In nuclear physics, beta decay is a type of radioactive decay in which a beta ray is emitted from an atomic nucleus. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino, or conversely a proton is converted into a neutron by the emission of a positron with a neutrino, thus changing the nuclide type. Neither the beta particle nor its associated neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons; the probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release or Q value must be positive. Beta decay is a consequence of the weak force, characterized by lengthy decay times.
Nucleons are composed of up quarks and down quarks, the weak force allows a quark to change type by the exchange of a W boson and the creation of an electron/antineutrino or positron/neutrino pair. For example, a neutron, composed of two down quarks and an up quark, decays to a proton composed of a down quark and two up quarks. Decay times for many nuclides that are subject to beta decay can be thousands of years. Electron capture is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak force, is the same. In electron capture, an inner atomic electron is captured by a proton in the nucleus, transforming it into a neutron, an electron neutrino is released; the two types of beta decay are known as beta beta plus. In beta minus decay, a neutron is converted to a proton, the process creates an electron and an electron antineutrino. Β+ decay is known as positron emission. Beta decay conserves a quantum number known as the lepton number, or the number of electrons and their associated neutrinos.
These particles have lepton number +1, while their antiparticles have lepton number −1. Since a proton or neutron has lepton number zero, β+ decay must be accompanied with an electron neutrino, while β− decay must be accompanied by an electron antineutrino. An example of electron emission is the decay of carbon-14 into nitrogen-14 with a half-life of about 5,730 years: 146C → 147N + e− + νeIn this form of decay, the original element becomes a new chemical element in a process known as nuclear transmutation; this new element has an unchanged mass number A, but an atomic number Z, increased by one. As in all nuclear decays, the decaying element is known as the parent nuclide while the resulting element is known as the daughter nuclide. Another example is the decay of hydrogen-3 into helium-3 with a half-life of about 12.3 years: 31H → 32He + e− + νeAn example of positron emission is the decay of magnesium-23 into sodium-23 with a half-life of about 11.3 s: 2312Mg → 2311Na + e+ + νeβ+ decay results in nuclear transmutation, with the resulting element having an atomic number, decreased by one.
The beta spectrum, or distribution of energy values for the beta particles, is continuous. The total energy of the decay process is divided between the electron, the antineutrino, the recoiling nuclide. In the figure to the right, an example of an electron with 0.40 MeV energy from the beta decay of 210Bi is shown. In this example, the total decay energy is 1.16 MeV, so the antineutrino has the remaining energy: 1.16-0.40=0.76 MeV. An electron at the far right of the curve would have the maximum possible kinetic energy, leaving the energy of the neutrino to be only its small rest mass. Radioactivity was discovered in 1896 by Henri Becquerel in uranium, subsequently observed by Marie and Pierre Curie in thorium and in the new elements polonium and radium. In 1899, Ernest Rutherford separated radioactive emissions into two types: alpha and beta, based on penetration of objects and ability to cause ionization. Alpha rays could be stopped by thin sheets of paper or aluminium, whereas beta rays could penetrate several millimetres of aluminium.
In 1900, Paul Villard identified a still more penetrating type of radiation, which Rutherford identified as a fundamentally new type in 1903 and termed gamma rays. Alpha and gamma are the first three letters of the Greek alphabet. In 1900, Becquerel measured the mass-to-charge ratio for beta particles by the method of J. J. Thomson used to identify the electron, he found that m/e for a beta particle is the same as for Thomson's electron, therefore suggested that the beta particle is in fact an electron. In 1901, Rutherford and Frederick Soddy showed that alpha and beta radioactivity involves the transmutation of atoms into atoms of other chemical elements. In 1913, after the products of more radioactive decays were known and Kazimierz Fajans independently proposed their radioactive displacement law, which states that beta emission from one element produces another element one place to the right in the periodic table, while alpha emission produces an element two places to the left; the study of beta decay provided the first physical evidence for the existence of the neutrino.
In both alpha and gamma decay, the resulting particle has a narrow energy distribution, since the particle carries the energy from the diffe
Internal conversion is a radioactive decay process wherein an excited nucleus interacts electromagnetically with one of the orbital electrons of the atom. This causes 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 not from the nucleus. For this reason, the high-speed electrons resulting from internal conversion are not called beta particles, since the latter come from beta decay, where they are newly created in the nuclear decay process. Internal conversion is possible whenever gamma decay is possible, except in the case where the atom is ionised. During internal conversion, the atomic number does not change, thus no transmutation of one element to another takes place. Since an electron is lost from the atom, a hole appears in an electron shell, subsequently filled by other electrons that descend to that empty, lower energy level, in the process emit characteristic X-ray, Auger electron, or both.
The atom thus emits high-energy electrons and X-ray photons, none of which originate in that nucleus. The atom supplied the energy needed to eject the electron, which in turn caused the latter events and the other emissions. Since primary electrons from internal conversion carry a fixed part of the characteristic decay energy, they have a discrete energy spectrum, rather than the spread spectrum characteristic of beta particles. Whereas the energy spectrum of beta particles plots as a broad hump, the energy spectrum of internally converted electrons plots as a single sharp peak. In the quantum mechanical model of the electron, there is a non-zero probability of finding the electron within the nucleus. During the internal conversion process, the wavefunction of an inner shell electron is said to penetrate the volume of the atomic nucleus; when this happens, the electron may couple to an excited energy state of the nucleus and take the energy of the nuclear transition directly, without an intermediate gamma ray being first produced.
The kinetic energy of the emitted electron is equal to the transition energy in the nucleus, minus the binding energy of the electron to the atom. Most internal conversion electrons come from the K shell, as these two electrons have the highest probability of being within the nucleus. However, the s states in the L, M, N shells are able to couple to the nuclear fields and cause IC electron ejections from those shells. Ratios of K-shell to other L, M, or N shell internal conversion probabilities for various nuclides have been prepared. An amount of energy exceeding the atomic binding energy of the s electron must be supplied to that electron in order to eject it from the atom to result in IC. There are a few radionuclides in which the decay energy is not sufficient to convert a 1s electron, these nuclides, to decay by internal conversion, must decay by ejecting electrons from the L or M or N shells as these binding energies are lower. Although s electrons are more for IC processes due to their superior nuclear penetration compared to electrons with orbital angular momentum, spectral studies show that p electrons are ejected in the IC process.
After the IC electron has been emitted, the atom is left with a vacancy in one of its electron shells an inner one. This hole will be filled with an electron from one of the higher shells, which causes another outer electron to fill its place in turn, causing a cascade. One or more characteristic X-rays or Auger electrons will be emitted as the remaining electrons in the atom cascade down to fill the vacancies; the decay scheme on the left shows that 203Hg produces a continuous beta spectrum with maximum energy 214 keV, that leads to an excited state of the daughter nucleus 203Tl. This state decays quickly to the ground state of 203Tl, emitting a gamma quantum of 279 keV; the figure on the right shows the electron spectrum of 203Hg, measured by means of a magnetic spectrometer. It includes the continuous beta spectrum and K-, L-, M-lines due to internal conversion. Since the binding energy of the K electrons in 203Tl amounts to 85 keV, the K line has an energy of 279 - 85 = 194 keV; because of lesser binding energies, the L- and M-lines have higher energies.
Because of the finite energy resolution of the spectrometer, the "lines" have a Gaussian shape of finite width. Internal conversion is favoured whenever the energy available for a gamma transition is small, it is the primary mode of de-excitation for 0+→0+ transitions; the 0+→0+ transitions occur where an excited nucleus has zero-spin and positive parity, decays to a ground state which has zero-spin and positive parity. In such cases, de-excitation cannot take place by way of emission of a gamma ray, since this would violate conservation of angular momentum, hence other mechanisms like IC predominate; this shows that internal conversion is not a two-step process where a gamma ray would be first emitted and converted. The competition between internal conversion and gamma decay is quantified in the form of the internal conversion coefficient, defined as α = e / γ where e is the rate of conve
Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more than positively charged protons, which are repelled electrostatically. Neutron capture plays an important role in the cosmic nucleosynthesis of heavy elements. In stars it can proceed in two ways: as a slow process. Nuclei of masses greater than 56 cannot be formed by thermonuclear reactions, but can be formed by neutron capture. Neutron capture on protons yields a line at 2.223 MeV predicted and observed in solar flares. At small neutron flux, as in a nuclear reactor, a single neutron is captured by a nucleus. For example, when natural gold is irradiated by neutrons, the isotope 198Au is formed in a excited state, decays to the ground state of 198Au by the emission of γ rays. In this process, the mass number increases by one; this is written in short form 197Au198Au. If thermal neutrons are used, the process is called thermal capture.
The isotope 198Au is a beta emitter. In this process the atomic number rises by one; the r-process happens inside stars if the neutron flux density is so high that the atomic nucleus has no time to decay via beta emission in between neutron captures. The mass number therefore rises by a large amount. Only afterwards, the unstable nuclei decay via many β− decays to stable or unstable nuclei of high atomic number; the absorption neutron cross-section of an isotope of a chemical element is the effective cross sectional area that an atom of that isotope presents to absorption, is a measure of the probability of neutron capture. It is measured in barns. Absorption cross section is highly dependent on neutron energy; as a generality, the likelihood of absorption is proportional to the time the neutron is in the vicinity of the nucleus. The time spent in the vicinity of the nucleus is inversely proportional to the relative velocity between the neutron and nucleus. Other more specific issues modify this general principle.
Two of the most specified measures are the cross-section for thermal neutron absorption, resonance integral which considers the contribution of absorption peaks at certain neutron energies specific to a particular nuclide above the thermal range, but encountered as neutron moderation slows the neutron down from an original high energy. The thermal energy of the nucleus has an effect. In particular, the increase in uranium-238's ability to absorb neutrons at higher temperatures is a negative feedback mechanism that helps keep nuclear reactors under control. Neutron capture is involved in the formation of isotopes of chemical elements; as a consequence of this fact the energy of neutron capture intervenes in the standard enthalpy of formation of isotopes. Neutron activation analysis can be used to remotely detect the chemical composition of materials; this is because different elements release different characteristic radiation when they absorb neutrons. This makes it useful in many fields related to mineral security.
The most important neutron absorber is 10B as 10B4C in control rods, or boric acid as a coolant water additive in PWRs. Other important neutron absorbers that are used in nuclear reactors are xenon, hafnium, cobalt, titanium, erbium, europium and ytterbium; these occur in combinations such as Mo2B5, hafnium diboride, titanium diboride, dysprosium titanate and gadolinium titanate. Hafnium, one of the last stable elements to be discovered, presents an interesting case. Though hafnium is a heavier element, its electron configuration makes it identical with the element zirconium, they are always found in the same ores. However, their nuclear properties are different in a profound way. Hafnium absorbs neutrons avidly, it can be used in reactor control rods, whereas natural zirconium is transparent to neutrons. So, zirconium is a desirable construction material for reactor internal parts, including the metallic cladding of the fuel rods which contain either uranium, plutonium, or mixed oxides of the two elements.
Hence, it is quite important to be able to separate the zirconium from the hafnium in their occurring alloy. This can only be done inexpensively by using modern chemical ion-exchange resins. Similar resins are used in reprocessing nuclear fuel rods, when it is necessary to separate uranium and plutonium, sometimes thorium. Beta decay Induced radioactivity List of particles Neutron emission Radioactive decay Rays: α — β — γ — δ — ε p-process Thermal Neutron Capture Data Thermal Neutron Cross Sections at the International Atomic Energy Agency
The nuclear force is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electromagnetic force; the nuclear force binds nucleons into atomic nuclei. The nuclear force is powerfully attractive between nucleons at distances of about 1 femtometre, but it decreases to insignificance at distances beyond about 2.5 fm. At distances less than 0.7 fm, the nuclear force becomes repulsive. This repulsive component is responsible for the physical size of nuclei, since the nucleons can come no closer than the force allows. By comparison, the size of an atom, measured in angstroms, is five orders of magnitude larger; the nuclear force is not simple, since it depends on the nucleon spins, has a tensor component, may depend on the relative momentum of the nucleons.
The strong nuclear force is one of the fundamental forces of nature. The nuclear force plays an essential role in storing energy, used in nuclear power and nuclear weapons. Work is required to bring charged protons together against their electric repulsion; this energy is stored when the protons and neutrons are bound together by the nuclear force to form a nucleus. The mass of a nucleus is less than the sum total of the individual masses of the protons and neutrons; the difference in masses is known as the mass defect, which can be expressed as an energy equivalent. Energy is released; this energy is the electromagnetic potential energy, released when the nuclear force no longer holds the charged nuclear fragments together. A quantitative description of the nuclear force relies on equations that are empirical; these equations model the internucleon potential energies, or potentials. The constants for the equations are phenomenological, that is, determined by fitting the equations to experimental data.
The internucleon potentials attempt to describe the properties of nucleon–nucleon interaction. Once determined, any given potential can be used in, e.g. the Schrödinger equation to determine the quantum mechanical properties of the nucleon system. The discovery of the neutron in 1932 revealed that atomic nuclei were made of protons and neutrons, held together by an attractive force. By 1935 the nuclear force was conceived to be transmitted by particles called mesons; this theoretical development included a description of the Yukawa potential, an early example of a nuclear potential. Mesons, predicted by theory, were discovered experimentally in 1947. By the 1970s, the quark model had been developed, by which the mesons and nucleons were viewed as composed of quarks and gluons. By this new model, the nuclear force, resulting from the exchange of mesons between neighboring nucleons, is a residual effect of the strong force. While the nuclear force is associated with nucleons, more this force is felt between hadrons, or particles composed of quarks.
At small separations between nucleons the force becomes repulsive, which keeps the nucleons at a certain average separation if they are of different types. This repulsion arises from the Pauli exclusion force for identical nucleons. A Pauli exclusion force occurs between quarks of the same type within nucleons, when the nucleons are different. At distances larger than 0.7 fm the force becomes attractive between spin-aligned nucleons, becoming maximal at a center–center distance of about 0.9 fm. Beyond this distance the force drops exponentially, until beyond about 2.0 fm separation, the force is negligible. Nucleons have a radius of about 0.8 fm. At short distances, the attractive nuclear force is stronger than the repulsive Coulomb force between protons. However, the Coulomb force between protons has a much greater range as it varies as the inverse square of the charge separation, Coulomb repulsion thus becomes the only significant force between protons when their separation exceeds about 2 to 2.5 fm.
The nuclear force has a spin-dependent component. The force is stronger for particles with their spins aligned than for those with their spins anti-aligned. If two particles are the same, such as two neutrons or two protons, the force is not enough to bind the particles, since the spin vectors of two particles of the same type must point in opposite directions when the particles are near each other and are in the same quantum state; this requirement for fermions stems from the Pauli exclusion principle. For fermion particles of different types, such as a proton and neutron, particles may be close to each other and have aligned spins without violating the Pauli exclusion principle, the nuclear force may bind them, since the nuclear force is much stronger for spin-aligned particles, but if the particles' spins are anti-aligned the nuclear force is too weak to bind them if they are of different types. The nuclear force has a tensor component which depends on the interaction between the nucleon spins and the angular momentum of the nucleons, leading to deformation from a simple spherical shape
Isotopes are variants of a particular chemical element which differ in neutron number, in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom; the term isotope is formed from the Greek roots isos and topos, meaning "the same place". It was coined by a Scottish doctor and writer Margaret Todd in 1913 in a suggestion to chemist Frederick Soddy; the number of protons within the atom's nucleus is called atomic number and is equal to the number of electrons in the neutral atom. Each atomic number identifies a specific element, but not the isotope; the number of nucleons in the nucleus is the atom's mass number, each isotope of a given element has a different mass number. For example, carbon-12, carbon-13, carbon-14 are three isotopes of the element carbon with mass numbers 12, 13, 14, respectively; the atomic number of carbon is 6, which means that every carbon atom has 6 protons, so that the neutron numbers of these isotopes are 6, 7, 8 respectively.
A nuclide is a species of an atom with a specific number of protons and neutrons in the nucleus, for example carbon-13 with 6 protons and 7 neutrons. The nuclide concept emphasizes nuclear properties over chemical properties, whereas the isotope concept emphasizes chemical over nuclear; the neutron number has large effects on nuclear properties, but its effect on chemical properties is negligible for most elements. In the case of the lightest elements where the ratio of neutron number to atomic number varies the most between isotopes it has only a small effect, although it does matter in some circumstances; the term isotopes is intended to imply comparison, for example: the nuclides 126C, 136C, 146C are isotopes, but 4018Ar, 4019K, 4020Ca are isobars. However, because isotope is the older term, it is better known than nuclide, is still sometimes used in contexts where nuclide might be more appropriate, such as nuclear technology and nuclear medicine. An isotope and/or nuclide is specified by the name of the particular element followed by a hyphen and the mass number.
When a chemical symbol is used, e.g. "C" for carbon, standard notation is to indicate the mass number with a superscript at the upper left of the chemical symbol and to indicate the atomic number with a subscript at the lower left. Because the atomic number is given by the element symbol, it is common to state only the mass number in the superscript and leave out the atomic number subscript; the letter m is sometimes appended after the mass number to indicate a nuclear isomer, a metastable or energetically-excited nuclear state, for example 180m73Ta. The common pronunciation of the AZE notation is different from how it is written: 42He is pronounced as helium-four instead of four-two-helium, 23592U as uranium two-thirty-five or uranium-two-three-five instead of 235-92-uranium; some isotopes/nuclides are radioactive, are therefore referred to as radioisotopes or radionuclides, whereas others have never been observed to decay radioactively and are referred to as stable isotopes or stable nuclides.
For example, 14C is a radioactive form of carbon, whereas 12C and 13C are stable isotopes. There are about 339 occurring nuclides on Earth, of which 286 are primordial nuclides, meaning that they have existed since the Solar System's formation. Primordial nuclides include 32 nuclides with long half-lives and 253 that are formally considered as "stable nuclides", because they have not been observed to decay. In most cases, for obvious reasons, if an element has stable isotopes, those isotopes predominate in the elemental abundance found on Earth and in the Solar System. However, in the cases of three elements the most abundant isotope found in nature is one long-lived radioisotope of the element, despite these elements having one or more stable isotopes. Theory predicts that many "stable" isotopes/nuclides are radioactive, with long half-lives; some stable nuclides are in theory energetically susceptible to other known forms of decay, such as alpha decay or double beta decay, but no decay products have yet been observed, so these isotopes are said to be "observationally stable".
The predicted half-lives for these nuclides greatly exceed the estimated age of the universe, in fact there are 27 known radionuclides with half-lives longer than the age of the universe. Adding in the radioactive nuclides that have been created artificially, there are 3,339 known nuclides; these include 905 nuclides that are either stable or have half-lives
The atomic number or proton number of a chemical element is the number of protons found in the nucleus of an atom. It is identical to the charge number of the nucleus; the atomic number uniquely identifies a chemical element. In an uncharged atom, the atomic number is equal to the number of electrons; the sum of the atomic number Z and the number of neutrons, N, gives the mass number A of an atom. Since protons and neutrons have the same mass and the mass defect of nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units, is within 1% of the whole number A. Atoms with the same atomic number Z but different neutron numbers N, hence different atomic masses, are known as isotopes. A little more than three-quarters of occurring elements exist as a mixture of isotopes, the average isotopic mass of an isotopic mixture for an element in a defined environment on Earth, determines the element's standard atomic weight, it was these atomic weights of elements that were the quantities measurable by chemists in the 19th century.
The conventional symbol Z comes from the German word Zahl meaning number, before the modern synthesis of ideas from chemistry and physics denoted an element's numerical place in the periodic table, whose order is but not consistent with the order of the elements by atomic weights. Only after 1915, with the suggestion and evidence that this Z number was the nuclear charge and a physical characteristic of atoms, did the word Atomzahl come into common use in this context. Loosely speaking, the existence or construction of a periodic table of elements creates an ordering of the elements, so they can be numbered in order. Dmitri Mendeleev claimed. However, in consideration of the elements' observed chemical properties, he changed the order and placed tellurium ahead of iodine; this placement is consistent with the modern practice of ordering the elements by proton number, Z, but that number was not known or suspected at the time. A simple numbering based on periodic table position was never satisfactory, however.
Besides the case of iodine and tellurium several other pairs of elements were known to have nearly identical or reversed atomic weights, thus requiring their placement in the periodic table to be determined by their chemical properties. However the gradual identification of more and more chemically similar lanthanide elements, whose atomic number was not obvious, led to inconsistency and uncertainty in the periodic numbering of elements at least from lutetium onward. In 1911, Ernest Rutherford gave a model of the atom in which a central core held most of the atom's mass and a positive charge which, in units of the electron's charge, was to be equal to half of the atom's atomic weight, expressed in numbers of hydrogen atoms; this central charge would thus be half the atomic weight. In spite of Rutherford's estimation that gold had a central charge of about 100, a month after Rutherford's paper appeared, Antonius van den Broek first formally suggested that the central charge and number of electrons in an atom was equal to its place in the periodic table.
This proved to be the case. The experimental position improved after research by Henry Moseley in 1913. Moseley, after discussions with Bohr, at the same lab, decided to test Van den Broek's and Bohr's hypothesis directly, by seeing if spectral lines emitted from excited atoms fitted the Bohr theory's postulation that the frequency of the spectral lines be proportional to the square of Z. To do this, Moseley measured the wavelengths of the innermost photon transitions produced by the elements from aluminum to gold used as a series of movable anodic targets inside an x-ray tube; the square root of the frequency of these photons increased from one target to the next in an arithmetic progression. This led to the conclusion that the atomic number does correspond to the calculated electric charge of the nucleus, i.e. the element number Z. Among other things, Moseley demonstrated that the lanthanide series must have 15 members—no fewer and no more—which was far from obvious from the chemistry at that time.
After Moseley's death in 1915, the atomic numbers of all known elements from hydrogen to uranium were examined by his method. There were seven elements which were not found and therefore identified as still undiscovered, corresponding to atomic numbers 43, 61, 72, 75, 85, 87 and 91. From 1918 to 1947, all seven of these missing elements were discovered. By this time the first four transuranium elements had been discovered, so that the periodic table was complete with no gaps as far as curium. In 1915 the rea