1.
Nuclear physics
–
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of matter are also studied. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, discoveries in nuclear physics have led to applications in many fields. Such applications are studied in the field of nuclear engineering, Particle physics evolved out of nuclear physics and the two fields are typically taught in close association. Nuclear astrophysics, the application of physics to astrophysics, is crucial in explaining the inner workings of stars. The discovery of the electron by J. J. Thomson a year later was an indication that the atom had internal structure, in the years that followed, radioactivity was extensively investigated, notably by Marie and Pierre Curie as well as by Ernest Rutherford and his collaborators. By the turn of the physicists had also discovered three types of radiation emanating from atoms, which they named alpha, beta, and gamma radiation. Experiments by Otto Hahn in 1911 and by James Chadwick in 1914 discovered that the beta decay spectrum was continuous rather than discrete. That is, electrons were ejected from the atom with a range of energies, rather than the discrete amounts of energy that were observed in gamma. This was a problem for physics at the time, because it seemed to indicate that energy was not conserved in these decays. The 1903 Nobel Prize in Physics was awarded jointly to Becquerel for his discovery and to Marie, Rutherford was awarded the Nobel Prize in Chemistry in 1908 for his investigations into the disintegration of the elements and the chemistry of radioactive substances. In 1905 Albert Einstein formulated the idea of mass–energy equivalence, in 1906 Ernest Rutherford published Retardation of the α Particle from Radium in passing through matter. Hans Geiger expanded on this work in a communication to the Royal Society with experiments he and Rutherford had done, passing alpha particles through air, aluminum foil and gold leaf. More work was published in 1909 by Geiger and Ernest Marsden, in 1911–1912 Rutherford went before the Royal Society to explain the experiments and propound the new theory of the atomic nucleus as we now understand it. The plum pudding model had predicted that the particles should come out of the foil with their trajectories being at most slightly bent. But Rutherford instructed his team to look for something that shocked him to observe and he likened it to firing a bullet at tissue paper and having it bounce off. As an example, in this model consisted of a nucleus with 14 protons and 7 electrons. The Rutherford model worked well until studies of nuclear spin were carried out by Franco Rasetti at the California Institute of Technology in 1929
Nuclear physics
–
Nuclear physics
2.
Atomic nucleus
–
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
Atomic nucleus
–
Nuclear physics
3.
Nucleon
–
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
Nucleon
4.
Proton
–
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
Proton
–
Ernest Rutherford at the first
Solvay Conference, 1911
Proton
–
The quark structure of the proton. The
color assignment of individual quarks is arbitrary, but all three colors must be present. Forces between quarks are mediated by
gluons.
5.
Neutron
–
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
Neutron
–
Institut Laue–Langevin (ILL) in Grenoble, France – a major neutron research facility.
Neutron
–
The
quark structure of the neutron. The color assignment of individual quarks is arbitrary, but all three colors must be present. Forces between quarks are mediated by
gluons.
Neutron
–
Cold neutron source providing neutrons at about the temperature of liquid hydrogen
6.
Nuclear matter
–
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
Nuclear matter
–
Phases of nuclear matter with equal numbers of neutrons and protons; Compare with Siemens & Jensen.
Nuclear matter
–
Cross-section of neutron star. Densities are in terms of ρ 0 the saturation nuclear matter density, where nucleons begin to touch. Patterned after Haensel et al., page 12
7.
Nuclear force
–
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
Nuclear force
Nuclear force
–
Nuclear physics
Nuclear force
–
Corresponding potential energy (in units of MeV) of two nucleons as a function of distance as computed from the Reid potential. The potential well is a minimum at a distance of about 0.8 fm. With this potential nucleons can become bound with a negative "binding energy."
8.
Nuclear structure
–
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
Nuclear structure
–
Nuclear physics
9.
Nuclear reaction
–
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
Nuclear reaction
–
In this symbolic representing of a nuclear reaction,
lithium-6 (6 3 Li) and
deuterium (2 1 H) react to form the highly excited intermediate nucleus 8 4 Be which then decays immediately into two
alpha particles of
helium-4 (4 2 He).
Protons are symbolically represented by red spheres, and
neutrons by blue spheres.
10.
Nuclear model
–
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
Nuclear model
–
Nuclear physics
11.
Semi-empirical mass formula
–
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
Semi-empirical mass formula
–
A graphical representation of the semi-empirical binding energy formula. The binding energy per nucleon in MeV (highest numbers in dark red, in excess of 8.5 MeV per nucleon) is plotted for various
nuclides as a function of Z, the
atomic number (on the y-axis), vs. N, the
neutron number (on the x-axis). The highest binding energies are seen for Z = 26 (iron).
Semi-empirical mass formula
–
Nuclear physics
12.
Nuclear shell model
–
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
Nuclear shell model
–
Partly filled valence orbitals for both neutrons and protons appear at energies over the filled inert core orbitals, in the shell model of the atomic nucleus
13.
Nuclide
–
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
Nuclide
–
Nuclear physics
14.
Isotope
–
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
Isotope
–
The three naturally-occurring
isotopes of hydrogen. The fact that each isotope has one proton makes them all variants of
hydrogen: the identity of the isotope is given by the number of neutrons. From left to right, the isotopes are
protium (1 H) with zero neutrons,
deuterium (2 H) with one neutron, and
tritium (3 H) with two neutrons.
Isotope
–
Nuclear physics
Isotope
–
In the bottom right corner of
J. J. Thomson 's photographic plate are the separate impact marks for the two isotopes of
neon: neon-20 and neon-22.
15.
Atomic number
–
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
Atomic number
–
An explanation of the superscripts and subscripts seen in atomic number notation. Atomic number is the number of protons, and therefore also the total positive charge, in the atomic nucleus.
Atomic number
–
Russian chemist Dmitri Mendeleev created a periodic table of the elements that ordered them numerically by atomic weight, yet occasionally used chemical properties in contradiction to weight.
Atomic number
–
Niels Bohr's 1913
Bohr model of the atom required van den Broek's atomic number of nuclear charges, and Bohr believed that Moseley's work contributed greatly to the acceptance of the model.
Atomic number
–
Henry Moseley helped develop the concept of atomic number by showing experimentally (1913) that Van den Broek's 1911 hypothesis combined with the
Bohr model nearly correctly predicted atomic X-ray emissions.
16.
Isobar (nuclide)
–
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
Isobar (nuclide)
–
In this
chart of nuclides, isobars occur along diagonal lines running from the lower right to upper left. The
line of beta-stability includes the observationally stable nuclides shown in black; disconnected 'islands' are a consequence of the
Mattauch isobar rule.
17.
Isotone
–
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
Isotone
–
Nuclide half-lives colorcoded
18.
Neutron number
–
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
Neutron number
–
This diagram shows the
half-life (T ½) of various isotopes with Z protons and neutron number N.
19.
Isodiapher
–
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
Isodiapher
–
Nuclear physics
20.
Neutron excess
–
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
Neutron excess
–
This diagram shows the
half-life (T ½) of various isotopes with Z protons and neutron number N.
21.
Stable isotope
–
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
Stable isotope
–
Nuclear physics
22.
Magic number (physics)
–
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
Magic number (physics)
–
Graph of isotope stability.
23.
Even and odd atomic nuclei
–
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
Even and odd atomic nuclei
–
Nuclear physics
24.
Nuclear binding energy
–
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
Nuclear binding energy
–
A graphical representation of the semi-empirical binding energy formula. The binding energy per nucleon in MeV (highest numbers in dark red, in excess of 8.5 MeV per nucleon) is plotted for various
nuclides as a function of Z, the
atomic number (y-axis), vs. N, the number of
neutrons (x-axis). The highest numbers are seen for Z = 26 (iron).
Nuclear binding energy
–
Nuclear physics
25.
Nuclear drip line
–
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
Nuclear drip line
–
Nuclear physics
26.
Island of stability
–
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
Island of stability
–
Nuclear physics
27.
Valley of stability
–
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
Valley of stability
–
Measured (boxed) and predicted (shaded)
half-lives of
isotopes, sorted by number of protons and neutrons. The expected location of the island of stability is circled.
28.
Radioactive decay
–
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
Radioactive decay
–
Pierre and Marie Curie in their Paris laboratory, before 1907
Radioactive decay
–
Alpha decay is one type of radioactive decay, in which an atomic nucleus emits an
alpha particle, and thereby transforms (or "decays") into an atom with a
mass number decreased by 4 and
atomic number decreased by 2.
Radioactive decay
–
Taking an X-ray image with early
Crookes tube apparatus in 1896. The Crookes tube is visible in the centre. The standing man is viewing his hand with a
fluoroscope screen; this was a common way of setting up the tube. No precautions against radiation exposure are being taken; its hazards were not known at the time.
Radioactive decay
–
Gamma-ray energy spectrum of uranium ore (inset). Gamma-rays are emitted by decaying
nuclides, and the gamma-ray energy can be used to characterize the decay (which nuclide is decaying to which). Here, using the gamma-ray spectrum, several nuclides that are typical of the decay chain of 238 U have been identified: 226 Ra, 214 Pb, 214 Bi.
29.
Alpha decay
–
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
Alpha decay
–
Alpha source beneath a radiation detector
Alpha decay
–
Visual representation of alpha decay
.
