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Critical Mass
In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fission cross-section), density, shape, enrichment, purity, temperature, and surroundings. The concept is important in nuclear weapon design. Explanation of criticality When a nuclear chain reaction in a mass of fissile material is self-sustaining, the mass is said to be in a ''critical'' state in which there is no increase or decrease in power, temperature, or neutron population. A numerical measure of a critical mass is dependent on the effective neutron multiplication factor , the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material. When ''k'' = 1, the mass is critical, and the chain reaction is self-sustaining. A ''subcritical'' mass is a ...
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Doppler Broadening
In atomic physics, Doppler broadening is broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting (or absorbing) particles result in different Doppler shifts, the cumulative effect of which is the emission (absorption) line broadening. This resulting line profile is known as a Doppler profile. A particular case is the thermal Doppler broadening due to the thermal motion of the particles. Then, the broadening depends only on the frequency of the spectral line, the mass of the emitting particles, and their temperature, and therefore can be used for inferring the temperature of an emitting (or absorbing) body being spectroscopically investigated. Derivation When a particle moves (e.g., due to the thermal motion) towards the observer, the emitted radiation is shifted to a higher frequency. Likewise, when the emitter moves away, the frequency is lowered. For non-relativistic thermal ve ...
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Optical Depth
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to ''transmitted'' radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through the material. Spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged. In chemistry, a closely related quantity called "absorbance" or "decadic absorbance" is used instead of optical depth: the common logarithm of the ratio of incident to transmitted radiant power through a material, that is the optical depth divided by ln 10. Mathematical definitions Optical depth O ...
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Random Walk
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a ...
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Mean Free Path
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a result of one or more successive collisions with other particles. Scattering theory Imagine a beam of particles being shot through a target, and consider an infinitesimally thin slab of the target (see the figure). The atoms (or particles) that might stop a beam particle are shown in red. The magnitude of the mean free path depends on the characteristics of the system. Assuming that all the target particles are at rest but only the beam particle is moving, that gives an expression for the mean free path: :\ell = (\sigma n)^, where is the mean free path, is the number of target particles per unit volume, and is the effective cross-sectional area for collision. The area of the slab is , and its volume is . The typical number of st ...
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Barn (unit)
A barn (symbol: b) is a metric unit of area equal to (100  fm2). Originally used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions, today it is also used in all fields of high-energy physics to express the cross sections of any scattering process, and is best understood as a measure of the probability of interaction between small particles. A barn is approximately the cross-sectional area of a uranium nucleus. The barn is also the unit of area used in nuclear quadrupole resonance and nuclear magnetic resonance to quantify the interaction of a nucleus with an electric field gradient. While the barn never was an SI unit, the SI standards body acknowledged it in the 8th SI Brochure (superseded in 2019) due to its use in particle physics. Etymology During Manhattan Project research on the atomic bomb during World War II, American physicists at Purdue University needed a secretive name for a unit with which to quantify the cross-secti ...
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Prompt Neutron
In nuclear engineering, a prompt neutron is a neutron immediately emitted (neutron emission) by a nuclear fission event, as opposed to a delayed neutron decay which can occur within the same context, emitted after beta decay of one of the fission products anytime from a few milliseconds to a few minutes later. Prompt neutrons emerge from the fission of an unstable fissionable or fissile heavy nucleus almost instantaneously. There are different definitions for how long it takes for a prompt neutron to emerge. For example, the United States Department of Energy defines a prompt neutron as a neutron born from fission within 10−13 seconds after the fission event. The U.S. Nuclear Regulatory Commission defines a prompt neutron as a neutron emerging from fission within 10−14 seconds. This emission is controlled by the nuclear force and is extremely fast. By contrast, so-called delayed neutrons are delayed by the time delay associated with beta decay (mediated by the weak force) to t ...
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Neutron Capture
Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, which are repelled electrostatically. Neutron capture plays a significant role in the cosmic nucleosynthesis of heavy elements. In stars it can proceed in two ways: as a rapid process (r-process) or a slow process (s-process). Nuclei of masses greater than 56 cannot be formed by thermonuclear reactions (i.e., by nuclear fusion) but can be formed by neutron capture. Neutron capture on protons yields a line at 2.223 MeV predicted and commonly observed in solar flares. Neutron capture at small neutron flux At small neutron flux, as in a nuclear reactor, a single neutron is captured by a nucleus. For example, when natural gold (197Au) is irradiated by neutrons (n), the isotope 198Au is formed in a highly excited state, and quickly deca ...
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Actinide
The actinide () or actinoid () series encompasses the 15 metallic chemical elements with atomic numbers from 89 to 103, actinium through lawrencium. The actinide series derives its name from the first element in the series, actinium. The informal chemical symbol An is used in general discussions of actinide chemistry to refer to any actinide. The 1985 IUPAC ''Red Book'' recommends that ''actinoid'' be used rather than ''actinide'', since the suffix ''-ide'' normally indicates a negative ion. However, owing to widespread current use, ''actinide'' is still allowed. Since ''actinoid'' literally means ''actinium-like'' (cf. ''humanoid'' or ''android''), it has been argued for semantic reasons that actinium cannot logically be an actinoid, but IUPAC acknowledges its inclusion based on common usage. All the actinides are f-block elements, except the final one (lawrencium) which is a d-block element. Actinium has sometimes been considered d-block instead of lawrencium, but the class ...
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Critical Mass
In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fission cross-section), density, shape, enrichment, purity, temperature, and surroundings. The concept is important in nuclear weapon design. Explanation of criticality When a nuclear chain reaction in a mass of fissile material is self-sustaining, the mass is said to be in a ''critical'' state in which there is no increase or decrease in power, temperature, or neutron population. A numerical measure of a critical mass is dependent on the effective neutron multiplication factor , the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material. When ''k'' = 1, the mass is critical, and the chain reaction is self-sustaining. A ''subcritical'' mass is a ...
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Tamper (nuclear Weapons)
A tamper is an optional layer of dense material surrounding the fissile material. It is used in nuclear weapon design to reduce the critical mass of a nuclear weapon and to delay the expansion of the reacting material through its inertia. Due to its inertia it delays the thermal expansion of the fissioning fuel mass, keeping it supercritical for longer. Often the same layer serves both as tamper and as neutron reflector. The weapon disintegrates as the reaction proceeds and this stops the reaction, so the use of a tamper makes for a longer-lasting, more energetic, and more efficient explosion. The yield can be further enhanced through the use of a fissionable tamper. The first nuclear weapons used heavy natural uranium or tungsten carbide tampers, but a heavy tamper necessitates a larger high-explosive implosion system, and makes the entire device larger and heavier. The primary stage of a modern thermonuclear weapon may instead use a lightweight beryllium reflector, which is a ...
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Beryllium
Beryllium is a chemical element with the symbol Be and atomic number 4. It is a steel-gray, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other elements to form minerals. Notable gemstones high in beryllium include beryl ( aquamarine, emerald) and chrysoberyl. It is a relatively rare element in the universe, usually occurring as a product of the spallation of larger atomic nuclei that have collided with cosmic rays. Within the cores of stars, beryllium is depleted as it is fused into heavier elements. Beryllium constitutes about 0.0004 percent by mass of Earth's crust. The world's annual beryllium production of 220 tons is usually manufactured by extraction from the mineral beryl, a difficult process because beryllium bonds strongly to oxygen. In structural applications, the combination of high flexural rigidity, thermal stability, thermal conductivity and low density (1.85 times that of water) ma ...
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