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Neutron–proton Ratio
The neutron–proton ratio (N/Z ratio or nuclear ratio) of an atomic nucleus is the ratio of its number of neutrons to its number of protons. Among stable nuclei and naturally occurring nuclei, this ratio generally increases with increasing atomic number. This is because electrical repulsive forces between protons scale with distance differently than strong nuclear force attractions. In particular, most pairs of protons in large nuclei are not far enough apart, such that electrical repulsion dominates over the strong nuclear force, and thus proton density in stable larger nuclei must be lower than in stable smaller nuclei where more pairs of protons have appreciable short-range nuclear force attractions. For each element with atomic number ''Z'' small enough to occupy only the first three nuclear shells, that is up to that of calcium (''Z'' = 20), there exists a stable isotope with ''N''/''Z'' ratio of one, with the exception of beryllium (''N''/''Z'' = 1.25) and every element w ...
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Atomic Nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. 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. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of () for hydrogen (the diameter of a single proton) to about for uranium. These dimensions are much smaller than the diameter of the atom itself (nucleus + electron cloud), by a factor of about 26,634 (uranium atomic r ...
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Positron Emission
Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emission is mediated by the weak force. The positron is a type of beta particle (β+), the other beta particle being the electron (β−) emitted from the β− decay of a nucleus. An example of positron emission (β+ decay) is shown with magnesium-23 decaying into sodium-23: : → + + Because positron emission decreases proton number relative to neutron number, positron decay happens typically in large "proton-rich" radionuclides. Positron decay results in nuclear transmutation, changing an atom of one chemical element into an atom of an element with an atomic number that is less by one unit. Positron emission occurs only very rarely naturally on earth, when induced by a cosmic ray or from one in a hundred thousand decays of pota ...
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Nuclear Drip Line
The nuclear drip line is the boundary beyond which atomic nuclei decay by the emission of a proton or neutron. 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 nucleons one at a time to a given nucleus will eventually lead to a newly formed nucleus that immediately decays by emitting a proton (or neutron). Colloquially speaking, the nucleon has ''leaked'' or ''dripped'' out of the nucleus, hence giving rise to the term ''drip line''. Drip lines are defined for protons and neutrons at the extreme of the proton-to-neutron ratio; at p:n ratios at or beyond the drip lines, no bound nuclei can exist. While the location of the proton drip line is well known for many elements, the location of the neutron drip line is only known for elements up to neon. General description Nuclear stability is limi ...
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Nuclear Fission
Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay. Nuclear fission of heavy elements was discovered on Monday 19 December 1938, by German chemist Otto Hahn and his assistant Fritz Strassmann in cooperation with Austrian-Swedish physicist Lise Meitner. Hahn understood that a "burst" of the atomic nuclei had occurred. Meitner explained it theoretically in January 1939 along with her nephew Otto Robert Frisch. Frisch named the process by analogy with biological fission of living cells. For heavy nuclides, it is an exothermic reaction which can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments (heating the bulk material where fission takes place). Like nuclear fusion, for fission to produce energy, the total binding en ...
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Isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) due to different numbers of neutrons in their nuclei. While all isotopes of a given element have almost the same chemical properties, they have different atomic masses and physical properties. The term isotope is formed from the Greek roots isos ( ἴσος "equal") and topos ( τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table. It was coined by Scottish doctor and writer Margaret Todd in 1913 in a suggestion to the British chemist Frederick Soddy. The number of protons within the atom's nucleus is called its atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atom ...
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Isotopes And Half-life
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) due to different numbers of neutrons in their nuclei. While all isotopes of a given element have almost the same chemical properties, they have different atomic masses and physical properties. The term isotope is formed from the Greek roots isos ( ἴσος "equal") and topos ( τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table. It was coined by Scottish doctor and writer Margaret Todd in 1913 in a suggestion to the British chemist Frederick Soddy. The number of protons within the atom's nucleus is called its atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic numbe ...
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Bethe–Weizsäcker Formula
In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) 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 and partly on empirical measurements. The formula represents 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. It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker, and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. The formula gives a good approximation for atomic masses and thereby other effects. However, it fails to explain the existence of lines of greater bindin ...
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Local Minimum
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function a ...
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Nuclear Binding Energy
Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means. The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, , where ''E'' is the nuclear b ...
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Fission Products
Nuclear fission products are the atomic fragments left after a large atomic nucleus undergoes nuclear fission. Typically, a large nucleus like that of uranium fissions by splitting into two smaller nuclei, along with a few neutrons, the release of heat energy (kinetic energy of the nuclei), and gamma rays. The two smaller nuclei are the ''fission products''. (See also Fission products (by element)). About 0.2% to 0.4% of fissions are ternary fissions, producing a third light nucleus such as helium-4 (90%) or tritium (7%). The fission products themselves are usually unstable and therefore radioactive. Due to being relatively neutron-rich for their atomic number, many of them quickly undergo beta decay. This releases additional energy in the form of beta particles, antineutrinos, and gamma rays. Thus, fission events normally result in beta and gamma radiation, even though this radiation is not produced directly by the fission event itself. The produced radionuclides have va ...
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Nuclear Waste
Radioactive waste is a type of hazardous waste that contains radioactive material. Radioactive waste is a result of many activities, including nuclear medicine, nuclear research, nuclear power generation, rare-earth mining, and nuclear weapons reprocessing. The storage and disposal of radioactive waste is regulated by government agencies in order to protect human health and the environment. Radioactive waste is broadly classified into low-level waste (LLW), such as paper, rags, tools, clothing, which contain small amounts of mostly short-lived radioactivity, intermediate-level waste (ILW), which contains higher amounts of radioactivity and requires some shielding, and high-level waste (HLW), which is highly radioactive and hot due to decay heat, so requires cooling and shielding. In nuclear reprocessing plants about 96% of spent nuclear fuel is recycled back into uranium-based and mixed-oxide (MOX) fuels. The residual 4% is minor actinides and fission products the latter of ...
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Beta Decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called ''positron emission''. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron e ...
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