1.
Atomic nucleus
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After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. Almost all of the mass of an atom is located in the nucleus, protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of 6985175000000000000♠1.75 fm for hydrogen to about 6986150000000000000♠15 fm for the heaviest atoms and these dimensions are much smaller than the diameter of the atom itself, by a factor of about 23,000 to about 145,000. The branch of physics concerned with the study and understanding of the nucleus, including its composition. The nucleus was discovered in 1911, as a result of Ernest Rutherfords efforts to test Thomsons plum pudding model of the atom, the electron had already been discovered earlier by J. J. Knowing that atoms are electrically neutral, Thomson postulated that there must be a charge as well. In his plum pudding model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge, to his surprise, many of the particles were deflected at very large angles. This justified the idea of an atom with a dense center of positive charge. The term nucleus is from the Latin word nucleus, a diminutive of nux, in 1844, Michael Faraday used the term to refer to the central point of an atom. The modern atomic meaning was proposed by Ernest Rutherford in 1912, the adoption of the term nucleus to atomic theory, however, was not immediate. In 1916, for example, Gilbert N, the nuclear strong force extends far enough from each baryon so as to bind the neutrons and protons together against the repulsive electrical force between the positively charged protons. The nuclear strong force has a short range, and essentially drops to zero just beyond the edge of the nucleus. The collective action of the charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations, which chemical element an atom represents is determined by the number of protons in the nucleus, the neutral atom will have an equal number of electrons orbiting that nucleus. Individual chemical elements can create more stable electron configurations by combining to share their electrons and it is that sharing of electrons to create stable electronic orbits about the nucleus that appears to us as the chemistry of our macro world. Protons define the entire charge of a nucleus, and hence its chemical identity, neutrons are electrically neutral, but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons explain the phenomenon of isotopes – varieties of the chemical element which differ only in their atomic mass. They are sometimes viewed as two different quantum states of the particle, the nucleon
2.
Nucleon
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In chemistry and physics, nucleons are the proton and the neutron, which are the constituents of the atomic nucleus, and are themselves composed of down and up quarks. The number of nucleons defines an isotopes mass number, the atom is made up of a nucleus surrounded by electrons. Until the 1960s, nucleons were thought to be elementary particles, now they are known to be composite particles, made of three quarks bound together by the so-called strong interaction. The interaction between two or more nucleons is called internucleon interactions or nuclear force, which is ultimately caused by the strong interaction. Nucleons sit at the boundary where particle physics and nuclear physics overlap, Particle physics, particularly quantum chromodynamics, provides the fundamental equations that explain the properties of quarks and of the strong interaction. These equations explain quantitatively how quarks can bind together into protons and neutrons, however, when multiple nucleons are assembled into an atomic nucleus, these fundamental equations become too difficult to solve directly. Instead, nuclides are studied within nuclear physics, which studies nucleons and their interactions by approximations and models and these models can successfully explain nuclide properties, for example, whether or not a certain nuclide undergoes radioactive decay. The proton and neutron are both baryons and both fermions, one carries a positive net charge and the other carries a zero net charge, the protons mass is only 0. 1% less than the neutrons. Thus, they can be viewed as two states of the nucleon, and together form an isospin doublet. In isospin space, neutrons can be transformed into protons via SU symmetries and these nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space. According to the Noether theorem, isospin is conserved with respect to the strong interaction, protons and neutrons are most important and best known for constituting atomic nuclei, but they can also be found on their own, not part of a larger nucleus. A proton on its own is the nucleus of the hydrogen-1 atom, a neutron on its own is unstable, but they can be found in nuclear reactions and are used in scientific analysis. Both the proton and neutron are made of three quarks, the proton is made of two up quarks and one down quark, while the neutron is one up quark and two down quarks. The quarks are held together by the force, or equivalently, by gluons. An up quark has electric charge + 2⁄3 e, and a down quark has charge − 1⁄3 e, so the electric charge of the proton and neutron are +e and 0. The word neutron comes from the fact that it is electrically neutral, the mass of the proton and neutron is quite similar, The proton is 1. 6726×10−27 kg or 938.27 MeV/c2, while the neutron is 1. 6749×10−27 kg or 939.57 MeV/c2. The neutron is roughly 0. 1% heavier, the similarity in mass can be explained roughly by the slight difference in mass of up quark and down quark composing the nucleons. However, detailed explanation remains a problem in particle physics
3.
Proton
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A proton is a subatomic particle, symbol p or p+, with a positive electric charge of +1e elementary charge and mass slightly less than that of a neutron. Protons and neutrons, each with masses of one atomic mass unit, are collectively referred to as nucleons. One or more protons are present in the nucleus of every atom, the number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number. Since each element has a number of protons, each element has its own unique atomic number. The word proton is Greek for first, and this name was given to the nucleus by Ernest Rutherford in 1920. In previous years, Rutherford had discovered that the nucleus could be extracted from the nuclei of nitrogen by atomic collisions. Protons were therefore a candidate to be a particle, and hence a building block of nitrogen. In the modern Standard Model of particle physics, protons are hadrons, and like neutrons, although protons were originally considered fundamental or elementary particles, they are now known to be composed of three valence quarks, two up quarks and one down quark. The rest masses of quarks contribute only about 1% of a protons mass, the remainder of a protons mass is due to quantum chromodynamics binding energy, which includes the kinetic energy of the quarks and the energy of the gluon fields that bind the quarks together. At sufficiently low temperatures, free protons will bind to electrons, however, the character of such bound protons does not change, and they remain protons. A fast proton moving through matter will slow by interactions with electrons and nuclei, the result is a protonated atom, which is a chemical compound of hydrogen. In vacuum, when electrons are present, a sufficiently slow proton may pick up a single free electron, becoming a neutral hydrogen atom. Such free hydrogen atoms tend to react chemically with other types of atoms at sufficiently low energies. When free hydrogen atoms react with other, they form neutral hydrogen molecules. Protons are spin-½ fermions and are composed of three quarks, making them baryons. Protons have an exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm. Protons and neutrons are both nucleons, which may be together by the nuclear force to form atomic nuclei. The nucleus of the most common isotope of the atom is a lone proton
4.
Neutron
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The neutron is a subatomic particle, symbol n or n0, with no net electric charge and a mass slightly larger than that of a proton. Protons and neutrons, each with approximately one atomic mass unit, constitute the nucleus of an atom. Their properties and interactions are described by nuclear physics, the nucleus consists of Z protons, where Z is called the atomic number, and N neutrons, where N is the neutron number. The atomic number defines the properties of the atom. The terms isotope and nuclide are often used synonymously, but they are chemical and nuclear concepts, the atomic mass number, symbol A, equals Z+N. For example, carbon has atomic number 6, and its abundant carbon-12 isotope has 6 neutrons, some elements occur in nature with only one stable isotope, such as fluorine. Other elements occur with many stable isotopes, such as tin with ten stable isotopes, even though it is not a chemical element, the neutron is included in the table of nuclides. Within the nucleus, protons and neutrons are bound together through the nuclear force, neutrons are produced copiously in nuclear fission and fusion. They are a contributor to the nucleosynthesis of chemical elements within stars through fission, fusion. The neutron is essential to the production of nuclear power, in the decade after the neutron was discovered in 1932, neutrons were used to induce many different types of nuclear transmutations. These events and findings led to the first self-sustaining nuclear reactor, free neutrons, or individual neutrons free of the nucleus, are effectively a form of ionizing radiation, and as such, are a biological hazard, depending upon dose. A small natural background flux of free neutrons exists on Earth, caused by cosmic ray showers. Dedicated neutron sources like neutron generators, research reactors and spallation sources produce free neutrons for use in irradiation, neutrons and protons are both nucleons, which are attracted and bound together by the nuclear force to form atomic nuclei. The nucleus of the most common isotope of the atom is a lone proton. The nuclei of the hydrogen isotopes deuterium and tritium contain one proton bound to one. All other types of nuclei are composed of two or more protons and various numbers of neutrons. The most common nuclide of the chemical element lead, 208Pb has 82 protons and 126 neutrons. The free neutron has a mass of about 1. 675×10−27 kg, the neutron has a mean square radius of about 0. 8×10−15 m, or 0.8 fm, and it is a spin-½ fermion
5.
Nuclear matter
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Nuclear matter is an idealized system of interacting nucleons that exists in several phases that as yet are not fully established. It is not matter in a nucleus, but a hypothetical substance consisting of a number of protons and neutrons interacting by only nuclear forces. Volume and the number of particles are infinite, but the ratio is finite, infinite volume implies no surface effects and translational invariance. A common idealization is symmetric nuclear matter, which consists of numbers of protons and neutrons. Some authors use matter in a broader sense, and refer to the model described above as infinite nuclear matter, and consider it as a toy model. In a neutron star, pressure rises from zero to a large value in the center. Methods capable of treating finite regions have applied to stars. One such model for finite nuclei is the drop model. QCD vacuum Quark–gluon plasma Degenerate matter Neutron-degenerate matter Strange matter Nuclear structure Neutronium Nuclear physics
6.
Nuclear force
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The nuclear force is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the force almost identically. The nuclear force binds nucleons into atomic nuclei, the nuclear force is powerfully attractive between nucleons at distances of about 1 femtometer, but it rapidly decreases to insignificance at distances beyond about 2.5 fm. At distances less than 0.7 fm, the force becomes repulsive. This repulsive component is responsible for the size of nuclei. By comparison, the size of an atom, measured in angstroms, is five orders of magnitude larger. The nuclear force is not simple, however, since it depends on the spins, has a tensor component. The nuclear force is not one of the forces of nature. The nuclear force plays an role in storing energy that is used in nuclear power. Work is required to bring charged protons together against their electric repulsion and 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 masses of the protons and neutrons. The difference in masses is known as the defect, which can be expressed as an energy equivalent. Energy is released when a heavy nucleus breaks apart into two or more lighter nuclei and this energy is the electromagnetic potential energy that is 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 partly empirical and 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 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, 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 example of a nuclear potential
7.
Nuclear structure
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Understanding the structure of the atomic nucleus is one of the central challenges in nuclear physics. The liquid drop model is one of the first models of nuclear structure and it describes the nucleus as a semiclassical fluid made up of neutrons and protons, with an internal repulsive electrostatic force proportional to the number of protons. The quantum mechanical nature of these particles appears via the Pauli exclusion principle, thus the fluid is actually what is known as a Fermi liquid. The coefficients a V, a S, a C, a A and this simple model reproduces the main features of the binding energy of nuclei. The expression shell model is ambiguous in that it refers to two different eras in the state of the art and it was previously used to describe the existence of nucleon shells in the nucleus according to an approach closer to what is now called mean field theory. Nowadays, it refers to an analogous to the configuration interaction formalism used in quantum chemistry. We shall introduce the latter here, systematic measurements of the binding energy of atomic nuclei show systematic deviations with respect to those estimated from the liquid drop model. In particular, some nuclei having certain values for the number of protons and/or neutrons are more tightly together than predicted by the liquid drop model. These nuclei are called singly/doubly magic and this observation led scientists to assume the existence of a shell structure of nucleons within the nucleus, like that of electrons within atoms. Strictly speaking, one should not speak of energies of individual nucleons, however, as an approximation one may envision an average nucleus, within which nucleons propagate individually. Owing to their character, they may only occupy discrete energy levels. These levels are by no means uniformly distributed, some intervals of energy are crowded, a shell is such a set of levels separated from the other ones by a wide empty gap. The energy levels are found by solving the Schrödinger equation for a single nucleon moving in the potential generated by all other nucleons. Each level may be occupied by a nucleon, or empty, some levels accommodate several different quantum states with the same energy, they are said to be degenerate. This occurs in if the average nucleus has some symmetry. The concept of shells allows one to understand why some nuclei are more tightly than others. This is because two nucleons of the same kind cannot be in the same state, so the lowest-energy state of the nucleus is one where nucleons fill all energy levels from the bottom up to some level. A nucleus with full shells is exceptionally stable, as will be explained, therefore, nuclei which have a full outer proton shell will be more tightly bound and have a higher binding energy than other nuclei with a similar total number of protons
8.
Nuclear reaction
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Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. Nuclear reaction is a term implying a change in a nuclide. Natural nuclear reactions occur in the interaction between rays and matter, and nuclear reactions can be employed artificially to obtain nuclear energy, at an adjustable rate. The complete equation therefore reads, or more simply, Instead of using the equations in the style above. This style of the form AD is equivalent to A + b producing c + D, the reaction above would be written as Li-6α. In 1919, Ernest Rutherford was able to accomplish transmutation of nitrogen into oxygen at the University of Manchester and this was the first observation of an induced nuclear reaction, that is, a reaction in which particles from one decay are used to transform another atomic nucleus. Kinetic energy may be released during the course of a reaction or kinetic energy may have to be supplied for the reaction to take place, in a nuclear reaction, the total energy is conserved. The missing rest mass must therefore reappear as kinetic energy released in the reaction, using Einsteins mass-energy equivalence formula E = mc², the amount of energy released can be determined. We first need the energy equivalent of one atomic unit,1 u c² = × ² =1.49242 × 10−10 kg ² =1.49242 × 10−10 J × =931.49 MeV. Hence, the energy released is 0.0238 ×931 MeV =22.2 MeV, expressed differently, the mass is reduced by 0. 3%, corresponding to 0. 3% of 90 PJ/kg is 270 TJ/kg. Consequently, alpha particles appear frequently on the hand side of nuclear reactions. When the product nucleus is metastable, this is indicated by placing an asterisk next to its atomic number and this energy is eventually released through nuclear decay. A small amount of energy may also emerge in the form of X-rays, generally, the product nucleus has a different atomic number, and thus the configuration of its electron shells is wrong. As the electrons rearrange themselves and drop to lower energy levels, for the particular case discussed above, the reaction energy has already been calculated as Q =22.2 MeV. Hence, The reaction energy is positive for exothermal reactions and negative for endothermal reactions, on the one hand, it is the difference between the sums of kinetic energies on the final side and on the initial side. But on the hand, it is also the difference between the nuclear rest masses on the initial side and on the final side. If the reaction equation is balanced, that not mean that the reaction really occurs. The rate at which reactions occur depends on the energy, the particle flux
9.
Nuclear model
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After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. Almost all of the mass of an atom is located in the nucleus, protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of 6985175000000000000♠1.75 fm for hydrogen to about 6986150000000000000♠15 fm for the heaviest atoms and these dimensions are much smaller than the diameter of the atom itself, by a factor of about 23,000 to about 145,000. The branch of physics concerned with the study and understanding of the nucleus, including its composition. The nucleus was discovered in 1911, as a result of Ernest Rutherfords efforts to test Thomsons plum pudding model of the atom, the electron had already been discovered earlier by J. J. Knowing that atoms are electrically neutral, Thomson postulated that there must be a charge as well. In his plum pudding model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge, to his surprise, many of the particles were deflected at very large angles. This justified the idea of an atom with a dense center of positive charge. The term nucleus is from the Latin word nucleus, a diminutive of nux, in 1844, Michael Faraday used the term to refer to the central point of an atom. The modern atomic meaning was proposed by Ernest Rutherford in 1912, the adoption of the term nucleus to atomic theory, however, was not immediate. In 1916, for example, Gilbert N, the nuclear strong force extends far enough from each baryon so as to bind the neutrons and protons together against the repulsive electrical force between the positively charged protons. The nuclear strong force has a short range, and essentially drops to zero just beyond the edge of the nucleus. The collective action of the charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations, which chemical element an atom represents is determined by the number of protons in the nucleus, the neutral atom will have an equal number of electrons orbiting that nucleus. Individual chemical elements can create more stable electron configurations by combining to share their electrons and it is that sharing of electrons to create stable electronic orbits about the nucleus that appears to us as the chemistry of our macro world. Protons define the entire charge of a nucleus, and hence its chemical identity, neutrons are electrically neutral, but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons explain the phenomenon of isotopes – varieties of the chemical element which differ only in their atomic mass. They are sometimes viewed as two different quantum states of the particle, the nucleon
10.
Semi-empirical mass formula
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In nuclear physics, the semi-empirical mass formula is used to approximate the mass and various other properties of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory, the theory is based on the liquid drop model proposed by George Gamow, which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. The liquid drop model in nuclear physics treats the nucleus as a drop of incompressible fluid of very high density. It was first proposed by George Gamow and then developed by Niels Bohr, the nucleus is made of nucleons, which are held together by the nuclear force. This is very similar to the structure of liquid drop made of microscopic molecules. This is a model that does not explain all the properties of the nucleus. It also helps to predict the binding energy and to assess how much is available for consumption. Mathematical analysis of the theory delivers an equation which attempts to predict the energy of a nucleus in terms of the numbers of protons and neutrons it contains. This equation has five terms on its right hand side and these correspond to the cohesive binding of all the nucleons by the nuclear force, a surface energy term, the electrostatic mutual repulsion of the protons, an asymmetry term and a pairing term. When an assembly of nucleons of the size is packed together into the smallest volume. So, this energy is proportional to the volume. A nucleon at the surface of a nucleus interacts with other nucleons than one in the interior of the nucleus. This surface energy term takes that into account and is negative and is proportional to the surface area. The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy, an energy associated with the Pauli exclusion principle. An energy which is a term that arises from the tendency of proton pairs. An even number of particles is more stable than an odd number, in the following formulae, let A be the total number of nucleons, Z the number of protons, and N the number of neutrons, so that A = Z + N. The coefficients a V, a S, a C, a A, the term a V A is known as the volume term. The volume of the nucleus is proportional to A, so this term is proportional to the volume, the basis for this term is the strong nuclear force
11.
Nuclear shell model
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The first shell model was proposed by Dmitry Ivanenko in 1932. The shell model is analogous to the atomic shell model which describes the arrangement of electrons in an atom. When adding nucleons to a nucleus, there are points where the binding energy of the next nucleon is significantly less than the last one. This observation, that there are certain magic numbers of nucleons,2,8,20,28,50,82,126 which are tightly bound than the next higher number, is the origin of the shell model. The shells for protons and for neutrons are independent of each other, therefore, one can have magic nuclei where one nucleon type or the other is at a magic number, and doubly magic nuclei, where both are. Some semimagic numbers have been found, notably Z=40 giving nuclear shell filling for the elements,16 may also be a magic number. In order to get these numbers, the shell model starts from an average potential with a shape something between the square well and the harmonic oscillator. To this potential a spin orbit term is added, nevertheless, the magic numbers of nucleons, as well as other properties, can be arrived at by approximating the model with a three-dimensional harmonic oscillator plus a spin-orbit interaction. A more realistic but also complicated potential is known as Woods Saxon potential and this would give, for example, in the first two levels We can imagine ourselves building a nucleus by adding protons and neutrons. These will always fill the lowest available level, thus the first two protons fill level zero, the next six protons fill level one, and so on. Therefore nuclei which have a full outer shell will have a higher binding energy than other nuclei with a similar total number of protons. All this is true for neutrons as well and this means that the magic numbers are expected to be those in which all occupied shells are full. We see that for the first two numbers we get 2 and 8, in accord with experiment, however the full set of magic numbers does not turn out correctly. These can be computed as follows, In a three-dimensional harmonic oscillator the total degeneracy at level n is 2, due to the spin, the degeneracy is doubled and is. Thus the magic numbers would be ∑ n =0 k =3 for all integer k and this gives the following magic numbers,2,8,20,40,70,112. Which agree with experiment only in the first three entries and these numbers are twice the tetrahedral numbers from the Pascal Triangle. In particular, the first six shells are, level 0,2 states =2, level 2,2 states +10 states =12. Level 3,6 states +14 states =20, level 4,2 states +10 states +18 states =30
12.
Nuclide
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A nuclide is an atomic species characterized by the specific constitution of its nucleus, i. e. by its number of protons Z, its number of neutrons N, and its nuclear energy state. The word nuclide was proposed by Truman P. Kohman in 1947, Kohman originally suggested nuclide as referring to a species of nucleus defined by containing a certain number of neutrons and protons. The word thus was originally intended to focus on the nucleus, nuclide refers to a nucleus rather than to an atom. Identical nuclei belong to one nuclide, for each nucleus of the carbon-13 nuclide is composed of 6 protons and 7 neutrons. The nuclide concept emphasizes nuclear properties over chemical properties, while 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. Since isotope is the term, it is better known than nuclide. A set of nuclides with equal number, i. e. of the same chemical element but different neutron numbers, are called isotopes of the element. Particular nuclides are still often loosely called isotopes, but the term nuclide is the one in general. In similar manner, a set of nuclides with equal mass number A, but different atomic number, are called isobars, and isotones are nuclides of equal neutron number but different proton numbers. The name isotone has been derived from the isotope to emphasize that in the first group of nuclides it is the number of neutrons that is constant. See Isotope#Notation for an explanation of the used for different nuclide or isotope types. Nuclear isomers are members of a set of nuclides with equal number and equal mass number. An example is the two states of the single isotope 99 43Tc shown among the decay schemes, each of these two states qualifies as a different nuclide, illustrating one way that nuclides may differ from isotopes. The most long-lived non-ground state nuclear isomer is the nuclide tantalum-180m and this nuclide occurs primordially, and has never been observed to decay to the ground state. There are about 254 nuclides in nature that have never observed to decay. They occur among the 80 different elements that have one or more stable isotopes, see stable isotope and primordial nuclide. Unstable nuclides are radioactive and are called radionuclides and their decay products are called radiogenic nuclides. About 254 stable and about 85 unstable nuclides exist naturally on Earth, natural radionuclides may be conveniently subdivided into three types
13.
Isotope
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Isotopes are variants of a particular chemical element which differ in neutron number. All isotopes of an element have the same number of protons in each atom. The number of protons within the 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 atoms mass number, and each isotope of a given element has a different mass number. For example, carbon-12, carbon-13 and carbon-14 are three isotopes of the element carbon with mass numbers 12,13 and 14 respectively. The atomic number of carbon is 6, which means that carbon atom has 6 protons. Nuclide refers to a rather than to an atom. Identical nuclei belong to one nuclide, for each nucleus of the carbon-13 nuclide is composed of 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. Because isotope is the term, it is better known than nuclide. An isotope and/or nuclide is specified by the name of the particular element followed by a hyphen, when a chemical symbol is used, e. g. C for carbon, standard notation is to indicate the number with a superscript at the upper left of the chemical symbol. Because the atomic number is given by the element symbol, it is common to only the mass number in the superscript. The letter m is sometimes appended after the number to indicate a nuclear isomer. For example, 14C is a form of carbon, whereas 12C. There are about 339 naturally occurring nuclides on Earth, of which 286 are primordial nuclides, primordial nuclides include 32 nuclides with very long half-lives and 254 that are formally considered as stable nuclides, because they have not been observed to decay. In most cases, for reasons, if an element has stable isotopes. Theory predicts that many apparently stable isotopes/nuclides are radioactive, with extremely long half-lives, of the 254 nuclides never observed to decay, only 90 of these are theoretically stable to all known forms of decay
14.
Atomic number
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The atomic number or proton number of a chemical element is the number of protons found in the nucleus of an atom of that element. It is identical to the number of the nucleus. The atomic number identifies a chemical element. In an uncharged atom, the number is also equal to the number of electrons. The atomic number Z, should not be confused with the mass number A and this number of neutrons, N, completes the weight, A = Z + N. Atoms with the atomic number Z but different neutron numbers N. Historically, it was these atomic weights of elements that were the quantities measurable by chemists in the 19th century. Only after 1915, with the suggestion and evidence that this Z number was also the nuclear charge, loosely speaking, the existence or construction of a periodic table of elements creates an ordering of the elements, and so they can be numbered in order. Dmitri Mendeleev claimed that he arranged his first periodic tables in order of atomic weight, however, in consideration of the elements observed chemical properties, he changed the order slightly and placed tellurium ahead of iodine. This placement is consistent with the practice of ordering the elements by proton number, Z. A simple numbering based on periodic table position was never entirely satisfactory and this central charge would thus be approximately half the atomic weight. This proved eventually to be the case, the experimental position improved dramatically after research by Henry Moseley in 1913. 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 and this led to the conclusion that the atomic number does closely correspond to the calculated electric charge of the nucleus, i. e. the element number Z. Among other things, Moseley demonstrated that the series must have 15 members—no fewer. After Moseleys death in 1915, the 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, from 1918 to 1947, all seven of these missing elements were discovered. By this time the first four transuranium elements had also been discovered, in 1915 the reason for nuclear charge being quantized in units of Z, which were now recognized to be the same as the element number, was not understood
15.
Isobar (nuclide)
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Isobars are atoms of different chemical elements that have the same number of nucleons. Correspondingly, isobars differ in number but have the same mass number. An example of a series of isobars would be 40S, 40Cl, 40Ar, 40K, the nuclei of these nuclides all contain 40 nucleons, however, they contain varying numbers of protons and neutrons. The term isobars for nuclides was suggested by Alfred Walter Stewart in 1918 and it is derived from the Greek word isos, meaning equal and baros, meaning weight. The same mass number implies neither the same mass of nuclei, for odd A, it is admitted that δ =0 and the mass dependence on Z is convex. This explains that beta-decay is energetically favorable for neutron-rich nuclides, both decay modes do not change the mass number, hence an original nucleus and its daughter nucleus are isobars. In both aforementioned cases, a nucleus decays to its lighter isobar. For even A the δ term has the form, δ = Z a P A −12 where aP is another constant and this term, subtracted from the mass expression above, is positive for even-even nuclei and negative for odd-odd nuclei. This means that even-even nuclei, which have not a strong neutron excess or neutron deficiency, have higher binding energy than their odd-odd isobar neighbors and it implies that even-even nuclei are lighter and more stable. The difference is especially strong for small A and this effect is also predicted by other nuclear models and has important consequences. The Mattauch isobar rule states that if two adjacent elements on the table have isotopes of the same mass number, one of these isobars must be a radionuclide. No observationally stable isobars exist for mass numbers 5,8,147,151, as well as for 209, three observationally stable isobars exist for 124. Isotopes Isotones Nuclear isomers Magic number Electron capture Sprawls, Perry,5 – Characteristics and Structure of Matter
16.
Isotone
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Two nuclides are isotones if they have the same neutron number N, but different proton number Z. For example, boron-12 and carbon-13 nuclei both contain 7 neutrons, and so are isotones, similarly, 36S, 37Cl, 38Ar, 39K, and 40Ca nuclei are all isotones of 20 because they all contain 20 neutrons. Despite its similarity to the Greek for same stretching, the term was formed by the German physicist K. Guggenheimer by changing the p in isotope from p for proton to n for neutron, the largest numbers of observationally stable nuclides exist for isotones 50 and 82. Neutron numbers for which there are no stable isotones are 19,21,35,39,45,61,89,115,123, in contrast, the proton numbers for which there are no stable isotopes are 43,61, and 83 or more. This is related to magic numbers, the number of nucleons forming complete shells within the nucleus, e. g.2,8,20,28,50,82. No more than one stable nuclide has the same odd neutron number, except for 1,5,7,55, odd neutron numbers for which there is a stable nuclide and a primordial radionuclide are 27,65,81,85, and 105. Neutron numbers for which there are two primordial nuclides are 88 and 112, isotopes are nuclides having the same number of protons, e. g. carbon-12 and carbon-13. Isobars are nuclides having the mass number, e. g. carbon-12 and boron-12. Nuclear isomers are different excited states of the type of nucleus. A transition from one isomer to another is accompanied by emission or absorption of a gamma ray, or the process of internal conversion
17.
Neutron number
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The neutron number, symbol N, is the number of neutrons in a nuclide. Atomic number plus neutron number equals mass number, Z+N=A, the difference between the neutron number and the atomic number is known as the neutron excess, D = N - Z = A - 2Z. Neutron number is rarely written explicitly in nuclide symbol notation, in order of increasing explicitness and decreasing frequency of usage, Nuclides that have the same neutron number but a different proton number are called isotones. This word was formed by replacing the p in isotope with n for neutron, Nuclides that have the same mass number are called isobars. Nuclides that have the same neutron excess are called isodiaphers, chemical properties are primarily determined by proton number, which determines which chemical element the nuclide is a member of, neutron number has only a slight influence. Neutron number is primarily of interest for nuclear properties, for example, actinides with odd neutron number are usually fissile while actinides with even neutron number are usually not fissile. Only 57 stable nuclides have an odd number, compared to 200 with an even neutron number. No odd-neutron-number isotope is the most naturally abundant isotope in its element, except for beryllium-9 which is the only stable isotope, nitrogen-14. Only two stable nuclides have fewer neutrons than protons, hydrogen-1 and helium-3
18.
Isodiapher
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For example, for both 234 90Th and 238 92U the difference between the neutron number and proton number is N − Z =54. One large family of isodiaphers has zero neutron excess, N=Z and it contains many primordial isotopes of elements up to calcium. It includes ubiquitous 12 6C,16 8O, and 14 7N, the daughter nuclide of an alpha decay is an isodiapher of the original nucleus
19.
Neutron excess
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The neutron number, symbol N, is the number of neutrons in a nuclide. Atomic number plus neutron number equals mass number, Z+N=A, the difference between the neutron number and the atomic number is known as the neutron excess, D = N - Z = A - 2Z. Neutron number is rarely written explicitly in nuclide symbol notation, in order of increasing explicitness and decreasing frequency of usage, Nuclides that have the same neutron number but a different proton number are called isotones. This word was formed by replacing the p in isotope with n for neutron, Nuclides that have the same mass number are called isobars. Nuclides that have the same neutron excess are called isodiaphers, chemical properties are primarily determined by proton number, which determines which chemical element the nuclide is a member of, neutron number has only a slight influence. Neutron number is primarily of interest for nuclear properties, for example, actinides with odd neutron number are usually fissile while actinides with even neutron number are usually not fissile. Only 57 stable nuclides have an odd number, compared to 200 with an even neutron number. No odd-neutron-number isotope is the most naturally abundant isotope in its element, except for beryllium-9 which is the only stable isotope, nitrogen-14. Only two stable nuclides have fewer neutrons than protons, hydrogen-1 and helium-3
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Stable isotope
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The term stable isotope has a similar meaning to stable nuclide, but is preferably used when speaking of nuclides of a specific element. Hence, the plural form stable isotopes usually refers to isotopes of the same element, the relative abundance of such stable isotopes can be measured experimentally, yielding an isotope ratio that can be used as a research tool. Theoretically, such stable isotopes could include the radiogenic daughter products of radioactive decay, however, the expression stable isotope ratio is preferably used to refer to isotopes whose relative abundances are affected by isotope fractionation in nature. This field is termed stable isotope geochemistry, measurement of the ratios of naturally occurring stable isotopes plays an important role in isotope geochemistry, but stable isotopes are also finding uses in ecological and biological studies. Other workers have used oxygen isotope ratios to reconstruct historical atmospheric temperatures, the long history of study of these elements is in part because the proportions of stable isotopes in these light and volatile elements is relatively easy to measure. However, recent advances in isotope ratio mass spectrometry now enable the measurement of isotope ratios in heavier elements, such as iron, copper, zinc, molybdenum. The variations in oxygen and hydrogen isotope ratios have applications in hydrology since most samples will lie between two extremes, ocean water and Arctic/Antarctic snow, stable isotopes of water are also used in partitioning water sources for plant transpiration and groundwater recharge. Another application is in paleotemperature measurement for paleoclimatology, for example, one technique is based on the variation in isotopic fractionation of oxygen by biological systems with temperature. Species of Foraminifera incorporate oxygen as calcium carbonate in their shells, the ratio of the oxygen isotopes oxygen-16 and oxygen-18 incorporated into the calcium carbonate varies with temperature and the oxygen isotopic composition of the water. This oxygen remains fixed in the calcium carbonate when the dies, falls to the sea bed. In forensic science, research suggests that the variation in certain isotope ratios in drugs derived from plant sources can be used to determine the drugs continent of origin and it also has applications in doping control, to distinguish between endogenous and exogenous sources of hormones. Chondrite meteorites are classified using the isotope ratios. In addition, a signature of carbon-13 confirms the non-terrestrial origin for organic compounds found in carbonaceous chondrites
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Magic number (physics)
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In nuclear physics, a magic number is a number of nucleons such that they are arranged into complete shells within the atomic nucleus. The seven most widely recognized magic numbers as of 2007 are 2,8,20,28,50,82, large isotopes with magic numbers of nucleons are said to exist in an island of stability. Unlike the magic numbers 2–126, which are realized in spherical nuclei, before this was realized, higher magic numbers, such as 184,258,350, and 462, were predicted based on simple calculations that assumed spherical shapes, these are generated by the formula 2. It is now believed that the sequence of spherical magic numbers cannot be extended in this way, further predicted magic numbers are 114,122,124, and 164 for protons as well as 184,196,236, and 318 for neutrons. It seemed a little magic to him, and that is how the words ‘Magic Numbers’ were coined. ”Nuclei which have neutron number and proton numbers each equal to one of the magic numbers are called double magic. Examples of double magic isotopes include helium-4, oxygen-16, calcium-40, calcium-48, nickel-48, nickel-78, double-magic effects may allow existence of stable isotopes which otherwise would not have been expected. An example is calcium-40, with 20 neutrons and 20 protons, both calcium-48 and nickel-48 are double magic because calcium-48 has 20 protons and 28 neutrons while nickel-48 has 28 protons and 20 neutrons. Calcium-48 is very neutron-rich for such an element, but like calcium-40. Nickel-48, discovered in 1999, is the most proton-rich isotope known beyond helium-3, at the other extreme, nickel-78 is also doubly magical, with 28 protons and 50 neutrons, a ratio observed only in much heavier elements apart from tritium with one proton and two neutrons. Magic number shell effects are seen in ordinary abundances of elements, helium-4 is among the most abundant nuclei in the universe, Magic effects can keep unstable nuclides from decaying as rapidly as would otherwise be expected. For example, the nuclides tin-100 and tin-132 are examples of doubly magic isotopes of tin that are unstable, and represent endpoints beyond which stability drops off rapidly. In December 2006 hassium-270, with 108 protons and 162 neutrons, was discovered by a team of scientists led by the Technical University of Munich having the half-life of 22 seconds. Hassium-270 evidently forms part of an island of stability, and may even be double magic, Nuclear shells are said to occur when the separation between energy levels is significantly greater than the local mean separation. In the shell model for the nucleus, magic numbers are the numbers of nucleons at which a shell is filled. For instance the magic number 8 occurs when 1s1/2, 1p3/2, 1p1/2 energy levels are filled as there is an energy gap between the 1p1/2 and the next highest 1d5/2 energy levels. The atomic analog to nuclear magic numbers are numbers of electrons leading to discontinuities in the ionization energy. These occur for the noble gases helium, neon, argon, krypton, xenon, radon and oganesson, hence, the atomic magic numbers are 2,10,18,36,54,86 and 118. In 2007, Jozsef Garai from Florida International University proposed a formula describing the periodicity of the nucleus in the periodic system based on the double tetrahedron
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Even and odd atomic nuclei
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In nuclear physics, properties of a nucleus depend on evenness or oddness of its atomic number Z, neutron number N and, consequently, of their sum, the mass number A. Most notably, oddness of both Z and N tends to lower the nuclear binding energy, making odd nuclei, generally, less stable. This effect is not only experimentally observed, but is included to the semi-empirical mass formula and explained by other nuclear models. This remarkable difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay, also, the nuclear spin is integer for all even-A nuclei and non-integer for all odd-A nuclei. The neutron–proton ratio is not the only factor affecting nuclear stability, adding neutrons to isotopes can vary their nuclear spins and nuclear shapes, causing differences in neutron capture cross-sections and gamma spectroscopy and nuclear magnetic resonance properties. If too many or too few neutrons are present with regard to the binding energy optimum. Unstable nuclides with a number of neutrons or protons decay by beta decay, electron capture or other exotic means, such as spontaneous fission. Even-mass-number nuclides, which comprise 153/254 = ~ 60% of all nuclides, are bosons. Almost all are even-proton, even-neutron nuclides, which necessarily have spin 0 because of pairing. The remainder of the stable nuclides are 5 odd-proton, odd-neutron stable nuclides (see below. Beta decay of an even–even nucleus produces a nucleus. An even number of protons or of neutrons are stable because of pairing effects. For example, the beta emitter 116Cd has a half-life of 2. 9×1019 years. This makes for a number of stable even–even nuclides, up to three for some mass numbers, and up to seven for some atomic numbers. There are 148 stable even–even nuclides, forming ~58% of the 254 stable nuclides, there are also 19 primordial long-lived even–even nuclides. As a result, many of the 41 even-numbered elements from 2 to 82 have many primordial isotopes, half of these even-numbered elements have six or more stable isotopes. All even–even nuclides have spin 0 in their ground state, only five stable nuclides contain both an odd number of protons and an odd number of neutrons. The first four odd–odd nuclides occur in low mass nuclides, for changing a proton to a neutron or vice versa would lead to a very lopsided proton–neutron ratio
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Nuclear binding energy
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Nuclear binding energy is the energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are called nucleons. The term nuclear binding energy may also refer to the balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse, or when heavy nuclei split and this energy may be made available as nuclear energy and can be used to produce electricity as in or in a nuclear weapon. When a large nucleus splits into pieces, excess energy is emitted as photons, the nuclear binding energies and forces are on the order of a million times greater than the electron binding energies of light atoms like hydrogen. Nuclear binding energy is explained by the principles involved in nuclear physics. Energy is consumed or liberated because of differences in the binding energy between the incoming and outgoing products of the nuclear transmutation. The best-known classes of nuclear transmutations are fission and fusion. Nuclear energy may be liberated by atomic fission, when atomic nuclei are broken apart into lighter nuclei. The energy from fission is used to generate power in hundreds of locations worldwide. Nuclear energy is released during atomic fusion, when light nuclei like hydrogen are combined to form heavier nuclei such as helium. The Sun and other stars use nuclear fusion to generate thermal energy which is radiated from the surface. In any exothermic nuclear process, nuclear mass might ultimately be converted to thermal energy, in order to quantify the energy released or absorbed in any nuclear transmutation, one must know the nuclear binding energies of the nuclear components involved in the transmutation. Electrons and nuclei are kept together by electrostatic attraction, the force of electric attraction does not hold nuclei together, because all protons carry a positive charge and repel each other. Thus, electric forces do not hold together, because they act in the opposite direction. It has been established that binding neutrons to nuclei clearly requires a non-electrical attraction, therefore, another force, called the nuclear force holds the nucleons of nuclei together. This force is a residuum of the interaction, which binds quarks into nucleons at an even smaller level of distance. The nuclear force must be stronger than the electric repulsion at short distances, unlike gravity or electrical forces, the nuclear force is effective only at very short distances
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Nuclear drip line
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An arbitrary combination of protons and neutrons does not necessarily yield a stable nucleus. One can think of moving up and/or to the right across the table of nuclides by adding one type of nucleon to a given nucleus. However, adding one at a time to a given nucleus will eventually lead to a newly formed nucleus that immediately decays by emitting a proton. Colloquially speaking, the nucleon has leaked or dripped out of the nucleus, drip lines are defined for protons, neutrons, and alpha particles, and these all play important roles in nuclear physics. The nucleon drip lines are at the extreme of the ratio, at p, n ratios at or beyond the driplines. The location of the drip line is not well known for most of the nuclear chart, whereas the proton. Nuclear stability is limited to those combinations of protons and neutrons described by the chart of the nuclides, the boundaries of this valley are the neutron drip line on the neutron rich side, and the proton drip line on the proton-rich side. The alpha drip line is more difficult to visualize as it also branches down through the center of the chart. These limits exist because of decay, whereby an exothermic nuclear transition can occur by the emission of one or more nucleons. To understand the concept, one needs to apply the principle of conservation of energy to nuclear binding energy. For example, to determine if 12C, the most common isotope of carbon, can undergo proton emission to 11B, one finds that about 16 MeV must be added to the system for this process to be allowed. While Q-values can be used to any nuclear transmutation, for particle decay, the particle separation energy quantity S, is also used. In other words, the proton separation energy Sp indicates how much energy should be added to a nucleus to remove a single proton. Thus, the drip lines defined the boundaries where the particle separation energy is less than or equal to zero. Of the three types of naturally occurring radioactivities, only alpha decay is a type of resulting from the nuclear strong force. The other proton and neutron decays occurred much earlier in the life of the atomic species, thus, alpha-decay can be considered either a form of particle decay or, less frequently, as a special case of nuclear fission. For alpha decay, the timescale can be longer than for proton or neutron emission owing to the high Coulomb barrier seen by an alpha-cluster in a nucleus. Such particle decays are not commonly known because particle decay is governed by the strong force, as well as the Coulomb force in the case of charged particles
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Island of stability
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Although predictions of the exact location differ somewhat, Klaus Blaum expects the island of stability to occur in the atomic mass region near the isotope 300 120Ubn. Estimates about the amount of stability on the island are usually around a half-life of minutes or days, although the nuclear shell model has existed since the 1960s, the existence of such superheavy, relatively stable isotopes has not been demonstrated. Like the rest of the elements, the isotopes on the island of stability have never been found in nature. However, scientists have not found a way to carry out such a reaction, with an isotope graph of protons and neutrons with the third dimension of height being the binding energy, the stability region can be visualized as a valley. The possibility of an island of stability was first proposed by Glenn T. Seaborg in the late 1960s. The hypothesis is based upon the shell model, which implies that the atomic nucleus is built up in shells in a manner similar to the structure of the much larger electron shells in atoms. In both cases, shells are just groups of quantum energy levels that are close to each other. A filled shell would have numbers of neutrons and protons. This idea of a magic number derives from the counterpart of electron shells, the magic number for electron shells is 8. This completes the shell and makes it stable, similarly, it is believed that there are complete shells in the nucleus that stabilize the nucleus. Of particular note is 298Fl, which would be doubly magic, studies from the early 1990s, and previous to that time, have shown that superheavy elements do not have perfectly spherical nuclei. A shell is considered stable when it is in a spherical form, a change in the shape of the nucleus changes the position of neutrons and protons in the shell, thus skewing the numbers. Recent research indicates that large nuclei are deformed, causing magic numbers to shift, a nucleus can have a magic number of neutrons or a magic number of protons. When the nucleus has magic numbers of protons and neutrons, it can be said to be doubly magic. Hassium-270 is now believed to be a doubly magic deformed nucleus and it has a half-life of 3.6 seconds. Whilst elements with atomic numbers expected for the island of stability have been produced and these synthesised isotopes have contained too few neutrons to reach the supposed stable region. It is possible that these elements possess unusual chemical properties and, if they have isotopes with adequate lifespans, the longest-lived observed isotopes of each of the heaviest elements are shown in the following table. For comparison, the element with atomic number below 100 is francium with a half-life of 22 minutes
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Valley of stability
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In nuclear physics, the valley of stability is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclides are composed of protons and neutrons, the line of stable nuclides down the center of the valley of stability is known as the line of beta stability. The sides of the valley correspond to increasing instability to beta decay, the decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the drip lines. Regions of instability within the valley at high atomic number also include radioactive decay by alpha radiation or spontaneous fission, the shape of the valley is roughly an elongated paraboloid corresponding to the nuclide binding energies as a function of neutron and atomic numbers. The nuclides within the valley of stability encompass the entire table of nuclides, the chart of those nuclides is known as a Segrè chart, after the physicist Emilio Segrè. The Segrè chart may be considered a map of the nuclear valley, the region of proton and neutron combinations outside of the valley of stability is referred to as the sea of instability. Scientists have long searched for long-lived heavy isotopes outside of the valley of stability, all atomic nuclei are composed of protons and neutrons bound together by the nuclear force. The mass number, A, of a nuclide is the sum of atomic and neutron numbers, not all nuclides are stable, however. According to Byrne, stable nuclides are defined as those having a greater than 1018 years. An essential property of this and all nuclide decays is that the energy of the decay product is less than that of the original nuclide. The difference between the initial and final nuclide binding energies is carried away by the energies of the decay products, often the beta particle. The concept of the valley of stability is a way of organizing all of the according to binding energy as a function of neutron and proton numbers. Most stable nuclides have roughly equal numbers of protons and neutrons, the greater the number of protons, the more neutrons are required to stabilize a nuclide, however, so nuclides with larger values for Z require an even larger number of neutrons, N>Z, to be stable. The valley of stability is formed by the negative of binding energy, the stable nuclides have high binding energy, and these nuclides lie along the bottom of the valley of stability. Nuclides with weaker binding energy have combinations of N and Z that lie off of the line of stability, unstable nuclides can be formed in nuclear reactors or supernovas, for example. Such nuclides often decay in sequences of reactions called decay chains that take the resulting nuclides sequentially down the slopes of the valley of stability, the sequence of decays take nuclides toward greater binding energies, and the nuclides terminating the chain are stable. The protons and neutrons that comprise an atomic nucleus behave almost identically within the nucleus, the approximate symmetry of isospin treats these particles as identical, but in a different quantum state
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Radioactive decay
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A material containing such unstable nuclei is considered radioactive. Certain highly excited short-lived nuclear states can decay through neutron emission, or more rarely, however, for a collection of atoms, the collections expected decay rate is characterized in terms of their measured decay constants or half-lives. This is the basis of radiometric dating, the half-lives of radioactive atoms have no known upper limit, spanning a time range of over 55 orders of magnitude, from nearly instantaneous to far longer than the age of the universe. A radioactive nucleus with spin can have no defined orientation. If there are multiple particles produced during a single decay, as in decay, their relative angular distribution. Such a parent process could be a previous decay, or a nuclear reaction, the decaying nucleus is called the parent radionuclide, and the process produces at least one daughter nuclide. Except for gamma decay or internal conversion from an excited state. When the number of changes, an atom of a different chemical element is created. The first decay processes to be discovered were alpha decay, beta decay, alpha decay occurs when the nucleus ejects an alpha particle. This is the most common process of emitting nucleons, but highly excited nuclei can eject single nucleons, or in the case of cluster decay, specific light nuclei of other elements. Beta decay occurs when the nucleus emits an electron or positron, the nucleus may capture an orbiting electron, causing a proton to convert into a neutron in a process called electron capture. All of these result in a well-defined nuclear transmutation. By contrast, there are radioactive decay processes that do not result in a nuclear transmutation, another type of radioactive decay results in products that vary, appearing as two or more fragments of the original nucleus with a range of possible masses. For a summary table showing the number of stable and radioactive nuclides in each category, there are 29 naturally occurring chemical elements on Earth that are radioactive. They are those that contain 34 radionuclides that date before the time of formation of the solar system, well-known examples are uranium and thorium, but also included are naturally occurring long-lived radioisotopes, such as potassium-40. Radioactivity was discovered in 1896 by the French scientist Henri Becquerel and these materials glow in the dark after exposure to light, and he suspected that the glow produced in cathode ray tubes by X-rays might be associated with phosphorescence. He wrapped a photographic plate in black paper and placed various phosphorescent salts on it, all results were negative until he used uranium salts. The uranium salts caused a blackening of the plate in spite of the plate being wrapped in black paper and these radiations were given the name Becquerel Rays
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Alpha decay
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An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. Alpha decay typically occurs in the heaviest nuclides, in practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitters being the lightest isotopes of tellurium. Alpha decay is by far the most common form of cluster decay and it is the most common form because of the combined extremely high binding energy and relatively small mass of the alpha particle. Like other cluster decays, alpha decay is fundamentally a quantum tunneling process, unlike beta decay, it is governed by the interplay between both the nuclear force and the electromagnetic force. Alpha particles have a kinetic energy of 5 MeV and have a speed of about 15,000,000 m/s. There is surprisingly small variation around this energy, due to the dependence of the half-life of this process on the energy produced. Approximately 99% of the helium produced on Earth is the result of the decay of underground deposits of minerals containing uranium or thorium. The helium is brought to the surface as a by-product of natural gas production, Alpha particles were first described in the investigations of radioactivity by Ernest Rutherford in 1899, and by 1907 they were identified as He2+ ions. By 1928, George Gamow had solved the theory of alpha decay via tunneling, the alpha particle is trapped in a potential well by the nucleus. The nuclear force holding an atomic nucleus together is very strong, however, the nuclear force is also short range, dropping quickly in strength beyond about 1 femtometre, while the electromagnetic force has unlimited range. A nucleus with 210 or more nucleons is so large that the nuclear force holding it together can just barely counterbalance the electromagnetic repulsion between the protons it contains. Alpha decay occurs in such nuclei as a means of increasing stability by reducing size, one curiosity is why alpha particles, helium nuclei, should be preferentially emitted as opposed to other particles like a single proton or neutron or other atomic nuclei. Single proton emission, or the emission of any particle with an odd number of nucleons would violate this conservation law, the rest of the answer comes from the very high binding energy of the alpha particle. For example, performing the calculation for uranium-232 shows that alpha particle emission would need only 5.4 MeV, while a single proton emission would require 6.1 MeV. Most of this energy becomes the kinetic energy of the alpha particle itself. However, since the numbers of most alpha emitting radioisotopes exceed 210. These disintegration energies however are substantially smaller than the barrier provided by the nuclear force. An alpha particle can be thought of as being inside a potential barrier whose walls are 25 MeV, however, decay alpha particles only have kinetic energies of 4 MeV to about 9 MeV, far less than the energy needed to escape
29.
Beta decay
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In nuclear physics, beta decay is a type of radioactive decay in which a beta ray, and a neutrino are emitted from an atomic nucleus. Neither the beta particle nor its associated neutrino exist within the prior to beta decay. 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 binding energy. The binding energies of all existing nuclides form what is called the valley of stability. Beta decay is a consequence of the force, which is characterized by relatively lengthy decay times. Nucleons are composed of up or down quarks, and the force allows a quark to change type by the exchange of a W boson. For example, a neutron, composed of two quarks and an up quark, decays to a proton composed of a down quark. 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 atomic electron is captured by a proton in the nucleus, transforming it into a neutron. The two types of decay are known as beta minus and beta plus. β+ decay is known as positron emission. Beta decay conserves a number known as the lepton number, or the number of electrons. 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. This new element has a mass number A, but an atomic number Z that is increased by one. As in all nuclear decays, the element is known as the parent nuclide while the resulting element is known as the daughter nuclide. The beta spectrum, or distribution of values for the beta particles, is continuous. The total energy of the process is divided between the electron, the antineutrino, and the recoiling nuclide. In the figure to the right, an example of an electron with 0.40 MeV energy from the decay of 210Bi is shown
30.
Double beta decay
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In nuclear physics, double beta decay is a type of radioactive decay in which two protons are simultaneously transformed into two neutrons, or vice versa, inside an atomic nucleus. As in single beta decay, this allows the atom to move closer to the optimal ratio of protons and neutrons. As a result of transformation, the nucleus emits two detectable beta particles, which are electrons or positrons. There are two types of beta decay, ordinary double beta decay and neutrinoless double beta decay. In ordinary double beta decay, which has observed in several isotopes. In neutrinoless double beta decay, a process that has never been observed. The idea of double beta decay was first proposed by Maria Goeppert-Mayer in 1935, in 1937, Ettore Majorana demonstrated that all results of beta decay theory remain unchanged if the neutrino were its own antiparticle, now known as a Majorana particle. It is not yet known whether the neutrino is a Majorana particle and, relatedly, the predicted half-lives were on the order of 1015–16 years. Efforts to observe the process in laboratory date back to at least 1948 when Edward L. Fireman made the first attempt to measure the half-life of the 124Sn isotope with a geiger counter. Radiometric experiments through about 1960 produced negative results or false positives, in 1950, for the first time the double beta decay half-life of 130Te was measured by geochemical methods to be 1. 4×1021 years, reasonably close to the modern value. In 1956, after the V-A nature of weak interactions was established, despite significant progress in experimental techniques in 1960–70s, double beta decay was not observed in a laboratory until the 1980s. Experiments had only been able to establish the bound for the half-life—about 1021 years. At the same time, geochemical experiments detected the double beta decay of 82Se, Double beta decay was first observed in a laboratory in 1987 by the group of Michael Moe at UC Irvine in 82Se. Since then, many experiments have observed ordinary double beta decay in other isotopes, none of those experiments have produced positive results for the neutrinoless process, raising the half-life lower bound to approximately 1025 years. Geochemical experiments continued through the 1990s, producing results for several isotopes. Double beta decay is the rarest known kind of decay, as of 2012 it has been observed in only 12 isotopes. In double beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted, the process can be thought as a sum of two beta minus decays. In order for beta decay to be possible, the nucleus must have a larger binding energy than the original nucleus
31.
Positron emission
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Positron emission is mediated by the weak force. The positron is a type of particle, the other beta particle being the electron emitted from the β− decay of a nucleus. Positron decay results in nuclear transmutation, changing an atom of one element into an atom of an element with an atomic number that is less by one unit. Positron emission should not be confused with electron emission or beta decay, which occurs when a neutron turns into a proton and the nucleus emits an electron. This was the first example of β+ decay, the Curies termed the phenomenon artificial radioactivity, since 30 15P is a short-lived nuclide which does not exist in nature. The discovery of radioactivity would be cited when the husband. Isotopes which undergo this decay and thereby emit positrons include carbon-11, potassium-40, nitrogen-13, oxygen-15, aluminium-26, sodium-22, fluorine-18, the two most common types of quarks are up quarks, which have a charge of +2/3, and down quarks, with a −1/3 charge. Quarks arrange themselves in sets of three such that they make protons and neutrons, in a proton, whose charge is +1, there are two up quarks and one down quark. Neutrons, with no charge, have one up quark and two down quarks, via the weak interaction, quarks can change flavor from down to up, resulting in electron emission. Positron emission happens when an up quark changes into a down quark, nuclei which decay by positron emission may also decay by electron capture. For low-energy decays, electron capture is energetically favored by 2mec2 =1.022 MeV, as the energy of the decay goes up, so does the branching ratio towards positron emission. However, if the difference is less than 2mec2, then positron emission cannot occur. Certain isotopes are stable in galactic cosmic rays, because the electrons are stripped away, a positron is ejected from the parent nucleus, and the daughter atom must shed an orbital electron to balance charge. Isotopes which increase in mass under the conversion of a proton to a neutron, or which decrease in mass by less than 2me and these isotopes are used in positron emission tomography, a technique used for medical imaging. Note that the energy emitted depends on the isotope that is decaying, the short-lived positron emitting isotopes 11C, 13N, 15O and 18F used for positron emission tomography are typically produced by proton irradiation of natural or enriched targets. The LIVEChart of Nuclides - IAEA with filter on β+ decay
32.
Electron capture
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Electron capture is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shell. This process thereby changes a proton to a neutron and simultaneously causes the emission of an electron neutrino. P + e− → n + ν e The daughter nuclide, if it is in an excited state, usually, a gamma ray is emitted during this transition, but nuclear de-excitation may also take place by internal conversion. Following capture of an electron from the atom, an outer electron replaces the electron that was captured. Following electron capture, the number is reduced by one, the neutron number is increased by one. Simple electron capture results in an atom, since the loss of the electron in the electron shell is balanced by a loss of positive nuclear charge. However, an atomic ion may result from further Auger electron emission. Electron capture is an example of interaction, one of the four fundamental forces. Electron capture is always an alternate mode for radioactive isotopes that do have sufficient energy to decay by positron emission. It is sometimes called Inverse beta decay, though this term can refer to the interaction of an electron antineutrino with a proton. For example, rubidium-83 will decay to krypton-83 solely by electron capture, the theory of electron capture was first discussed by Gian-Carlo Wick in a 1934 paper, and then developed by Hideki Yukawa and others. K-electron capture was first observed by Luis Alvarez, in vanadium-48 and he reported it in a 1937 paper in Physical Review. Alvarez went on to study electron capture in gallium-67 and other nuclides, radioactive isotopes that decay by pure electron capture can be inhibited from radioactive decay if they are fully ionized. Anomalies in elemental distributions are thought to be partly a result of this effect on electron capture, chemical bonds can also affect the rate of electron capture to a small degree 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 and this relatively large effect is due to the fact that beryllium is a small atom whose valence electrons are close to the nucleus. Electron capture happens most often in the heavier neutron-deficient elements where the change is smallest. When the loss of mass in a reaction is greater than zero but less than 2m. Some common radioisotopes that decay by electron capture include, For a full list, the LIVEChart of Nuclides - IAEA with filter on electron capture
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Gamma ray
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Gamma ray, denoted by the lower-case Greek letter gamma, is penetrating electromagnetic radiation of a kind arising from the radioactive decay of atomic nuclei. It consists of photons in the highest observed range of photon energy, paul Villard, a French chemist and physicist, discovered gamma radiation in 1900 while studying radiation emitted by radium. In 1903, Ernest Rutherford named this radiation gamma rays, Rutherford had previously discovered two other types of radioactive decay, which he named alpha and beta rays. Gamma rays are able to ionize atoms, and are thus biologically hazardous. The decay of a nucleus from a high energy state to a lower energy state. Natural sources of gamma rays on Earth are observed in the decay of radionuclides. There are rare terrestrial natural sources, such as lightning strikes and terrestrial gamma-ray flashes, However, a large fraction of such astronomical gamma rays are screened by Earths atmosphere and can only be detected by spacecraft. Gamma rays typically have frequencies above 10 exahertz, and therefore have energies above 100 keV and wavelengths less than 10 picometers, However, this is not a strict definition, but rather only a rule-of-thumb description for natural processes. Electromagnetic radiation from radioactive decay of nuclei is referred to as gamma rays no matter its energy. This radiation commonly has energy of a few hundred keV, in astronomy, gamma rays are defined by their energy, and no production process needs to be specified. The energies of gamma rays from astronomical sources range to over 10 TeV, a notable example is the extremely powerful bursts of high-energy radiation referred to as long duration gamma-ray bursts, of energies higher than can be produced by radioactive decay. These bursts of gamma rays are thought to be due to the collapse of stars called hypernovae, the first gamma ray source to be discovered historically was the radioactive decay process called gamma decay. In this type of decay, a nucleus emits a gamma ray almost immediately upon formation. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900, However, Villard did not consider naming them as a different fundamental type. Rutherford also noted that gamma rays were not deflected by a field, another property making them unlike alpha. Gamma rays were first thought to be particles with mass, like alpha, Rutherford initially believed that they might be extremely fast beta particles, but their failure to be deflected by a magnetic field indicated that they had no charge. In 1914, gamma rays were observed to be reflected from crystal surfaces, Rutherford and his coworker Edward Andrade measured the wavelengths of gamma rays from radium, and found that they were similar to X-rays, but with shorter wavelengths and higher frequency. This was eventually recognized as giving them more energy per photon
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Internal conversion
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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. Internal conversion is possible whenever gamma decay is possible, except in the case where the atom is fully ionised, during internal conversion, the atomic number does not change, and thus no transmutation of one element to another takes place. 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. Whereas the energy spectrum of beta particles plots as a broad hump, in the quantum mechanical model of the electron, there is a finite probability of finding the electron within the nucleus. During the internal 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 energy state of the nucleus and take the energy of the nuclear transition directly. The kinetic energy of the 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 two electrons have the highest probability of being within the nucleus. However, the s states in the L, M, and N shells are also able to couple to the nuclear fields, ratios of K-shell to other L, M, or N shell internal conversion probabilities for various nuclides have been prepared. After the IC electron has been emitted, the atom is left with a vacancy in one of its electron shells, usually an inner one. This hole will be filled with an electron from one of the higher shells, consequently, 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 shows that 203Hg produces a continuous beta spectrum with maximum energy 214 keV. This state decays very fast to the state of 203Tl. The figure on the shows the electron spectrum of 203Hg. You can see the continuous spectrum and also the K-, L-. Since the binding energy of the K electrons in 203Tl amounts to 85 keV, because of lesser binding energies, the L- and M-lines have higher energies. Because of the energy resolution of the spectrometer, the lines have a Gaussian shape of finite width
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Spontaneous fission
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Spontaneous fission is a form of radioactive decay that is found only in very heavy chemical elements. The first nuclear fission process discovered was the fission induced by neutrons, because cosmic rays produce some neutrons, it was difficult to distinguish between induced and spontaneous events. Cosmic rays can be shielded by a thick layer of rock or water. Spontaneous fission was identified in 1940 by Soviet physicists Georgy Flyorov, cluster decay was shown to be a superasymmetric spontaneous fission process. The lightest natural nuclides that are subject to spontaneous fission are niobium-93. Spontaneous fission has never observed in the naturally occurring isotopes of these elements. In practice, these are stable isotopes, spontaneous fission is feasible over practical observation times only for atomic masses of 232 amu or more. These are elements at least as heavy as thorium-232 – which has a somewhat longer than the age of the universe. Thorium-232 is the lightest primordial nuclide that has evidence of undergoing spontaneous fission in its minerals. The known elements most susceptible to spontaneous fission are the synthetic high-atomic-number actinides and transactinides with atomic numbers from 100 onwards, hence, the spontaneous fission of these isotopes is usually negligible, except in using the exact branching ratios when finding the radioactivity of a sample of these elements. Within the framework of liquid drop model, the criterion for whether spontaneous fission can occur in a short enough to be observed by present methods, is approximately. Where Z is the number and A is the mass number. Spontaneous fission rates, In practice 239Pu will invariably contain an amount of 240Pu due to the tendency of 239Pu to absorb an additional neutron during production. 240Pus high rate of fission events makes it an undesirable contaminant. Weapons-grade plutonium contains no more than 7. 0% 240Pu, the rarely used gun-type atomic bomb has a critical insertion time of about one millisecond, and the probability of a fission during this time interval should be small. Almost all nuclear bombs use some kind of implosion method, spontaneous fission can occur much more rapidly when the nucleus of an atom undergoes superdeformation. Spontaneous fission gives much the result as induced nuclear fission. However, like other forms of decay, it occurs due to quantum tunneling
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Cluster decay
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Ternary fission into three fragments also produces products in the cluster size. The branching ratio with respect to alpha decay B = T a / T c is rather small, ta and Tc are the half-lives of the parent nucleus relative to alpha decay and cluster radioactivity, respectively. Cluster decay, like alpha decay, is a tunneling process, in order to be emitted. Theoretically any nucleus with Z >40 for which the energy is a positive quantity. Cluster decay exists in a position between alpha decay, and spontaneous fission, in which a heavy nucleus splits into two large fragments and an assorted number of neutrons. Spontaneous fission ends up with a distribution of daughter products. In cluster decay for a given radioisotope, the particle is a light nucleus. For heavier emitted clusters there is practically no qualitative difference between cluster decay and spontaneous cold fission. The first information about the nucleus was obtained at the beginning of the 20th century by studying radioactivity. For a long period of only three kinds of nuclear decay modes were known. They illustrate three of the interactions in nature, strong, weak, and electromagnetic. Spontaneous fission became popular soon after its discovery in 1940 by K. Petrzhak, there are many other kinds of radioactivity, e. g. cluster decay, proton decay, various beta-delayed decay modes, fission isomers, particle accompanied fission, etc. The height of the barrier, mainly of Coulomb nature. The spontaneous decay can only be explained by quantum tunneling in a way to the first application of the Quantum Mechanics to Nuclei given by G. Gamow for alpha decay. In 1980 A. Sandulescu, D. N. Poenaru, the first observation of heavy-ion radioactivity was that of a 30-MeV, carbon-14 emission from radium-223 by H. J. Rose and G. A. Usually the theory explains an already experimentally observed phenomenon, cluster decay is one of the rare examples of phenomena predicted before experimental discovery. Theoretical predictions were made in 1980, four years before experimental discovery, superasymmetric fission models are based on the macroscopic-microscopic approach using the asymmetrical two-center shell model level energies as input data for the shell and pairing corrections. Either the liquid drop model or the Yukawa-plus-exponential model extended to different charge-to-mass ratios have been used to calculate the macroscopic deformation energy, the first experimental report was published in 1984, when physicists at Oxford University discovered that 223Ra emits one 14C nucleus out of every billion alpha decays
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Neutron emission
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Neutron emission is a type of radioactive decay of atoms containing excess neutrons, in which a neutron is simply ejected from the nucleus. Neutron emission is one of the ways an atom reaches its stability, an atom is unstable, therefore radioactive, when the forces in the nucleus are unbalanced. The instability of the results from the nuclei having extra neutrons or extra protons. Two examples of isotopes that emit neutrons are beryllium-13 and helium-5, commonly, it is abbreviated with a lower case n. As only a neutron is lost in process, the atom does not gain or lose any protons. Instead, the atom will become a new isotope of the original element, Neutron emission usually happens from nuclei that are in an excited state, such as the excited 17O* produced from the beta decay of 17N. The neutron emission process itself is controlled by the force and therefore is extremely fast. This process allows unstable atoms to become more stable, a synonym for such neutron emission is prompt neutron production, of the type that is best known to occur simultaneously with induced nuclear fission. Induced fission happens only when a nucleus is bombarded with neutrons, gamma rays, many heavy isotopes, most notably californium-252, also emit prompt neutrons among the products of a similar spontaneous radioactive decay process, spontaneous fission. Spontaneous fission happens when a nucleus splits into two smaller nuclei and generally one or more neutrons. Most neutron emission outside prompt neutron production associated with fission, is from neutron-heavy isotopes produced as fission products. Thus, the delay in neutron emission is not from the process, but rather its precursor beta decay, which is controlled by the weak force. The beta decay half lives for the precursors to delayed neutron-emitter radioisotopes, are typically fractions of a second to tens of seconds, Neutron radiation Neutron source Neutron drip line Proton emission Why Are Some Atoms Radioactive. The LIVEChart of Nuclides - IAEA with filter on delayed neutron emission decay Nuclear Structure and Decay Data - IAEA with query on Neutron Separation Energy
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Proton emission
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Proton emission is a rare type of radioactive decay in which a proton is ejected from a nucleus. For a proton to escape a nucleus, the proton separation energy must be negative - the proton is therefore unbound, Proton emission is not seen in naturally occurring isotopes, proton emitters can be produced via nuclear reactions, usually using linear particle accelerators. Research in the field flourished after this breakthrough, and to more than 25 isotopes have been found to exhibit proton emission. The study of proton emission has aided the understanding of nuclear deformation, masses and structure, in 2002, the simultaneous emission of two protons was observed from the nucleus iron-45 in experiments at GSI and GANIL. In 2005 it was determined that zinc-54 can also undergo double proton decay. Proton drip line Diproton Free neutron Neutron emission Nuclear Structure and Decay Data - IAEA with query on Proton Separation Energy
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Decay energy
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The decay energy is the energy released by a radioactive decay. Radioactive decay is the process in which an atomic nucleus loses energy by emitting ionizing particles. 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, the energy difference of the reactants is often written as Q, Q = after − before, Q = −. Decay energy is usually quoted in terms of the energy units MeV or keV, types of radioactive decay include gamma ray beta decay alpha decay The decay energy is the mass difference dm between the parent and the daughter atom and particles. It is equal to the energy of radiation E. If A is the activity, i. e. the number of transforming atoms per time, M the molar mass, then the radiation power W is. The mass difference dm is 0. 003u, the radiated energy is approximately 2.8 MeV. The half life T of 5.27 year corresponds to the activity A=/T, where N is the number of atoms per mol
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Decay chain
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In nuclear science, the decay chain refers to the radioactive decay of different discrete radioactive decay products as a chained series of transformations. They are also known as radioactive cascades, most radioisotopes do not decay directly to a stable state, but rather undergo a series of decays until eventually a stable isotope is reached. Decay stages are referred to by their relationship to previous or subsequent stages, a parent isotope is one that undergoes decay to form a daughter isotope. One example of this is uranium decaying into thorium, the daughter isotope may be stable or it may decay to form a daughter isotope of its own. The daughter of an isotope is sometimes called a granddaughter isotope. Half-lives have been determined in laboratories for thousands of radioisotopes and these can range from nearly instantaneous to as much as 1019 years or more. The intermediate stages each emit the same amount of radioactivity as the original radioisotope, not only are unstable radium isotopes significant radioactivity emitters, but as the next stage in the decay chain they also generate radon, a heavy, inert, naturally occurring radioactive gas. Rock containing thorium and/or uranium emits radon gas that can accumulate in enclosed places such as basements or underground mines, radon exposure is considered the leading cause of lung cancer in non-smokers.5 billion years ago. All the elements created more than 4.5 billion years ago are termed primordial, at the time when they were created, those that were unstable began decaying immediately. There are only two methods to create isotopes, artificially, inside a man-made reactor, or through decay of a parent isotopic species. Unstable isotopes are in a struggle to become more stable. Stable isotopes have ratios of neutrons to protons in their nucleus that start out at 1 in stable helium-4, the elements heavier than that have to shed weight to achieve stability, most usually as alpha decay. This fact is made inevitable by the two decay methods possible, alpha radiation, which reduces the weight by 4 atomic mass units, and beta, which does not change the weight at all. The four paths are termed 4n, 4n +1, 4n +2, and 4n +3, there are other decay modes, but they invariably occur at a lower probability than alpha or beta decay. Three of those chains have a long-lived isotope near the top, they are bottlenecks in the process through which the chain flows very slowly, the three materials are uranium-238, uranium-235 and thorium-232. The fourth chain has no long lasting bottleneck isotope, so almost all of the isotopes in that chain have long since decayed down to very near the stability at the bottom. Near the end of that chain is bismuth-209, which was thought to be stable. Recently, however, Bi-209 was found to be unstable with a half-life of 19 billion billion years, the four most common modes of radioactive decay are, alpha decay, beta decay, inverse beta decay, and isomeric transition
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Decay product
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In nuclear physics, a decay product is the remaining nuclide left over from radioactive decay. Radioactive decay often proceeds via a sequence of steps, 234Th is the daughter of the parent 238U. 234mPa is the granddaughter of 238U and these might also be referred to as the daughter products of 238U. Decay products are important in understanding radioactive decay and the management of radioactive waste, for elements above lead in atomic number, the decay chain typically ends with an isotope of thallium or lead. In many cases members of the chain are far more radioactive than the original nuclide. Thus, although uranium is not dangerously radioactive when pure, some pieces of naturally occurring pitchblende are quite dangerous owing to their radium content, similarly, thorium gas mantles are very slightly radioactive when new, but become far more radioactive after only a few months of storage. Although it cannot be predicted whether any given atom of a substance will decay at any given time. Because of this, decay products are important to scientists in many fields who need to know the quantity or type of the parent product, such studies are done to measure pollution levels and for other matters
. Bibcode:1999CQGra..16.2471S. doi:10.1088/0264-9381/16/7/320.
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