In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, atomic nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum; the orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies. The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. In some ways, spin is like a vector quantity. All elementary particles of a given kind have the same magnitude of spin angular momentum, indicated by assigning the particle a spin quantum number; the SI unit of spin is the or, just as with classical angular momentum. In practice, spin is given as a dimensionless spin quantum number by dividing the spin angular momentum by the reduced Planck constant ħ, which has the same units of angular momentum, although this is not the full computation of this value.
The "spin quantum number" is called "spin", leaving its meaning as the unitless "spin quantum number" to be inferred from context. When combined with the spin-statistics theorem, the spin of electrons results in the Pauli exclusion principle, which in turn underlies the periodic table of chemical elements. Wolfgang Pauli in 1924 was the first to propose a doubling of electron states due to a two-valued non-classical "hidden rotation". In 1925, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested the simple physical interpretation of a particle spinning around its own axis, in the spirit of the old quantum theory of Bohr and Sommerfeld. Ralph Kronig anticipated the Uhlenbeck-Goudsmit model in discussion with Hendrik Kramers several months earlier in Copenhagen, but did not publish; the mathematical theory was worked out in depth by Pauli in 1927. When Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it; as the name suggests, spin was conceived as the rotation of a particle around some axis.
This picture is correct so far as spin obeys the same mathematical laws as quantized angular momenta do. On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta: Spin quantum numbers may take half-integer values. Although the direction of its spin can be changed, an elementary particle cannot be made to spin faster or slower; the spin of a charged particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur classically if the internal charge of the particle were distributed differently from its mass; the conventional definition of the spin quantum number, s, is s = n/2, where n can be any non-negative integer. Hence the allowed values of s are 1/2, 1, 3/2, 2, etc.. The value of s for an elementary particle depends only on the type of particle, cannot be altered in any known way; the spin angular momentum, S, of any physical system is quantized. The allowed values of S are S = ℏ s = h 4 π n, where h is the Planck constant and ℏ = h/2π is the reduced Planck constant.
In contrast, orbital angular momentum can only take on integer values of s. Those particles with half-integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons; the two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is. In contrast, bosons obey the rules of Bose–Einstein statistics and have no such restriction, so they may "bunch together" if in identical states. Composite particles can have spins different from their component particles. For example, a helium atom in the ground state has spin 0 and behaves like a boson though the quarks and electrons which make it up are all fermions; this has some profound consequences: Quarks and leptons, which make up what is classically known as matter, are all fermions with spin 1/2. The common idea that "matter takes up space" comes from the Pauli exclusion principle acting on these particles to prevent the fermions that make up matter from being in the same quantum state.
Further compaction would require electrons to occupy the same energy states, therefore a kind of pressure acts to resist the fermions being overly close. Elementary fermions with other spins are not known to exist. Elementary particles which are thought of as carrying forces are all bosons with spin 1, they include the photon which carries the electromagnetic force, the gluon, the W and Z bosons. The ability of bosons to occupy the same quantu
Half-life is the time required for a quantity to reduce to half its initial value. The term is used in nuclear physics to describe how unstable atoms undergo, or how long stable atoms survive, radioactive decay; the term is used more to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body; the converse of half-life is doubling time. The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s. Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206. Half-life is constant over the lifetime of an exponentially decaying quantity, it is a characteristic unit for the exponential decay equation; the accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.
A half-life describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states "half-life is the time required for half of the entities to decay". For example, if there is just one radioactive atom, its half-life is one second, there will not be "half of an atom" left after one second. Instead, the half-life is defined in terms of probability: "Half-life is the time required for half of the entities to decay on average". In other words, the probability of a radioactive atom decaying within its half-life is 50%. For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not one-half of the atoms remaining, only because of the random variation in the process; when there are many identical atoms decaying, the law of large numbers suggests that it is a good approximation to say that half of the atoms remain after one half-life. There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.
An exponential decay can be described by any of the following three equivalent formulas: where N0 is the initial quantity of the substance that will decay, N is the quantity that still remains and has not yet decayed after a time t, t1⁄2 is the half-life of the decaying quantity, τ is a positive number called the mean lifetime of the decaying quantity, λ is a positive number called the decay constant of the decaying quantity. The three parameters t1⁄2, τ, λ are all directly related in the following way: where ln is the natural logarithm of 2; some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T1⁄2 can be related to the half-lives t1 and t2 that the quantity would have if each of the decay processes acted in isolation: 1 T 1 / 2 = 1 t 1 + 1 t 2 For three or more processes, the analogous formula is: 1 T 1 / 2 = 1 t 1 + 1 t 2 + 1 t 3 + ⋯ For a proof of these formulas, see Exponential decay § Decay by two or more processes. There is a half-life describing any exponential-decay process.
For example: As noted above, in radioactive decay the half-life is the length of time after which there is a 50% chance that an atom will have undergone nuclear decay. It varies depending on the atom type and isotope, is determined experimentally. See List of nuclides; the current flowing through an RC circuit or RL circuit decays with a half-life of lnRC or lnL/R, respectively. For this example the term half time tends to be used, rather than "half life", but they mean the same thing. In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to fall to half of its initial value. In a first-order reaction the half-life of the reactant is ln/λ, where λ is the reaction rate constant; the term "half-life" is exclusively used for decay processes that are exponential, or exponential. In a decay process, not close to exponential, the half-life will change while the decay is happening. In this situation it is uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its "first half-life", "second half-life", etc. where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, so on.
A biological half-life or elimination half-life is the time it takes for a substance to lose one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value; the relationship between the biological and plasma half-lives of a subs
Plutonium-239 is an isotope of plutonium. Plutonium-239 is the primary fissile isotope used for the production of nuclear weapons, although uranium-235 has been used. Plutonium-239 is one of the three main isotopes demonstrated usable as fuel in thermal spectrum nuclear reactors, along with uranium-235 and uranium-233. Plutonium-239 has a half-life of 24,110 years; the nuclear properties of plutonium-239, as well as the ability to produce large amounts of nearly pure Pu-239 more cheaply than enriched weapons-grade uranium-235, led to its use in nuclear weapons and nuclear power plants. The fissioning of an atom of uranium-235 in the reactor of a nuclear power plant produces two to three neutrons, these neutrons can be absorbed by uranium-238 to produce plutonium-239 and other isotopes. Plutonium-239 can absorb neutrons and fission along with the uranium-235 in a reactor. Of all the common nuclear fuels, Pu-239 has the smallest critical mass. A spherical untamped critical mass is 10.2 cm in diameter.
Using appropriate triggers, neutron reflectors, implosion geometry and tampers, this critical mass can be reduced by more than twofold. This optimization requires a large nuclear development organization supported by a sovereign nation; the fission of one atom of Pu-239 generates 207.1 MeV = 3.318 × 10-11 J, i.e. 19.98 TJ/mol = 83.61 TJ/kg, or about 23,222,915 kilowatt hours/kg. Plutonium is made from U-238. Pu-239 is created in nuclear reactors by transmutation of individual atoms of one of the isotopes of uranium present in the fuel rods; when an atom of U-238 is exposed to neutron radiation, its nucleus will capture a neutron, changing it to U-239. This happens more with lower kinetic energy; the U-239 rapidly undergoes two β− decays — an emission of an electron and an anti-neutrino, leaving a proton — the first β− decay transforming the U-239 into neptunium-239, the second β− decay transforming the Np-239 into Pu-239: U 92 238 + n 0 1 ⟶ U 92 239 → 23.5 min β − Np 93 239 → 2.356 d β − Pu 94 239 Fission activity is rare, so after significant exposure, the Pu-239 is still mixed with a great deal of U-238, other components of the original material, fission products.
Only if the fuel has been exposed for a few days in the reactor, can the Pu-239 be chemically separated from the rest of the material to yield high-purity Pu-239 metal. Pu-239 has a higher probability for fission than U-235 and a larger number of neutrons produced per fission event, so it has a smaller critical mass. Pure Pu-239 has a reasonably low rate of neutron emission due to spontaneous fission, making it feasible to assemble a mass, supercritical before a detonation chain reaction begins. In practice, reactor-bred plutonium will invariably contain a certain amount of Pu-240 due to the tendency of Pu-239 to absorb an additional neutron during production. Pu-240 has a high rate of spontaneous fission events, making it an undesirable contaminant; as a result, plutonium containing a significant fraction of Pu-240 is not well-suited to use in nuclear weapons. It is because of this limitation that plutonium-based weapons must be implosion-type, rather than gun-type. Moreover, Pu-239 and Pu-240 cannot be chemically distinguished, so expensive and difficult isotope separation would be necessary to separate them.
Weapons-grade plutonium is defined as containing no more than 7% Pu-240. Plutonium is classified according to the percentage of the contaminant plutonium-240 that it contains: Supergrade 2–3% Weapons grade 3–7% Fuel grade 7–18% Reactor grade 18% or moreA nuclear reactor, used to produce plutonium for weapons therefore has a means for exposing U-238 to neutron radiation and for replacing the irradiated U-238 with new U-238. A reactor running on unenriched or moderately enriched uranium contains a great deal of U-238. However, most commercial nuclear power reactor designs require the entire reactor to shut down for weeks, in order to change the fuel elements, they therefore produce plutonium in a mix of isotopes, not well-suited to weapon construction. Such a reactor could have machinery added that would permit U-238 slugs to be placed near the core and changed or it could be shut down so proliferation is a concern. A few commercial power reactor designs, such as the reaktor bolshoy moshchnosti kanalniy and pressurized heavy water reactor, do permit refueling without shutdowns, they
Barium is a chemical element with symbol Ba and atomic number 56. It is a soft, silvery alkaline earth metal; because of its high chemical reactivity, barium is never found in nature as a free element. Its hydroxide, known in pre-modern times as baryta, does not occur as a mineral, but can be prepared by heating barium carbonate; the most common occurring minerals of barium are barite and witherite, both insoluble in water. The name barium originates from the alchemical derivative "baryta", from Greek βαρύς, meaning "heavy." Baric is the adjectival form of barium. Barium was identified as a new element in 1774, but not reduced to a metal until 1808 with the advent of electrolysis. Barium has few industrial applications, it was used as a getter for vacuum tubes and in oxide form as the emissive coating on indirectly heated cathodes. It is a component of YBCO and electroceramics, is added to steel and cast iron to reduce the size of carbon grains within the microstructure. Barium compounds are added to fireworks to impart a green color.
Barium sulfate is used as an insoluble additive to oil well drilling fluid, as well as in a purer form, as X-ray radiocontrast agents for imaging the human gastrointestinal tract. The soluble barium ion and soluble compounds are poisonous, have been used as rodenticides. Barium is a silvery-white metal, with a slight golden shade when ultrapure; the silvery-white color of barium metal vanishes upon oxidation in air yielding a dark gray oxide layer. Barium has good electrical conductivity. Ultrapure barium is difficult to prepare, therefore many properties of barium have not been measured yet. At room temperature and pressure, barium has a body-centered cubic structure, with a barium–barium distance of 503 picometers, expanding with heating at a rate of 1.8×10−5/°C. It is a soft metal with a Mohs hardness of 1.25. Its melting temperature of 1,000 K is intermediate between those of the lighter strontium and heavier radium; the density is again intermediate between those of radium. Barium is chemically similar to magnesium and strontium, but more reactive.
It always exhibits the oxidation state of +2, except in a few rare and unstable molecular species that are only characterised in the gas phase such as BaF. Reactions with chalcogens are exothermic. Reactions with other nonmetals, such as carbon, phosphorus and hydrogen, are exothermic and proceed upon heating. Reactions with water and alcohols are exothermic and release hydrogen gas: Ba + 2 ROH → Ba2 + H2↑ Barium reacts with ammonia to form complexes such as Ba6; the metal is attacked by most acids. Sulfuric acid is a notable exception because passivation stops the reaction by forming the insoluble barium sulfate on the surface. Barium combines with several metals, including aluminium, zinc and tin, forming intermetallic phases and alloys. Barium salts are white when solid and colorless when dissolved, barium ions provide no specific coloring, they are denser than the calcium analogs, except for the halides. Barium hydroxide was known to alchemists. Unlike calcium hydroxide, it absorbs little CO2 in aqueous solutions and is therefore insensitive to atmospheric fluctuations.
This property is used in calibrating pH equipment. Volatile barium compounds burn with a green to pale green flame, an efficient test to detect a barium compound; the color results from spectral lines at 455.4, 493.4, 553.6, 611.1 nm. Organobarium compounds are a growing field of knowledge: discovered are dialkylbariums and alkylhalobariums. Barium found in the Earth's crust is a mixture of seven primordial nuclides, barium-130, 132, 134 through 138. Barium-130 undergoes slow radioactive decay to xenon-130 by double beta plus decay, barium-132 theoretically decays to xenon-132, with half-lives a thousand times greater than the age of the Universe; the abundance is ≈ 0.1 %. The radioactivity of these isotopes is so weak. Of the stable isotopes, barium-138 composes 71.7% of all barium. In total, barium has about 40 known isotopes, ranging in mass between 114 and 153; the most stable artificial radioisotope is barium-133 with a half-life of 10.51 years. Five other isotopes have half-lives longer than a day.
Barium has 10 meta states, of which barium-133m1 is the most stable with a half-life of about 39 hours. Alchemists in the early Middle Ages knew about some barium minerals. Smooth pebble-like stones of mineral baryte were found in volcanic rock near Bologna, so were called "Bologna stones." Alchemists were attracted to them. The phosphorescent properties of baryte heated with organics were described by V. Casciorolus in 1602. Carl Scheele determined that baryte contained a new element in 1774, but could not isolate barium, only barium oxide. Johan Gottlieb Gahn isolated barium oxide two year
Table of nuclides
A table of nuclides or chart of nuclides is a two-dimensional graph in which one axis represents the number of neutrons and the other represents the number of protons in an atomic nucleus. Each point plotted on the graph thus represents the nuclide of a real or hypothetical chemical element; this system of ordering nuclides can offer a greater insight into the characteristics of isotopes than the better-known periodic table, which shows only elements instead of each of their isotopes. A chart or table of nuclides is a simple map to the nuclear, or radioactive, behaviour of nuclides, as it distinguishes the isotopes of an element, it contrasts with a periodic table, which only maps their chemical behavior, since isotopes do not differ chemically to any significant degree, with the exception of hydrogen. Nuclide charts organize nuclides along the X axis by their numbers of neutrons and along the Y axis by their numbers of protons, out to the limits of the neutron and proton drip lines; this representation was first published by Kurt Guggenheimer in 1934 and expanded by Giorgio Fea in 1935, Emilio Segrè in 1945 or G. Seaborg.
In 1958, Walter Seelmann-Eggebert and Gerda Pfennig published the first edition of the Karlsruhe Nuclide Chart. Its 7th edition was made available in 2006. Today, there are several nuclide charts, four of which have a wide distribution: the Karlsruhe Nuclide Chart, the Strasbourg Universal Nuclide Chart, the Chart of the Nuclides from the JAEA and the Nuclide Chart from Knolls Atomic Power Laboratory, it has become a basic tool of the nuclear community. The nuclide table below shows nuclides, including all with half-life of at least one day, they are arranged with increasing atomic numbers from left to right and increasing neutron numbers from top to bottom. Cell color denotes the half-life of each nuclide. In graphical browsers, each nuclide has a tool tip indicating its half-life; each color represents a certain range of length of half-life, the color of the border indicates the half-life of its nuclear isomer state. Some nuclides have multiple nuclear isomers, this table notes the longest one.
Dotted borders mean that a nuclide has a nuclear isomer, their color is represented the same way as for their normal counterparts. Isotopes are nuclides with the same number of protons but differing numbers of neutrons. Isotopes neighbor each other vertically, e.g. carbon-12, carbon-13, carbon-14 or oxygen-15, oxygen-16, oxygen-17. Isotones are nuclides with the same number of neutrons but differing number of protons. Isotones neighbor each other horizontally. Example: carbon-14, nitrogen-15, oxygen-16 in the sample table above. Isobars are nuclides with the same number of nucleons, i.e. mass number, but different numbers of protons and different number of neutrons. Isobars neighbor each other diagonally from lower-left to upper-right. Example: carbon-14, nitrogen-14, oxygen-14 in the sample table above. Isodiaphers are nuclides with the same difference between protons. Like isobars, they at right angles to the isobar lines. Examples: boron-10, carbon-12, nitrogen-14 where N−Z=0. Beyond the neutron drip line along the lower left, nuclides decay by neutron emission.
Beyond the proton drip line along the upper right, nuclides decay by proton emission. Drip lines have only been established for some elements; the island of stability is a hypothetical region of the table of nuclides that contains isotopes far more stable than other transuranic elements. There are no stable nuclides having an equal number of protons and neutrons in their nuclei with atomic number greater than 20 as can be "read" from the chart. Nuclei of greater atomic number require an excess of neutrons for stability; the only stable nuclides having an odd number of protons and an odd number of neutrons are hydrogen-2, lithium-6, boron-10, nitrogen-14 and tantalum-180m. This is because the mass-energy of such atoms is higher than that of their neighbors on the same isobaric chain, so most of them are unstable to beta decay. There are no stable nuclides with mass numbers 5 or 8. There are stable nuclides with all other mass numbers up to 208 with the exceptions of 147 and 151. With the possible exception of the pair tellurium-123 and antimony-123, odd mass numbers are never represented by more than one stable nuclide.
This is because the mass-energy is a convex function of atomic number, so all nuclides on an odd isobaric chain except one have a lower-energy neighbor to which they can decay by beta decay. There are no stable nuclides having atomic number greater than Z=82, although bismuth is stable for all practical human purposes. Elements with atomic numbers from 1 to 82 all have stable isotopes, with the exceptions of technetium and promethium. Interactive Chart of Nuclides app for mobiles: Android or Apple - for PC use The Live Chart of Nuclides - IAEA Another example of a Chart of Nuclides from Korea Data up to Jan 1999 only
In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy; the predominant neutron energy may be typified by fast neutrons. Fissile material can be used to fuel thermal-neutron reactors, fast-neutron reactors and nuclear explosives. According to the Ronen fissile rule, for a heavy element with 90 ≤ Z ≤ 100, its isotopes with 2 × Z − N = 43 ± 2, with few exceptions, are fissile."Fissile" is distinct from "fissionable". A nuclide capable of undergoing fission after capturing a neutron of high or low energy is referred to as "fissionable". A fissionable nuclide that can be induced to fission with low-energy thermal neutrons with a high probability is referred to as "fissile". Although the terms were synonymous, fissionable materials include those that can be fissioned only with high-energy neutrons; as a result, fissile materials are a subset of fissionable materials.
Uranium-235 fissions with low-energy thermal neutrons because the binding energy resulting from the absorption of a neutron is greater than the critical energy required for fission. By contrast, the binding energy released by uranium-238 absorbing a thermal neutron is less than the critical energy, so the neutron must possess additional energy for fission to be possible. Uranium-238 is a fissionable material but not a fissile material. An alternative definition defines fissile nuclides as those nuclides that can be made to undergo nuclear fission and produce neutrons from such fission that can sustain a nuclear chain reaction in the correct setting. Under this definition, the only nuclides that are fissionable but not fissile are those nuclides that can be made to undergo nuclear fission but produce insufficient neutrons, in either energy or number, to sustain a nuclear chain reaction; as such, while all fissile isotopes are fissionable, not all fissionable isotopes are fissile. In the arms control context in proposals for a Fissile Material Cutoff Treaty, the term "fissile" is used to describe materials that can be used in the fission primary of a nuclear weapon.
These are materials. Under all definitions above, uranium-238 is fissionable, but because it cannot sustain a neutron chain reaction, it is not fissile. Neutrons produced by fission of 238U have lower energies than the original neutron below 1 MeV, the fission threshold to cause subsequent fission of 238U, so fission of 238U does not sustain a nuclear chain reaction. Fast fission of 238U in the secondary stage of a nuclear weapon contributes to yield and to fallout; the fast fission of 238U makes a significant contribution to the power output of some fast-neutron reactors. In general, most actinide isotopes with an odd neutron number are fissile. Most nuclear fuels have an odd atomic mass number, an atomic number Z; this implies an odd number of neutrons. Isotopes with an odd number of neutrons gain an extra 1 to 2 MeV of energy from absorbing an extra neutron, from the pairing effect which favors numbers of both neutrons and protons; this energy is enough to supply the needed extra energy for fission by slower neutrons, important for making fissionable isotopes fissile.
More nuclides with an number of protons and an number of neutrons, located near a well-known curve in nuclear physics of atomic number vs. atomic mass number are more stable than others. They are more to "ignore" the neutron and let it go on its way, or else to absorb the neutron but without gaining enough energy from the process to deform the nucleus enough for it to fission; these "even-even" isotopes are less to undergo spontaneous fission, they have much longer partial half-lives for alpha or beta decay. Examples of these isotopes are uranium-238 and thorium-232. On the other hand, other than the lightest nuclides, nuclides with an odd number of protons and an odd number of neutrons are short-lived because they decay by beta-particle emission to their isobars with an number of protons and an number of neutrons becoming much more stable; the physical basis for this phenomenon comes from the pairing effect in nuclear binding energy, but this time from both proton–proton and neutron–neutron pairing.
The short half-life of such odd-odd heavy isotopes means that they are not available in quantity and are radioactive. To be a useful fuel for nuclear fission chain reactions, the material must: Be in the region of the binding energy curve where a fission chain reaction is possible Have a high probability of fission on neutron capture Release more than one neutron on average per neutron capture. Have a reasonably long half-life Be available in suitable quantitiesFissile nuclides in nuclear fuels include: Uranium-235 which occurs in natural uranium and enriched uranium Plutonium-239 bred from uranium-238 by neutron capture Plutonium-241 bred from plutonium-240 by neutron capture; the 240Pu comes from 239Pu by the same process. Uranium-2