutron emission is a type of radioactive decay in which an atom contains excess neutrons and a neutron is simply ejected from the nucleus. ... Spontaneous fission (SF) is a form of radioactive decay characteristic of very heavy isotopes, and is theoretically possible for any atomic nucleus whose mass is greater than or equal to 100 amu (elements near ruthenium). ... Cluster decay is the nuclear process in which a radioactive atom emits a cluster of neutrons and protons. ... In nuclear physics, beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ... Antineutrinos, the antiparticles of neutrinos, are neutral particles produced in nuclear beta decay. ... Positron emission is a type of beta decay, sometimes referred to as beta plus (β+). In beta plus decay, a proton is converted to a neutron via the weak nuclear force and a beta plus particle (a positron) and a neutrino are emitted. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... The neutrino is an elementary particle. ... Electron capture is a decay mode for isotopes that will occur when there are too many protons in the nucleus of an atom, and there isnt enough energy to emit a positron; however, it continues to be a viable decay mode for radioactive isotopes that can decay by positron... In the process of beta decay unstable nuclei decay by converting a neutron in the nucleus to a proton and emitting an electron and anti-neutrino. ... Double electron capture is a decay mode of atomic nucleus. ... This article is about electromagnetic radiation. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, microwaves, radio waves, and visible light are all forms of light. ... This article is about electromagnetic radiation. ... This article is about the nuclear process. ... Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... The term mass in special relativity can be used in different ways, occasionally leading to confusion. ...

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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. Nearly all the decay products of radioactive decay are themselves radioactive. ...


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. General Name, Symbol, Number bismuth, Bi, 83 Chemical series poor metals Group, Period, Block 15, 6, p Appearance lustrous reddish white Atomic mass 208. ...


Of the commonly occurring forms of radioactive decay, the only one that changes the number of aggregate protons and neutrons (nucleons) contained in the nucleus is alpha emission, which reduces it by four. Thus, the number of nucleons modulo 4 is preserved across any decay chain. In physics a nucleon is a collective name for the two baryons: the neutron and the proton. ... Modular arithmetic (sometimes called modulo arithmetic) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ...

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Occurrence and applications

According to the Big Bang theory, radioactive isotopes of the lightest elements (H, He, and traces of Li) were produced very shortly after the emergence of the universe. However, these nuclides are so highly unstable that virtually none of them have survived to today. Most radioactive nuclei are therefore relatively young, having formed in stars (particularly supernovae) and 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. According to the Big Bang theory, the universe originated in an infinitely dense and physically paradoxical singularity. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Atomic mass 4. ... General Name, Symbol, Number lithium, Li, 3 Chemical series alkali metals Group, Period, Block 1, 2, s Appearance silvery white/gray Atomic mass 6. ... The Pleiades, an open cluster of stars in the constellation of Taurus. ... Multiwavelength X-ray image of the remnant of Keplers Supernova, SN 1604. ... Carbon-14 is the radioactive isotope of carbon discovered February 27, 1940, by Martin Kamen and Sam Ruben. ...


Radioactive decay has been put to use in the technique of radioisotopic labelling, used to track the passage of a chemical substance through a complex system (such as a living organism). A sample of the substance is synthesized with a high concentration of unstable atoms. The presence of the substance in one or another part of the system is determined by detecting the locations of decay events. Radioisotopic labeling is a technique for tracking the passage of a sample of substance through a system. ... In biology and ecology, an organism (in Greek organon = instrument) is a living complex adaptive system of organs that influence each other in such a way that they function as a more or less stable whole. ...


On the premise that radioactive decay is truly random (rather than merely chaotic), it has been used in hardware random-number generators and is an invaluable tool in estimating the absolute ages of geological materials and young organic matter. // About Bees This article is about completely random and illogical things. ... A plot of the trajectory Lorenz system for values r = 28, σ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. ... In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. ...

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Radioactive decay rates

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


Constant quantities:

  • half life - symbol t1 / 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. Otherwise, The radiometric decay rates used in dating are totally reliable. They are one of the safest bets in all of science as concluded by [1])

Time-variable quantities: This article or section may need to be cleaned up and rewritten because it describes a work of fiction in a primarily in-universe style. ... Given an assembly of elements, the number of which decreases ultimately to zero, the lifetime (also called the mean lifetime) is a certain number that characterizes the rate of reduction (decay) of the assembly. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

  • Total activity - symbol A - number of decays an object undergoes per second.
  • Specific activity - symbol SA - 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.
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Activity measurements

The units in which activities are measured are: becquerel (symbol Bq) = number of disintegrations per second; curie (Ci) = 3.7 times 10^{10} disintegrations per second. Low activities are also measured in disintegrations per minute (dpm). The becquerel (symbol Bq) is the SI derived unit of radioactivity, defined as the activity of a quantity of radioactive material in which one nucleus decays per second. ... The curie (symbol Ci) is a former unit of radioactivity, defined as 3. ...

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Decay timing

See also: exponential decay It has been suggested that half-life be merged into this article or section. ...


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: Lambda (uppercase Λ, lowercase λ) is the 11th letter of the Greek alphabet. ... Graph of a differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ...

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. It has been suggested that half-life be merged into this article or section. ... The exponential function is one of the most important functions in mathematics. ... In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. ... Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), or they can be used for ordering (this is...


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: Given an assembly of elements, the number of which decreases ultimately to zero, the lifetime (also called the mean lifetime) is a certain number that characterizes the rate of reduction (decay) of the assembly. ... In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. ...

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: Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ...

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

This relationship between the half-life and the decay constant shows that highly radioactive substances are quickly spent, while those that radiate weakly endure longer. Half-lives of known radionuclides vary widely, from more than 1024 years for very nearly stable nuclides, to 10-6 seconds for highly unstable ones. To help compare orders of magnitude of different times, this page lists times longer than 1019 seconds (317 billion years) See also times of other orders of magnitude. ... To help compare orders of magnitude of different times this page lists times between 10-6 seconds and 10-5 seconds (1. ...

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See also

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Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... A Poisson process, named after the French mathematician Siméon-Denis Poisson (1781 - 1840), is a stochastic process which is defined in terms of the occurrences of events. ... Radiation in Physics is the process of emitting energy in the form of waves or particles. ... Clinac 2100 C accelerator Radiation therapy (or radiotherapy) is the medical use of ionizing radiation as part of cancer treatment to control malignant cells (not to be confused with radiology, the use of radiation in medical imaging and diagnosis). ... The radiation warning symbol (trefoil). ... Radiometric dating is a technique used to date materials based on a knowledge of the decay rates of naturally occurring isotopes, and the current abundances. ... This article about actinides in the environment is about the sources, environmental behaviour and effects of actinides in the environment. ... Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ...

External links


  Results from FactBites:
 
The Talk.Origins Archive Post of the Month: March 2001 (4747 words)
During b decay itself, a neutron changes into a proton, electron and electron-antineutrino, and the electron is expelled as a negative beta particle (b- - often written without the negative sign, but sometimes it is necessary to distinguish it from the rarer positive beta or positron decay b+).
Beta decay is in the present context treatable theoretically as if it resulted from a zero-range, current-current interaction, which transforms a proton (neutron) bound within a nucleus into a neutron (proton), with the simultaneous creation or absorption of an electron (positron) and a neutrino (anti-neutrino).
The naturally occurring nuclear beta decays were very early on shown experimentally to be directly associated with transitions between discrete stationary states of the parent and the daughter nucleus, most usually a transition from the ground state of the parent to the ground state or a low lying excited state of the daughter.
  More results at FactBites »


 

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